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7 Basic Qualty Tools & RootCause Analysis

ContentsArticles

Seven Basic Tools of Quality 1

Ishikawa diagram 2

Check sheet 6

Control chart 7

Histogram 15

Pareto chart 21

Scatter plot 23

Stratified sampling 25

Root cause analysis 27

5 Whys 31

Why–because analysis 33

Eight Disciplines Problem Solving 35

ReferencesArticle Sources and Contributors 38

Image Sources, Licenses and Contributors 39

Article LicensesLicense 40

Seven Basic Tools of Quality 1

Seven Basic Tools of QualityThe Seven Basic Tools of Quality is a designation given to a fixed set of graphical techniques identified as beingmost helpful in troubleshooting issues related to quality.[1] They are called basic because they are suitable for peoplewith little formal training in statistics and because they can be used to solve the vast majority of quality-relatedissues.[2] :198

The tools are:[3]

• The cause-and-effect or Ishikawa diagram• The check sheet• The control chart• The histogram• The Pareto chart• The scatter diagram• Stratification (alternately flow chart or run chart)

The designation arose in postwar Japan, inspired by the seven famous weapons of Benkei.[4] At that time, companiesthat had set about training their workforces in statistical quality control found that the complexity of the subjectintimidated the vast majority of their workers and scaled back training to focus primarily on simpler methods whichsuffice for most quality-related issues anyway.[2] :18

The Seven Basic Tools stand in contrast with more advanced statistical methods such as survey sampling, acceptancesampling, statistical hypothesis testing, design of experiments, multivariate analysis, and various methods developedin the field of operations research.[2] :199

References[1] Montgomery, Douglas (2005). Introduction to Statistical Quality Control (http:/ / www. eas. asu. edu/ ~masmlab/ montgomery/ ). Hoboken,

New Jersey: John Wiley & Sons, Inc.. pp. 148. ISBN 9780471656319. OCLC 56729567. .[2] Ishikawa, Kaoru (1985), What Is Total Quality Control? The Japanese Way (1 ed.), Englewood Cliffs, New Jersey: Prentice-Hall,

ISBN 9780139524332, OCLC 11467749[3] Nancy R. Tague (2004). "Seven Basic Quality Tools" (http:/ / www. asq. org/ learn-about-quality/ seven-basic-quality-tools/ overview/

overview. html). The Quality Toolbox. Milwaukee, Wisconsin: American Society for Quality. p. 15. . Retrieved 2010-02-05.[4] Ishikawa, Kaoru (1990), Introduction to Quality Control (1 ed.), Tokyo: 3A Corp, p. 98, ISBN 9784906224616, OCLC 23372992

Ishikawa diagram 2

Ishikawa diagram

Ishikawa diagram

One of the Seven Basic Tools of QualityFirst described by Kaoru Ishikawa

Purpose To break down (in successive layers of detail) root causes that potentially contribute to a particular effect

Ishikawa diagrams (also called fishbone diagrams, or herringbone diagrams , cause-and-effect diagrams, orFishikawa) are causal diagrams that show the causes of a certain event -- created by Kaoru Ishikawa (1990).[1]

Common uses of the Ishikawa diagram are product design and quality defect prevention, to identify potential factorscausing an overall effect. Each cause or reason for imperfection is a source of variation. Causes are usually groupedinto major categories to identify these sources of variation. The categories typically include:

• People: Anyone involved with the process• Methods: How the process is performed and the specific requirements for doing it, such as policies, procedures,

rules, regulations and laws• Machines: Any equipment, computers, tools etc. required to accomplish the job• Materials: Raw materials, parts, pens, paper, etc. used to produce the final product• Measurements: Data generated from the process that are used to evaluate its quality• Environment: The conditions, such as location, time, temperature, and culture in which the process operates

Overview

Ishikawa diagram, in fishbone shape, showing factors of Equipment, Process,People, Materials, Environment and Management, all affecting the overall

problem. Smaller arrows connect the sub-causes to major causes.

Ishikawa diagrams were proposed by KaoruIshikawa[2] in the 1960s, who pioneered qualitymanagement processes in the Kawasakishipyards, and in the process became one of thefounding fathers of modern management.

It was first used in the 1940s, and is consideredone of the seven basic tools of quality control.[3]

It is known as a fishbone diagram because of itsshape, similar to the side view of a fish skeleton.

Mazda Motors famously used an Ishikawadiagram in the development of the Miata sportscar, where the required result was "Jinba Ittai" or

Ishikawa diagram 3

"Horse and Rider as One". The main causes included such aspects as "touch" and "braking" with the lesser causesincluding highly granular factors such as "50/50 weight distribution" and "able to rest elbow on top of driver's door".Every factor identified in the diagram was included in the final design.

CausesCauses in the diagram are often categorized, such as to the 8 M's, described below. Cause-and-effect diagrams canreveal key relationships among various variables, and the possible causes provide additional insight into processbehavior.

Causes can be derived from brainstorming sessions. These groups can then be labeled as categories of the fishbone.They will typically be one of the traditional categories mentioned above but may be something unique to theapplication in a specific case. Causes can be traced back to root causes with the 5 Whys technique.

Typical categories are:

The 8 Ms (used in manufacturing)• Machine (technology)• Method (process)• Material (Includes Raw Material, Consumables and Information.)• Man Power (physical work)/Mind Power (brain work): Kaizens, Suggestions• Measurement (Inspection)• Milieu/Mother Nature (Environment)• Management/Money Power• Maintenance

The 8 Ps (used in service industry)• Product=Service• Price• Place• Promotion/Entertainment• People(key person)• Process• Physical Evidence• Productivity & Quality

1. power

The 4 Ss (used in service industry)• Surroundings• Suppliers• Systems• Skills

Questions to be asked while building a Fishbone DiagramMan/Operator – Was the document properly interpreted? – Was the information properly circulated to all the functions? – Did the recipient understand the information? – Was the proper training to perform the task administered to the person? – Was too much judgment required to perform the task? – Were guidelines for judgment available? – Did the environment influence the actions of the individual? – Are there distractions in the workplace?

Ishikawa diagram 4

– Is fatigue a mitigating factor? - Is his work efficiency acceptable? - Is he responsible/accountable? - Is hequalified? - Is he experienced? - Is he medically fit and healthy? – How much experience does the individual have inperforming this task? - can he carry out the operation without error?

Machines – Was the correct tool/tooling used? - Does it meet production requirements? - Does it meet processcapabilities? – Are files saved with the correct extension to the correct location? – Is the equipment affected by theenvironment? – Is the equipment being properly maintained (i.e., daily/weekly/monthly preventative maintenanceschedule) – Does the software or hardware need to be updated? – Does the equipment or software have the featuresto support our needs/usage? - Was the machine properly maintained? – Was the machine properly programmed? – Isthe tooling/fixturing adequate for the job? – Does the machine have an adequate guard? – Was the equipment usedwithin its capabilities and limitations? – Are all controls including emergency stop button clearly labeled and/orcolor coded or size differentiated? – Is the equipment the right application for the given job?

Measurement – Does the gauge have a valid calibration date? – Was the proper gauge used to measure the part,process, chemical, compound, etc.? – Was a gauge capability study ever performed? - Do measurements varysignificantly from operator to operator? - Do operators have a tough time using the prescribed gauge? - Is the gaugefixturing adequate? – Does the gauge have proper measurement resolution? – Did the environment influence themeasurements taken?

Material (Includes Raw Material, Consumables and Information ) – Is all needed information available andaccurate? – Can information be verified or cross-checked? – Has any information changed recently / do we have away of keeping the information up to date? – What happens if we don't have all of the information we need? – Is aMaterial Safety Data Sheet (MSDS) readily available? – Was the material properly tested? – Was the materialsubstituted? – Is the supplier’s process defined and controlled? - Was the raw material defective? - was the rawmaterial the wrong type for the job? – Were quality requirements adequate for the part's function? – Was thematerial contaminated? – Was the material handled properly (stored, dispensed, used & disposed)?

Method – Was the canister, barrel, etc. labeled properly? – Were the workers trained properly in the procedure? –Was the testing performed statistically significant? – Was data tested for true root cause? – How many “if necessary”and “approximately” phrases are found in this process? – Was this a process generated by an Integrated ProductDevelopment (IPD) Team? – Did the IPD Team employ Design for Environmental (DFE) principles? – Has acapability study ever been performed for this process? – Is the process under Statistical Process Control (SPC)? –Are the work instructions clearly written? – Are mistake-proofing devices/techniques employed? – Are the workinstructions complete? - Is the work standard upgraded and to current revision? – Is the tooling adequately designedand controlled? – Is handling/packaging adequately specified? – Was the process changed? – Was the designchanged? - Are the lighting and ventilation adequate? – Was a process Failure Modes Effects Analysis (FMEA) everperformed? – Was adequate sampling done? – Are features of the process critical to safety clearly spelled out to theOperator?

Environment – Is the process affected by temperature changes over the course of a day? – Is the process affected byhumidity, vibration, noise, lighting, etc.? – Does the process run in a controlled environment? – Are associatesdistracted by noise, uncomfortable temperatures, fluorescent lighting, etc.?

Management - Is management involvement seen? – Inattention to task – Task hazards not guarded properly – Other(horseplay, inattention....) – Stress demands – Lack of Process – Training or education lacking – Poor employeeinvolvement – Poor recognition of hazard – Previously identified hazards were not eliminated

Ishikawa diagram 5

CriticismIn a discussion of the nature of a cause it is customary to distinguish between necessary and sufficient conditions forthe occurrence of an event. A necessary condition for the occurrence of a specified event is a circumstance in whoseabsence the event cannot occur. A sufficient condition for the occurrence of an event is a circumstance in whosepresence the event must occur.[4] A sufficient condition naturally contains one or several necessary ones. Ishikawadiagrams are meant to use the necessary conditions and split the "sufficient" ones into the "necessary" parts. Somecritics failing this simple logic have asked which conditions (necessary or sufficient) are addressed by the diagram incase[5]

References[1] Ishikawa, Kaoru (1990); (Translator: J. H. Loftus); Introduction to Quality Control; 448 p; ISBN 4-906224-61-X OCLC 61341428[2] Hankins, Judy (2001). Infusion Therapy in Clinical Practice. pp. 42.[3] Nancy R. Tague (2004). "Seven Basic Quality Tools" (http:/ / www. asq. org/ learn-about-quality/ seven-basic-quality-tools/ overview/

overview. html). The Quality Toolbox. Milwaukee, Wisconsin: American Society for Quality. p. 15. . Retrieved 2010-02-05.[4] Copi, Irving M. (1968) Introduction to Logic, Third Edition. Macmillian. New York. p.322[5] Gregory, Frank Hutson (1992) Cause, Effect, Efficiency & Soft Systems Models, Warwick Business School Research Paper No. 42 (ISSN

0265-5976), later published in Journal of the Operational Research Society, vol. 44 (4), pp 333-344.

Further reading• Ishikawa, Kaoru (1990); (Translator: J. H. Loftus); Introduction to Quality Control; 448 p; ISBN 4-906224-61-X

OCLC 61341428• Dale, Barrie G. et al. (2007); Managing Quality 5th ed; ISBN 978-1-4051-4279-3 OCLC 288977828

External links• Article from HCI Australia on Cause and Effect Diagrams (http:/ / www. hci. com. au/ hcisite5/ library/ materials/

Cause and effect diagrams. htm)

Check sheet 6

Check sheet

Check sheet

One of the Seven Basic Tools of QualityPurpose To provide a structured way to collect quality-related data as a rough means for assessing a process or as an input to other analyses

The check sheet is a simple document that is used for collecting data in real-time and at the location where the datais generated. The document is typically a blank form that is designed for the quick, easy, and efficient recording ofthe desired information, which can be either quantitative or qualitative. When the information is quantitative, thechecksheet is sometimes called a tally sheet[1] .

A defining characteristic of a checksheet is that data is recorded by making marks ("checks") on it. A typicalchecksheet is divided into regions, and marks made in different regions have different significance. Data is read byobserving the location and number of marks on the sheet. 5 Basic types of Check Sheets:

• Classification: A trait such as a defect or failure mode must be classified into a category.• Location: The physical location of a trait is indicated on a picture of a part or item being evaluated.• Frequency: The presence or absence of a trait or combination of traits is indicated. Also number of occurrences of

a trait on a part can be indicated.• Measurement Scale: A measurement scale is divided into intervals, and measurements are indicated by checking

an appropriate interval.• Check List: The items to be performed for a task are listed so that, as each is accomplished, it can be indicated as

having been completed.

An example of a simple quality control checksheet

The check sheet is one of the sevenbasic tools of quality control.[2]

References[1] John R. Schultz (2006). "Measuring Service

Industry Performance: Some BasicConcepts" (http:/ / onlinelibrary. wiley. com/doi/ 10. 1002/ pfi. 2006. 4930450405/abstract). International Society forPerformance Improvement. p. 3. . Retrieved2011-10-06.

[2] Nancy R. Tague (2004). "Seven BasicQuality Tools" (http:/ / www. asq. org/learn-about-quality/ seven-basic-quality-tools/ overview/ overview. html). The Quality Toolbox. Milwaukee, Wisconsin: American Society forQuality. p. 15. . Retrieved 2010-02-05.

Control chart 7

Control chart

Control chart

One of the Seven Basic Tools of QualityFirst described by Walter A. Shewhart

Purpose To determine whether a process should undergo a formal examination for quality-related problems

Control charts, also known as Shewhart charts or process-behaviour charts, in statistical process control aretools used to determine whether or not a manufacturing or business process is in a state of statistical control.

OverviewIf analysis of the control chart indicates that the process is currently under control (i.e. is stable, with variation onlycoming from sources common to the process) then no corrections or changes to process control parameters areneeded or desirable. In addition, data from the process can be used to predict the future performance of the process.If the chart indicates that the process being monitored is not in control, analysis of the chart can help determine thesources of variation, which can then be eliminated to bring the process back into control. A control chart is a specifickind of run chart that allows significant change to be differentiated from the natural variability of the process.

The control chart can be seen as part of an objective and disciplined approach that enables correct decisionsregarding control of the process, including whether or not to change process control parameters. Process parametersshould never be adjusted for a process that is in control, as this will result in degraded process performance.[1] Aprocess that is stable but operating outside of desired limits (e.g. scrap rates may be in statistical control but abovedesired limits) needs to be improved through a deliberate effort to understand the causes of current performance andfundamentally improve the process.[2]

The control chart is one of the seven basic tools of quality control.[3]

HistoryThe control chart was invented by Walter A. Shewhart while working for Bell Labs in the 1920s. The company's engineers had been seeking to improve the reliability of their telephony transmission systems. Because amplifiers and other equipment had to be buried underground, there was a business need to reduce the frequency of failures and repairs. By 1920 the engineers had already realized the importance of reducing variation in a manufacturing process. Moreover, they had realized that continual process-adjustment in reaction to non-conformance actually increased variation and degraded quality. Shewhart framed the problem in terms of Common- and special-causes of variation and, on May 16, 1924, wrote an internal memo introducing the control chart as a tool for distinguishing between the two. Dr. Shewhart's boss, George Edwards, recalled: "Dr. Shewhart prepared a little memorandum only about a page in length. About a third of that page was given over to a simple diagram which we would all recognize today as a

Control chart 8

schematic control chart. That diagram, and the short text which preceded and followed it, set forth all of the essentialprinciples and considerations which are involved in what we know today as process quality control."[4] Shewhartstressed that bringing a production process into a state of statistical control, where there is only common-causevariation, and keeping it in control, is necessary to predict future output and to manage a process economically.

Dr. Shewhart created the basis for the control chart and the concept of a state of statistical control by carefullydesigned experiments. While Dr. Shewhart drew from pure mathematical statistical theories, he understood datafrom physical processes typically produce a "normal distribution curve" (a Gaussian distribution, also commonlyreferred to as a "bell curve"). He discovered that observed variation in manufacturing data did not always behave thesame way as data in nature (Brownian motion of particles). Dr. Shewhart concluded that while every processdisplays variation, some processes display controlled variation that is natural to the process, while others displayuncontrolled variation that is not present in the process causal system at all times.[5]

In 1924 or 1925, Shewhart's innovation came to the attention of W. Edwards Deming, then working at theHawthorne facility. Deming later worked at the United States Department of Agriculture and then became themathematical advisor to the United States Census Bureau. Over the next half a century, Deming became the foremostchampion and proponent of Shewhart's work. After the defeat of Japan at the close of World War II, Deming servedas statistical consultant to the Supreme Commander of the Allied Powers. His ensuing involvement in Japanese life,and long career as an industrial consultant there, spread Shewhart's thinking, and the use of the control chart, widelyin Japanese manufacturing industry throughout the 1950s and 1960s.

Chart detailsA control chart consists of:

• Points representing a statistic (e.g., a mean, range, proportion) of measurements of a quality characteristic insamples taken from the process at different times [the data]

• The mean of this statistic using all the samples is calculated (e.g., the mean of the means, mean of the ranges,mean of the proportions)

• A center line is drawn at the value of the mean of the statistic• The standard error (e.g., standard deviation/sqrt(n) for the mean) of the statistic is also calculated using all the

samples• Upper and lower control limits (sometimes called "natural process limits") that indicate the threshold at which the

process output is considered statistically 'unlikely' are drawn typically at 3 standard errors from the center line

The chart may have other optional features, including:

• Upper and lower warning limits, drawn as separate lines, typically two standard errors above and below the centerline

• Division into zones, with the addition of rules governing frequencies of observations in each zone• Annotation with events of interest, as determined by the Quality Engineer in charge of the process's quality

Control chart 9

Chart usageIf the process is in control (and the process statistic is normal), 99.7300% of all the points will fall between thecontrol limits. Any observations outside the limits, or systematic patterns within, suggest the introduction of a new(and likely unanticipated) source of variation, known as a special-cause variation. Since increased variation meansincreased quality costs, a control chart "signaling" the presence of a special-cause requires immediate investigation.

This makes the control limits very important decision aids. The control limits tell you about process behavior andhave no intrinsic relationship to any specification targets or engineering tolerance. In practice, the process mean (andhence the center line) may not coincide with the specified value (or target) of the quality characteristic because theprocess' design simply cannot deliver the process characteristic at the desired level.

Control charts limit specification limits or targets because of the tendency of those involved with the process (e.g.,machine operators) to focus on performing to specification when in fact the least-cost course of action is to keepprocess variation as low as possible. Attempting to make a process whose natural center is not the same as the targetperform to target specification increases process variability and increases costs significantly and is the cause of muchinefficiency in operations. Process capability studies do examine the relationship between the natural process limits(the control limits) and specifications, however.

The purpose of control charts is to allow simple detection of events that are indicative of actual process change. Thissimple decision can be difficult where the process characteristic is continuously varying; the control chart providesstatistically objective criteria of change. When change is detected and considered good its cause should be identifiedand possibly become the new way of working, where the change is bad then its cause should be identified andeliminated.

The purpose in adding warning limits or subdividing the control chart into zones is to provide early notification ifsomething is amiss. Instead of immediately launching a process improvement effort to determine whether specialcauses are present, the Quality Engineer may temporarily increase the rate at which samples are taken from theprocess output until it's clear that the process is truly in control. Note that with three-sigma limits, common-causevariations result in signals less than once out of every twenty-two points for skewed processes and about once out ofevery three hundred seventy (1/370.4) points for normally-distributed processes.[6] The two-sigma warning levelswill be reached about once for every twenty-two (1/21.98) plotted points in normally-distributed data. (For example,the means of sufficiently large samples drawn from practically any underlying distribution whose variance exists arenormally distributed, according to the Central Limit Theorem.)

Control chart 10

Choice of limitsShewhart set 3-sigma (3-standard error) limits on the following basis.

• The coarse result of Chebyshev's inequality that, for any probability distribution, the probability of an outcomegreater than k standard deviations from the mean is at most 1/k2.

• The finer result of the Vysochanskii-Petunin inequality, that for any unimodal probability distribution, theprobability of an outcome greater than k standard deviations from the mean is at most 4/(9k2).

• The empirical investigation of sundry probability distributions reveals that at least 99% of observations occurredwithin three standard deviations of the mean.

Shewhart summarized the conclusions by saying:

... the fact that the criterion which we happen to use has a fine ancestry in highbrow statistical theoremsdoes not justify its use. Such justification must come from empirical evidence that it works. As thepractical engineer might say, the proof of the pudding is in the eating.

Though he initially experimented with limits based on probability distributions, Shewhart ultimately wrote:

Some of the earliest attempts to characterize a state of statistical control were inspired by the belief thatthere existed a special form of frequency function f and it was early argued that the normal lawcharacterized such a state. When the normal law was found to be inadequate, then generalizedfunctional forms were tried. Today, however, all hopes of finding a unique functional form f are blasted.

The control chart is intended as a heuristic. Deming insisted that it is not a hypothesis test and is not motivated by theNeyman-Pearson lemma. He contended that the disjoint nature of population and sampling frame in most industrialsituations compromised the use of conventional statistical techniques. Deming's intention was to seek insights intothe cause system of a process ...under a wide range of unknowable circumstances, future and past.... He claimedthat, under such conditions, 3-sigma limits provided ... a rational and economic guide to minimum economic loss...from the two errors:

1. Ascribe a variation or a mistake to a special cause (assignable cause) when in fact the cause belongs to thesystem (common cause). (Also known as a Type I error)

2. Ascribe a variation or a mistake to the system (common causes) when in fact the cause was a special cause(assignable cause). (Also known as a Type II error)

Calculation of standard deviationAs for the calculation of control limits, the standard deviation (error) required is that of the common-cause variationin the process. Hence, the usual estimator, in terms of sample variance, is not used as this estimates the totalsquared-error loss from both common- and special-causes of variation.

An alternative method is to use the relationship between the range of a sample and its standard deviation derived byLeonard H. C. Tippett, an estimator which tends to be less influenced by the extreme observations which typifyspecial-causes.

Control chart 11

Rules for detecting signalsThe most common sets are:

• The Western Electric rules• The Wheeler rules (equivalent to the Western Electric zone tests[7] )• The Nelson rules

There has been particular controversy as to how long a run of observations, all on the same side of the centre line,should count as a signal, with 6, 7, 8 and 9 all being advocated by various writers.

The most important principle for choosing a set of rules is that the choice be made before the data is inspected.Choosing rules once the data have been seen tends to increase the Type I error rate owing to testing effects suggestedby the data.

Alternative basesIn 1935, the British Standards Institution, under the influence of Egon Pearson and against Shewhart's spirit, adoptedcontrol charts, replacing 3-sigma limits with limits based on percentiles of the normal distribution. This movecontinues to be represented by John Oakland and others but has been widely deprecated by writers in theShewhart-Deming tradition.

Performance of control chartsWhen a point falls outside of the limits established for a given control chart, those responsible for the underlyingprocess are expected to determine whether a special cause has occurred. If one has, it is appropriate to determine ifthe results with the special cause are better than or worse than results from common causes alone. If worse, then thatcause should be eliminated if possible. If better, it may be appropriate to intentionally retain the special cause withinthe system producing the results.

It is known that even when a process is in control (that is, no special causes are present in the system), there isapproximately a 0.27% probability of a point exceeding 3-sigma control limits. So, even an in control process plottedon a properly constructed control chart will eventually signal the possible presence of a special cause, even thoughone may not have actually occurred. For a Shewhart control chart using 3-sigma limits, this false alarm occurs onaverage once every 1/0.0027 or 370.4 observations. Therefore, the in-control average run length (or in-control ARL)of a Shewhart chart is 370.4.

Meanwhile, if a special cause does occur, it may not be of sufficient magnitude for the chart to produce animmediate alarm condition. If a special cause occurs, one can describe that cause by measuring the change in themean and/or variance of the process in question. When those changes are quantified, it is possible to determine theout-of-control ARL for the chart.

It turns out that Shewhart charts are quite good at detecting large changes in the process mean or variance, as theirout-of-control ARLs are fairly short in these cases. However, for smaller changes (such as a 1- or 2-sigma change inthe mean), the Shewhart chart does not detect these changes efficiently. Other types of control charts have beendeveloped, such as the EWMA chart, the CUSUM chart and the real-time contrasts chart, which detect smallerchanges more efficiently by making use of information from observations collected prior to the most recent datapoint.

Most control charts work best for numeric data with Gaussian assumptions. The real-time contrasts chart wasproposed able to handle process data with complex characteristics, e.g. high-dimensional, mix numerical andcategorical, missing-valued, non-Gaussian, non-linear relationship.

Control chart 12

CriticismsSeveral authors have criticised the control chart on the grounds that it violates the likelihood principle. However, theprinciple is itself controversial and supporters of control charts further argue that, in general, it is impossible tospecify a likelihood function for a process not in statistical control, especially where knowledge about the causesystem of the process is weak.

Some authors have criticised the use of average run lengths (ARLs) for comparing control chart performance,because that average usually follows a geometric distribution, which has high variability and difficulties.

Some authors have criticized that most control charts focus on numeric data. Nowadays, process data can be muchmore complex, e.g. non-Gaussian, mix numerical and categorical, missing-valued.[8]

Types of charts

Chart Process observation Process observationsrelationships

Processobservations type

Size of shiftto detect

and R chart Quality characteristic measurement within onesubgroup

Independent Variables Large (≥1.5σ)

and s chart Quality characteristic measurement within onesubgroup

Independent Variables Large (≥1.5σ)

Shewhart individuals controlchart (ImR chart or XmRchart)

Quality characteristic measurement for oneobservation

Independent Variables† Large (≥1.5σ)

Three-way chart Quality characteristic measurement within onesubgroup

Independent Variables Large (≥1.5σ)

p-chart Fraction nonconforming within one subgroup Independent Attributes† Large (≥1.5σ)

np-chart Number nonconforming within one subgroup Independent Attributes† Large (≥1.5σ)

c-chart Number of nonconformances within one subgroup Independent Attributes† Large (≥1.5σ)

u-chart Nonconformances per unit within one subgroup Independent Attributes† Large (≥1.5σ)

EWMA chart Exponentially weighted moving average of qualitycharacteristic measurement within one subgroup

Independent Attributes orvariables

Small (<1.5σ)

CUSUM chart Cumulative sum of quality characteristicmeasurement within one subgroup

Independent Attributes orvariables

Small (<1.5σ)

Time series model Quality characteristic measurement within onesubgroup

Autocorrelated Attributes orvariables

N/A

Regression control chart Quality characteristic measurement within onesubgroup

Dependent of processcontrol variables

Variables Large (≥1.5σ)

Real-time contrasts chart Sliding window of quality characteristicmeasurement within one subgroup

Independent Attributes orvariables

Small (<1.5σ)

† Some practitioners also recommend the use of Individuals charts for attribute data, particularly when the assumptions of either binomially-distributed data (p- and np-charts) or Poisson-distributed data (u- and c-charts) are violated.[9] Two primary justifications are given for this practice. First, normality is not necessary for statistical control, so the Individuals chart may be used with non-normal data.[10] Second, attribute charts derive the measure of dispersion directly from the mean proportion (by assuming a probability distribution), while Individuals charts derive

Control chart 13

the measure of dispersion from the data, independent of the mean, making Individuals charts more robust thanattributes charts to violations of the assumptions about the distribution of the underlying population.[11] It issometimes noted that the substitution of the Individuals chart works best for large counts, when the binomial andPoisson distributions approximate a normal distribution. i.e. when the number of trials n > 1000 for p- and np-chartsor λ > 500 for u- and c-charts.

Critics of this approach argue that control charts should not be used then their underlying assumptions are violated,such as when process data is neither normally distributed nor binomially (or Poisson) distributed. Such processes arenot in control and should be improved before the application of control charts. Additionally, application of the chartsin the presence of such deviations increases the type I and type II error rates of the control charts, and may make thechart of little practical use.

Notes[1] McNeese, William (July 2006). "Over-controlling a Process: The Funnel Experiment" (http:/ / www. spcforexcel. com/

overcontrolling-process-funnel-experiment). BPI Consulting, LLC. . Retrieved 2010-03-17.[2] Wheeler, Donald J. (2000). Understanding Variation. Knoxville, Tennessee: SPC Press. ISBN 0-945320-53-1.[3] Nancy R. Tague (2004). "Seven Basic Quality Tools" (http:/ / www. asq. org/ learn-about-quality/ seven-basic-quality-tools/ overview/

overview. html). The Quality Toolbox. Milwaukee, Wisconsin: American Society for Quality. p. 15. . Retrieved 2010-02-05.[4] Western Electric - A Brief History (http:/ / www. porticus. org/ bell/ doc/ western_electric. doc)[5] "Why SPC?" British Deming Association SPC Press, Inc. 1992[6] Wheeler, Donald J. (1). "Are You Sure We Don't Need Normally Distributed Data?" (http:/ / www. qualitydigest. com/ inside/

quality-insider-column/ are-you-sure-we-don-t-need-normally-distributed-data. html). Quality Digest. . Retrieved 7 December 2010.[7] Wheeler, Donald J.; Chambers, David S. (1992). Understanding statistical process control (2 ed.). Knoxville, Tennessee: SPC Press. p. 96.

ISBN 9780945320135. OCLC 27187772[8] Deng, H.; Runger, G.; Tuv, E. (2011). "System monitoring with real-time contrasts" (http:/ / enpub. fulton. asu. edu/ hdeng3/

RealtimeJQT2011. pdf). Journal of Quality Technology (forthcoming). .[9] Wheeler, Donald J. (2000). Understanding Variation: the key to managing chaos. SPC Press. p. 140. ISBN 0945320531.[10] Staufer, Rip (1 Apr 2010). "Some Problems with Attribute Charts" (http:/ / www. qualitydigest. com/ inside/ quality-insider-article/

some-problems-attribute-charts. html). Quality Digest. . Retrieved 2 Apr 2010.[11] Wheeler, Donald J.. "What About Charts for Count Data?" (http:/ / www. qualitydigest. com/ jul/ spctool. html). Quality Digest. . Retrieved

2010-03-23.

Bibliography• Deming, W E (1975) "On probability as a basis for action." The American Statistician. 29(4), pp146–152• Deming, W E (1982) Out of the Crisis: Quality, Productivity and Competitive Position ISBN 0-521-30553-5.• Deng, H, & Runger, G & Tuv, Eugene (2011). "System monitoring with real-time contrasts" Journal of Quality

Technology. forthcoming.• Mandel, B J (1969). "The Regression Control Chart" Journal of Quality Technology. 1 (1), pp 1–9.• Oakland, J (2002) Statistical Process Control ISBN 0-7506-5766-9.• Shewhart, W A (1931) Economic Control of Quality of Manufactured Product ISBN 0-87389-076-0.• Shewhart, W A (1939) Statistical Method from the Viewpoint of Quality Control ISBN 0-486-65232-7.• Wheeler, D J (2000) Normality and the Process-Behaviour Chart ISBN 0-945320-56-6.• Wheeler, D J & Chambers, D S (1992) Understanding Statistical Process Control ISBN 0-945320-13-2.• Wheeler, Donald J. (1999). Understanding Variation: The Key to Managing Chaos - 2nd Edition. SPC Press, Inc.

ISBN 0-945320-53-1.

Control chart 14

External linksNote: Before adding your company's link, please read WP:Spam#External_link_spamming andWP:External_links#Links_normally_to_be_avoided.

• NIST/SEMATECH e-Handbook of Statistical Methods (http:/ / www. itl. nist. gov/ div898/ handbook/ index.htm)

• Monitoring and Control with Control Charts (http:/ / www. itl. nist. gov/ div898/ handbook/ pmc/ pmc. htm)

Histogram 15

Histogram

Histogram

One of the Seven Basic Tools of QualityFirst described by Karl Pearson

Purpose To roughly assess the probability distribution of a given variable by depicting the frequencies of observations occurring incertain ranges of values

In statistics, a histogram is a graphical representation showing a visual impression of the distribution of data. It is anestimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson.[1] Ahistogram consists of tabular frequencies, shown as adjacent rectangles, erected over discrete intervals (bins), withan area equal to the frequency of the observations in the interval. The height of a rectangle is also equal to thefrequency density of the interval, i.e., the frequency divided by the width of the interval. The total area of thehistogram is equal to the number of data. A histogram may also be normalized displaying relative frequencies. Itthen shows the proportion of cases that fall into each of several categories, with the total area equaling 1. Thecategories are usually specified as consecutive, non-overlapping intervals of a variable. The categories (intervals)must be adjacent, and often are chosen to be of the same size.[2]

Histograms are used to plot density of data, and often for density estimation: estimating the probability densityfunction of the underlying variable. The total area of a histogram used for probability density is always normalized to1. If the length of the intervals on the x-axis are all 1, then a histogram is identical to a relative frequency plot.

An alternative to the histogram is kernel density estimation, which uses a kernel to smooth samples. This willconstruct a smooth probability density function, which will in general more accurately reflect the underlyingvariable.

The histogram is one of the seven basic tools of quality control.[3]

Histogram 16

Etymology

An example histogram of the heights of 31 BlackCherry trees.

The etymology of the word histogram is uncertain. Sometimes it issaid to be derived from the Greek histos 'anything set upright' (as themasts of a ship, the bar of a loom, or the vertical bars of a histogram);and gramma 'drawing, record, writing'. It is also said that Karl Pearson,who introduced the term in 1895, derived the name from "historicaldiagram".[4]

Examples

The U.S. Census Bureau found that there were 124 million people whowork outside of their homes.[5] Using their data on the time occupiedby travel to work, Table 2 below shows the absolute number of peoplewho responded with travel times "at least 15 but less than 20 minutes"is higher than the numbers for the categories above and below it. This

is likely due to people rounding their reported journey time. The problem of reporting values as somewhat arbitrarilyrounded numbers is a common phenomenon when collecting data from people.

Histogram of travel time, US 2000 census. Area under the curve equals the total numberof cases. This diagram uses Q/width from the table.

Data by absolute numbers

Interval Width Quantity Quantity/width

0 5 4180 836

5 5 13687 2737

10 5 18618 3723

15 5 19634 3926

20 5 17981 3596

25 5 7190 1438

30 5 16369 3273

35 5 3212 642

Histogram 17

40 5 4122 824

45 15 9200 613

60 30 6461 215

90 60 3435 57

This histogram shows the number of cases per unit interval so that the height of each bar is equal to the proportion oftotal people in the survey who fall into that category. The area under the curve represents the total number of cases(124 million). This type of histogram shows absolute numbers, with Q in thousands.

Histogram of travel time, US 2000 census. Area under the curve equals 1. This diagramuses Q/total/width from the table.

Data by proportion

Interval Width Quantity (Q) Q/total/width

0 5 4180 0.0067

5 5 13687 0.0221

10 5 18618 0.0300

15 5 19634 0.0316

20 5 17981 0.0290

25 5 7190 0.0116

30 5 16369 0.0264

35 5 3212 0.0052

40 5 4122 0.0066

45 15 9200 0.0049

60 30 6461 0.0017

90 60 3435 0.0005

This histogram differs from the first only in the vertical scale. The height of each bar is the decimal percentage of thetotal that each category represents, and the total area of all the bars is equal to 1, the decimal equivalent of 100%.The curve displayed is a simple density estimate. This version shows proportions, and is also known as a unit areahistogram.

Histogram 18

In other words, a histogram represents a frequency distribution by means of rectangles whose widths represent classintervals and whose areas are proportional to the corresponding frequencies. The intervals are placed together inorder to show that the data represented by the histogram, while exclusive, is also continuous. (E.g., in a histogram itis possible to have two connecting intervals of 10.5–20.5 and 20.5–33.5, but not two connecting intervals of10.5–20.5 and 22.5–32.5. Empty intervals are represented as empty and not skipped.)[6]

Shape or form of a distributionThe histogram provides important informations about the shape of a distribution. According to the values presented,the histogram is either highly or moderately skewed to the left or right. A symmetrical shape is also possible,although a histogram is never perfectly symmetrical. If the histogram is skewed to the left, or negatively skewed, thetail extends further to the left. An example for a distribution skewed to the left might be the relative frequency ofexam scores. Most of the scores are above 70 percent and only a few low scores occure. An example for adistribution skewed to the right or positively skewed is a histogram showing the relative frequency of housingvalues. A relatively small number of expensive homes create the skeweness to the right. The tail extends further tothe right. The shape of a symmetrical distribution mirrors the skeweness of the left or right tail. For example thehistogram of data for IQ scores. Histograms can be unimodal, bi-modal or multi-modal, depending on the dataset.[7]

Activities and demonstrationsThe SOCR resource pages contain a number of hands-on interactive activities demonstrating the concept of ahistogram, histogram construction [8] and manipulation [9] using Java applets and charts [10].

Mathematical definition

An ordinary and a cumulative histogram of the same data. The data shown is a randomsample of 10,000 points from a normal distribution with a mean of 0 and a standard

deviation of 1.

In a more general mathematical sense,a histogram is a function mi that countsthe number of observations that fallinto each of the disjoint categories(known as bins), whereas the graph ofa histogram is merely one way torepresent a histogram. Thus, if we let nbe the total number of observationsand k be the total number of bins, thehistogram mi meets the followingconditions:

Histogram 19

Cumulative histogramA cumulative histogram is a mapping that counts the cumulative number of observations in all of the bins up to thespecified bin. That is, the cumulative histogram Mi of a histogram mj is defined as:

Number of bins and widthThere is no "best" number of bins, and different bin sizes can reveal different features of the data. Some theoreticianshave attempted to determine an optimal number of bins, but these methods generally make strong assumptions aboutthe shape of the distribution. Depending on the actual data distribution and the goals of the analysis, different binwidths may be appropriate, so experimentation is usually needed to determine an appropriate width. There are,however, various useful guidelines and rules of thumb.[11]

The number of bins k can be assigned directly or can be calculated from a suggested bin width h as:

The braces indicate the ceiling function.

Sturges' formula[12]

which implicitly bases the bin sizes on the range of the data, and can perform poorly if n < 30.

Scott's choice[13]

where is the sample standard deviation.

Square-root choice

which takes the square root of the number of data points in the sample (used by Excel histograms and many others).

Freedman–Diaconis' choice[14]

which is based on the interquartile range, denoted by IQR.

Choice based on minimization of an estimated L2 risk function[15]

where and are mean and biased variance of a histogram with bin-width , and

.

Histogram 20

References[1] Pearson, K. (1895). "Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material". Philosophical

Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 186: 343–326. Bibcode 1895RSPTA.186..343P.doi:10.1098/rsta.1895.0010.

[2] Howitt, D. and Cramer, D. (2008) Statistics in Psychology. Prentice Hall[3] Nancy R. Tague (2004). "Seven Basic Quality Tools" (http:/ / www. asq. org/ learn-about-quality/ seven-basic-quality-tools/ overview/

overview. html). The Quality Toolbox. Milwaukee, Wisconsin: American Society for Quality. p. 15. . Retrieved 2010-02-05.[4] M. Eileen Magnello (December 1856). "Karl Pearson and the Origins of Modern Statistics: An Elastician becomes a Statistician" (http:/ /

www. rutherfordjournal. org/ article010107. html). The New Zealand Journal for the History and Philosophy of Science and Technology 1volume. ISSN 1177–1380. .

[5] US 2000 census (http:/ / www. census. gov/ prod/ 2004pubs/ c2kbr-33. pdf).[6] Dean, S., & Illowsky, B. (2009, February 19). Descriptive Statistics: Histogram. Retrieved from the Connexions Web site: http:/ / cnx. org/

content/ m16298/ 1. 11/[7] Anderson, David R. "Statistics for Business and Economics", 2010, volume 2, p. 32–33.[8] http:/ / wiki. stat. ucla. edu/ socr/ index. php/ SOCR_EduMaterials_ModelerActivities_MixtureModel_1[9] http:/ / wiki. stat. ucla. edu/ socr/ index. php/ SOCR_EduMaterials_Activities_PowerTransformFamily_Graphs[10] http:/ / www. socr. ucla. edu/ htmls/ SOCR_Charts. html[11] e.g. § 5.6 "Density Estimation", W. N. Venables and B. D. Ripley, Modern Applied Statistics with S, Springer, 4th edition[12] Sturges, H. A. (1926). "The choice of a class interval". J. American Statistical Association: 65–66.[13] Scott, David W. (1979). "On optimal and data-based histograms". Biometrika 66 (3): 605–610. doi:10.1093/biomet/66.3.605.[14] The Freedman–Diaconis rule isFreedman, David; Diaconis, P. (1981). "On the histogram as a density estimator: L2 theory". Zeitschrift für

Wahrscheinlichkeitstheorie und verwandte Gebiete 57 (4): 453–476. doi:10.1007/BF01025868.[15] Shimazaki, H.; Shinomoto, S. (2007). "A method for selecting the bin size of a time histogram" (http:/ / www. mitpressjournals. org/ doi/

abs/ 10. 1162/ neco. 2007. 19. 6. 1503). Neural Computation 19 (6): 1503–1527. doi:10.1162/neco.2007.19.6.1503. PMID 17444758. .

Further reading• Lancaster, H.O. An Introduction to Medical Statistics. John Wiley and Sons. 1974. ISBN 0 471 51250-8

External links• Journey To Work and Place Of Work (http:/ / www. census. gov/ population/ www/ socdemo/ journey. html)

(location of census document cited in example)• Smooth histogram for signals and images from a few samples (http:/ / www. mathworks. com/ matlabcentral/

fileexchange/ 30480-histconnect)• Histograms: Construction, Analysis and Understanding with external links and an application to particle Physics.

(http:/ / quarknet. fnal. gov/ toolkits/ ati/ histograms. html)• A Method for Selecting the Bin Size of a Histogram (http:/ / 2000. jukuin. keio. ac. jp/ shimazaki/ res/ histogram.

html)• Interactive histogram generator (http:/ / www. shodor. org/ interactivate/ activities/ histogram/ )• Matlab function to plot nice histograms (http:/ / www. mathworks. com/ matlabcentral/ fileexchange/

27388-plot-and-compare-nice-histograms-by-default)

Pareto chart 21

Pareto chart

Pareto chart

One of the Seven Basic Tools of QualityFirst described by Joseph M. Juran

Purpose To assess the most frequently-occurring defects by category†

A Pareto chart, named after Vilfredo Pareto, is a type of chart that contains both bars and a line graph, whereindividual values are represented in descending order by bars, and the cumulative total is represented by the line.

Simple example of a Pareto chart using hypothetical data showing the relative frequencyof reasons for arriving late at work

The left vertical axis is the frequencyof occurrence, but it can alternativelyrepresent cost or another important unitof measure. The right vertical axis isthe cumulative percentage of the totalnumber of occurrences, total cost, ortotal of the particular unit of measure.Because the reasons are in decreasingorder, the cumulative function is aconcave function. To take the exampleabove, in order to lower the amount oflate arriving by 80%, it is sufficient tosolve the first three issues.

The purpose of the Pareto chart is tohighlight the most important among a(typically large) set of factors. Inquality control, it often represents themost common sources of defects, the

highest occurring type of defect, or the most frequent reasons for customer complaints, and so on. Wilkinson (2006)devised an algorithm for producing statistically-based acceptance limits (similar to confidence intervals) for each barin the Pareto chart.

These charts can be generated by simple spreadsheet programs, such as OpenOffice.org Calc and Microsoft Exceland specialized statistical software tools as well as online quality charts generators.

The Pareto chart is one of the seven basic tools of quality control.[1]

Pareto chart 22

References[1] Nancy R. Tague (2004). "Seven Basic Quality Tools" (http:/ / www. asq. org/ learn-about-quality/ seven-basic-quality-tools/ overview/

overview. html). The Quality Toolbox. Milwaukee, Wisconsin: American Society for Quality. p. 15. . Retrieved 2010-02-05.

Further reading• Hart, K. M., & Hart, R. F. (1989). Quantitative methods for quality improvement. Milwaukee, WI: ASQC Quality

Press.• Juran, J. M. (1962). Quality control handbook. New York: McGraw-Hill.• Juran, J. M., & Gryna, F. M. (1970). Quality planning and analysis. New York: McGraw-Hill.• Montgomery, D. C. (1985). Statistical quality control. New York: Wiley.• Montgomery, D. C. (1991). Design and analysis of experiments, 3rd ed. New York: Wiley.• Pyzdek, T. (1989). What every engineer should know about quality control. New York: Marcel Dekker.• Vaughn, R. C. (1974). Quality control. Ames, IA: Iowa State Press.• Wilkinson, L. (2006). "Revising the Pareto Chart". The American Statistician 60: 332–334.

Scatter plot 23

Scatter plot

Scatter plot

One of the Seven Basic Tools of QualityFirst described by Francis Galton

Purpose To identify the type of relationship (if any) between two variables

Waiting time between eruptions and the duration of the eruptionfor the Old Faithful Geyser in Yellowstone National Park,

Wyoming, USA. This chart suggests there are generally two"types" of eruptions: short-wait-short-duration, and

long-wait-long-duration.

A scatter plot or scattergraph is a type of mathematicaldiagram using Cartesian coordinates to display values fortwo variables for a set of data.

The data is displayed as a collection of points, eachhaving the value of one variable determining the positionon the horizontal axis and the value of the other variabledetermining the position on the vertical axis.[2] This kindof plot is also called a scatter chart, scattergram, scatterdiagram or scatter graph.

Overview

A scatter plot is used when a variable exists that is underthe control of the experimenter. If a parameter exists thatis systematically incremented and/or decremented by theother, it is called the control parameter or independentvariable and is customarily plotted along the horizontalaxis. The measured or dependent variable is customarilyplotted along the vertical axis. If no dependent variableexists, either type of variable can be plotted on either axisand a scatter plot will illustrate only the degree of correlation (not causation) between two variables.

A scatter plot can suggest various kinds of correlations between variables with a certain confidence interval.Correlations may be positive (rising), negative (falling), or null (uncorrelated). If the pattern of dots slopes fromlower left to upper right, it suggests a positive correlation

Scatter plot 24

A 3D scatter plot allows for the visualization of multivariate dataof up to four dimensions. The Scatter plot takes multiple scalarvariables and uses them for different axes in phase space. The

different variables are combined to form coordinates in the phasespace and they are displayed using glyphs and colored using

another scalar variable.[1]

between the variables being studied. If the pattern of dotsslopes from upper left to lower right, it suggests anegative correlation. A line of best fit (alternatively called'trendline') can be drawn in order to study the correlationbetween the variables. An equation for the correlationbetween the variables can be determined by establishedbest-fit procedures. For a linear correlation, the best-fitprocedure is known as linear regression and is guaranteedto generate a correct solution in a finite time. Nouniversal best-fit procedure is guaranteed to generate acorrect solution for arbitrary relationships. A scatter plotis also very useful when we wish to see how twocomparable data sets agree with each other. In this case,an identity line, i.e., a y=x line, or an 1:1 line, is oftendrawn as a reference. The more the two data sets agree,the more the scatters tend to concentrate in the vicinity ofthe identity line; if the two data sets are numericallyidentical, the scatters fall on the identity line exactly.

One of the most powerful aspects of a scatter plot,however, is its ability to show nonlinear relationshipsbetween variables. Furthermore, if the data is represented by a mixture model of simple relationships, theserelationships will be visually evident as superimposed patterns.

The scatter diagram is one of the seven basic tools of quality control.[3]

ExampleFor example, to display values for "lung capacity" (first variable) and how long that person could hold his breath, aresearcher would choose a group of people to study, then measure each one's lung capacity (first variable) and howlong that person could hold his breath (second variable). The researcher would then plot the data in a scatter plot,assigning "lung capacity" to the horizontal axis, and "time holding breath" to the vertical axis.

A person with a lung capacity of 400 ml who held his breath for 21.7 seconds would be represented by a single doton the scatter plot at the point (400, 21.7) in the Cartesian coordinates. The scatter plot of all the people in the studywould enable the researcher to obtain a visual comparison of the two variables in the data set, and will help todetermine what kind of relationship there might be between the two variables.

References[1] Visualizations that have been created with VisIt (https:/ / wci. llnl. gov/ codes/ visit/ gallery. html). at wci.llnl.gov. Last updated: November 8,

2007.[2] Utts, Jessica M. Seeing Through Statistics 3rd Edition, Thomson Brooks/Cole, 2005, pp 166-167. ISBN 0-534-39402-7[3] Nancy R. Tague (2004). "Seven Basic Quality Tools" (http:/ / www. asq. org/ learn-about-quality/ seven-basic-quality-tools/ overview/

overview. html). The Quality Toolbox. Milwaukee, Wisconsin: American Society for Quality. p. 15. . Retrieved 2010-02-05.

External links• What is a scatterplot? (http:/ / www. psychwiki. com/ wiki/ What_is_a_scatterplot?)• Correlation scatter-plot matrix - for ordered-categorical data (http:/ / www. r-statistics. com/ 2010/ 04/

correlation-scatter-plot-matrix-for-ordered-categorical-data/ ) - Explanation and R code

Scatter plot 25

• Tool for visualizing scatter plots (http:/ / www. icanplot. org)• Density scatterplot for large datasets (http:/ / www. r-bloggers. com/ ggplot2-for-big-data/ ) (hundreds of millions

of points)

Stratified samplingIn statistics, stratified sampling is a method of sampling from a population.

In statistical surveys, when subpopulations within an overall population vary, it is advantageous to sample eachsubpopulation (stratum) independently. Stratification is the process of dividing members of the population intohomogeneous subgroups before sampling. The strata should be mutually exclusive: every element in the populationmust be assigned to only one stratum. The strata should also be collectively exhaustive: no population element canbe excluded. Then random or systematic sampling is applied within each stratum. This often improves therepresentativeness of the sample by reducing sampling error. It can produce a weighted mean that has less variabilitythan the arithmetic mean of a simple random sample of the population.

In computational statistics, stratified sampling is a method of variance reduction when Monte Carlo methods areused to estimate population statistics from a known population.

Stratified sampling strategies1. Proportionate allocation uses a sampling fraction in each of the strata that is proportional to that of the total

population. For instance, if the population consists of 60% in the male stratum and 40% in the female stratum,then the relative size of the two samples (three males, two females) should reflect this proportion.

2. Optimum allocation (or Disproportionate allocation) - Each stratum is proportionate to the standard deviation ofthe distribution of the variable. Larger samples are taken in the strata with the greatest variability to generate theleast possible sampling variance.

A real-world example of using stratified sampling would be for a political survey. If the respondents needed toreflect the diversity of the population, the researcher would specifically seek to include participants of variousminority groups such as race or religion, based on their proportionality to the total population as mentioned above. Astratified survey could thus claim to be more representative of the population than a survey of simple randomsampling or systematic sampling.

Similarly, if population density varies greatly within a region, stratified sampling will ensure that estimates can bemade with equal accuracy in different parts of the region, and that comparisons of sub-regions can be made withequal statistical power. For example, in Ontario a survey taken throughout the province might use a larger samplingfraction in the less populated north, since the disparity in population between north and south is so great that asampling fraction based on the provincial sample as a whole might result in the collection of only a handful of datafrom the north.

Randomized stratification can also be used to improve population representativeness in a study.

DisadvantagesStratified sampling is not useful when the population cannot be exhaustively partitioned into disjoint subgroups. Itwould be a misapplication of the technique to make subgroups' sample sizes proportional to the amount of dataavailable from the subgroups, rather than scaling sample sizes to subgroup sizes (or to their variances, if known tovary significantly e.g. by means of an F Test). Data representing each subgroup are taken to be of equal importanceif suspected variation among them warrants stratified sampling. If, on the other hand, the very variances vary somuch, among subgroups, that the data need to be stratified by variance, there is no way to make the subgroup sample

Stratified sampling 26

sizes proportional (at the same time) to the subgroups' sizes within the total population. (What is the most efficientway to partition sampling resources among groups that vary in both their means and their variances?)

Practical exampleIn general the size of the sample in each stratum is taken in proportion to the size of the stratum. This is calledproportional allocation. Suppose that in a company there are the following staff:

• male, full time: 90• male, part time: 18• female, full time: 9• female, part time: 63• Total: 180

and we are asked to take a sample of 40 staff, stratified according to the above categories.

The first step is to find the total number of staff (180) and calculate the percentage in each group.

• % male, full time = 90 / 180 = 50%• % male, part time = 18 / 180 = 10%• % female, full time = 9 / 180 = 5%• % female, part time = 63 / 180 = 35%

This tells us that of our sample of 40,

• 50% should be male, full time.• 10% should be male, part time.• 5% should be female, full time.• 35% should be female, part time.

• 50% of 40 is 20.• 10% of 40 is 4.• 5% of 40 is 2.• 35% of 40 is 14.

Another easy way without having to calculate the percentage is to multiply each group size by the sample size anddivide by the total population size (size of entire staff):

• male, full time = 90 x (40 / 180) = 20• male, part time = 18 x (40 / 180) = 4• female, full time = 9 x (40 / 180) = 2• female, part time = 63 x (40 / 180) = 14[1]

References[1] http:/ / www. coventry. ac. uk/ ec/ ~nhunt/ meths/ strati. html Accessed 2008/01/27

Root cause analysis 27

Root cause analysisRoot cause analysis (RCA) is a class of problem solving methods aimed at identifying the root causes of problemsor events.

Root Cause Analysis is any structured approach to identifying the factors that resulted in the nature, the magnitude,the location, and the timing of the harmful outcomes (consequences) of one or more past events in order to identifywhat behaviors, actions, inactions, or conditions need to be changed to prevent recurrence of similar harmfuloutcomes and to identify the lessons to be learned to promote the achievement of better consequences.

The practice of RCA is predicated on the belief that problems are best solved by attempting to address, correct oreliminate root causes, as opposed to merely addressing the immediately obvious symptoms. By directing correctivemeasures at root causes, it is more probable that problem recurrence will be prevented. However, it is recognized thatcomplete prevention of recurrence by one corrective action is not always possible.

Nevertheless, in the U.S. nuclear power industry the NRC requires that "In the case of significant conditions adverseto quality, the measures shall assure that the cause of the condition is determined and corrective action taken toprevent repetition." [10CFR50, Appendix B, Criterion XVI, Sentence 2)] In practice more than one "cause" isallowed and more than one corrective action is not forbidden.

Conversely, there may be several effective measures (methods) that address the root causes of a problem. Thus, RCAis often considered to be an iterative process, and is frequently viewed as a tool of continuous improvement.

RCA is typically used as a reactive method of identifying event(s) causes, revealing problems and solving them.Analysis is done after an event has occurred. Insights in RCA may make it useful as a pro-active method. In thatevent, RCA can be used to forecast or predict probable events even before they occur. While one follows the other,RCA is a completely separate process to Incident Management.

Root cause analysis is not a single, sharply defined methodology; there are many different tools, processes, andphilosophies for performing RCA analysis. However, several very-broadly defined approaches or "schools" can beidentified by their basic approach or field of origin: safety-based, production-based, process-based, failure-based,and systems-based.

• Safety-based RCA descends from the fields of accident analysis and occupational safety and health.• Production-based RCA has its origins in the field of quality control for industrial manufacturing.• Process-based RCA is basically a follow-on to production-based RCA, but with a scope that has been expanded to

include business processes.• Failure-based RCA is rooted in the practice of failure analysis as employed in engineering and maintenance.• Systems-based RCA has emerged as an amalgamation of the preceding schools, along with ideas taken from

fields such as change management, risk management, and systems analysis.

Despite the different approaches among the various schools of root cause analysis, there are some commonprinciples. It is also possible to define several general processes for performing RCA.

General principles of root cause analysis1. The primary aim of RCA is to identify the factors that resulted in the nature, the magnitude, the location, and the

timing of the harmful outcomes (consequences) of one or more past events in order to identify what behaviors,actions, inactions, or conditions need to be changed to prevent recurrence of similar harmful outcomes and toidentify the lessons to be learned to promote the achievement of better consequences. ("Success" is defined as thenear-certain prevention of recurrence.)

2. To be effective, RCA must be performed systematically, usually as part of an investigation, with conclusions androot causes identified backed up by documented evidence. Usually a team effort is required.

Root cause analysis 28

3. There may be more than one root cause for an event or a problem, the difficult part is demonstrating thepersistence and sustaining the effort required to develop them.

4. The purpose of identifying all solutions to a problem is to prevent recurrence at lowest cost in the simplest way. Ifthere are alternatives that are equally effective, then the simplest or lowest cost approach is preferred.

5. Root causes identified depend on the way in which the problem or event is defined. Effective problem statementsand event descriptions (as failures, for example) are helpful, or even required.

6. To be effective, the analysis should establish a sequence of events or timeline to understand the relationshipsbetween contributory (causal) factors, root cause(s) and the defined problem or event to prevent in the future.

7. Root cause analysis can help to transform a reactive culture (that reacts to problems) into a forward-lookingculture that solves problems before they occur or escalate. More importantly, it reduces the frequency of problemsoccurring over time within the environment where the RCA process is used.

8. RCA is a threat to many cultures and environments. Threats to cultures often meet with resistance. There may beother forms of management support required to achieve RCA effectiveness and success. For example, a"non-punitory" policy towards problem identifiers may be required.

Evaluating s root cause analysisRoot Cause Analysis Reports, like other 'deliverables' can vary in quality. Each stakeholder can have their ownqualitative and quantitative acceptance criteria. There are some general possiblilities for evaluating root causeanalysis outputs.

First: Is it readable? If it is readable it will be grammatically correct, the sentences will make sense, it will be free oninternal inconsistencies, terms will be defined, it will contain appropriate graphics, and the like.

Second: Does it contain a complete set of all of the causal relationships? If it did contain a "complete set of all of thecausal relationships" one could (at least): 1. Trace the causal relationships from the harmful outcomes to the deepestconditions, behaviors, actions, and inactions. 2. Show that the important attributes of the harmful outcomes werecompletely explained by the deepest conditions, behaviors, actions, and inactions.

General process for performing and documenting an RCA-based CorrectiveActionNotice that RCA (in steps 3, 4 and 5) forms the most critical part of successful corrective action, because it directsthe corrective action at the true root cause of the problem. The root cause is secondary to the goal of prevention, butwithout knowing the root cause, we cannot determine what an effective corrective action for the defined problemwill be.

1. Define the problem or describe the event factually. Include the qualitative and quantitative attributes (properties)of the harmful outcomes. This usually includes specifying the natures, the magnitudes, the locations, and thetimings.

2. Gather data and evidence, classifying that along a timeline of events to the final failure or crisis. For everybehavior, condition, action, and inaction specify in the "timeline" what should have been when it differs from theactual.

3. Ask "why" and identify the causes associated with each step in the sequence towards the defined problem orevent. "Why" is taken to mean "What were the factors that directly resulted in the effect?"

4. Classify causes into causal factors that relate to an event in the sequence, and root causes, that if applied can beagreed to have interrupted that step of the sequence chain.

5. If there are multiple root causes, which is often the case, reveal those clearly for later optimum selection. identifyall other harmful factors that have equal or better claim to be called "root causes."

6. Identify corrective action(s) that will with certainty prevent recurrence of each harmful effect, includingoutcomes and factors. Check that each corrective action would, if pre-implemented before the event, have reduced

Root cause analysis 29

or prevented specific harmful effects.7. Identify solutions that effective, prevent recurrence with reasonable certainty with consensus agreement of the

group, are within your control, meet your goals and objectives and do not cause introduce other new, unforeseenproblems.

8. Implement the recommended root cause correction(s).9. Ensure effectiveness by observing the implemented recommendation solutions.10. Other methodologies for problem solving and problem avoidance may be useful.11. Identify and address the other instances of each harmful outcome and harmful factor.

Root cause analysis techniques• Re-enactment-for example having the participants in the event do it over the way it was done (with due care to

avoid the same harmful outcomes).• Re-enactment using a computer or a simulator.• Comparative re-enactment-doing it over the right way as well as the way it was actually done.• Re-construction-reassembling all of the available accident debris to see clues as to how the disassembly occurred.• Barrier analysis - a technique often used in process industries. It is based on tracing energy flows, with a focus on

barriers to those flows, to identify how and why the barriers did not prevent the energy flows from causing harm.• Bayesian inference• Change analysis - an investigation technique often used for problems or accidents. It is based on comparing a

situation that does not exhibit the problem to one that does, in order to identify the changes or differences thatmight explain why the problem occurred.

• "Delta Work"-comparing the way an episode did happen with the way it was intended to happen.• Current Reality Tree - A method developed by Eliahu M. Goldratt in his theory of constraints that guides an

investigator to identify and relate all root causes using a cause-effect tree whose elements are bound by rules oflogic (Categories of Legitimate Reservation). The CRT begins with a brief list of the undesirables things we seearound us, and then guides us towards one or more root causes. This method is particularly powerful when thesystem is complex, there is no obvious link between the observed undesirable things, and a deep understanding ofthe root cause(s) is desired.

• Failure mode and effects analysis• Fault tree analysis• Five whys emphasizes recursive depth, using the heuristic that you're probably not done until you've looked five

levels deep.• Ishikawa diagrams emphasize initial breadth, using a checklist of types of causes that should be considered.• Why-Because analysis emphasizes recursive breadth, using the concepts of necessary and sufficient causes.• Pareto analysis "80/20 rule"• RPR Problem Diagnosis - An ITIL-aligned method for diagnosing IT problems.• Kepner-Tregoe Approach• Project Management Approaches. An adverse event can be viewed as a project whose final product was harm.

The event can be understood by re-casting it in the classical Project Management devices such as WorkBreakdown Structure, Gantt Chart, and Planning Logic Network.

Common cause analysis (CCA) common modes analysis (CMA) are evolving engineering techniques for complextechnical systems to determine if common root causes in hardware, software or highly integrated systems interactionmay contribute to human error or improper operation of a system. Systems are analyzed for root causes and causalfactors to determine probability of failure modes, fault modes, or common mode software faults due to escapedrequirements. Also ensuring complete testing and verification are methods used for ensuring complex systems aredesigned with no common causes that cause severe hazards. Common cause analysis are sometimes required as partof the safety engineering tasks for theme parks, commercial/military aircraft, spacecraft, complex control systems,

Root cause analysis 30

large electrical utility grids, nuclear power plants, automated industrial controls, medical devices or other safetysafety-critical systems with complex functionality.

A major issue with common cause analysis is that it often depends on previously completed weak, ineffective, anderroneous root cause analyses on individual events.

Basic elements of root cause using Management Oversight Risk Tree (MORT)Approach Classification• Materials

• Defective raw material• Wrong type for job• Lack of raw material

• Man Power

• Inadequate capability• Lack of Knowledge• Lack of skill• Stress• Improper motivation

• Machine / Equipment

• Incorrect tool selection• Poor maintenance or design• Poor equipment or tool placement• Defective equipment or tool

• Environment

• Disordered workplace• Poor job design and/or layout of work• Surfaces poorly maintained• Inability to meet physical demands of the task• Forces of nature

• Management

• Lack of management involvement• Inattention to task• Task hazards not dealt with properly• Other (horseplay, inattention....)• Stress demands• Lack of Process• Lack of Communication

• Methods

• No or poor procedures• Practices are not the same as written procedures• Poor communication

• Management system

• Training or education lacking• Poor employee involvement• Poor recognition of hazard• Previously identified hazards were not eliminated

Root cause analysis 31

ReferencesDepartment of Energy, Management Oversight Risk Tree (MORT) NASA

5 WhysThe 5 Whys is a questions-asking method used to explore the cause/effect relationships underlying a particularproblem. Ultimately, the goal of applying the 5 Whys method is to determine a root cause of a defect or problem.

ExampleThe following example demonstrates the basic process:

• The vehicle will not start. (the problem)

1. Why? - The battery is dead. (first why)2. Why? - The alternator is not functioning. (second why)3. Why? - The alternator belt has broken. (third why)4. Why? - The alternator belt was well beyond its useful service life and not replaced. (fourth why)5. Why? - The vehicle was not maintained according to the recommended service schedule. (fifth why, a root cause)6. Why? - Replacement parts are not available because of the extreme age of the vehicle. (sixth why, optional

footnote)

• Start maintaining the vehicle according to the recommended service schedule. (5th Why solution)• Purchase a different vehicle that is maintainable. (6th Why solution)

The questioning for this example could be taken further to a sixth, seventh, or even greater level. This would belegitimate, as the "five" in 5 Whys is not gospel; rather, it is postulated that five iterations of asking why is generallysufficient to get to a root cause. The real key is to encourage the trouble-shooter to avoid assumptions and logic trapsand instead to trace the chain of causality in direct increments from the effect through any layers of abstraction to aroot cause that still has some connection to the original problem. Note that in this example the fifth why suggests abroken process or an alterable behaviour, which is typical of reaching the root-cause level.

It's interesting to note that the last answer points to a process. This is actually one of the most important aspects inthe 5 Why approach...the real root cause should point toward a process. You will observe that the process is notworking well or that the process does not even exist. Untrained facilitators will often observe that answers seem topoint towards classical answers such as not enough time, not enough investments, or not enough manpower. Theseanswers may sometimes be true but in most cases they lead to answers out of our control. Therefore, instead ofsimply asking the question why?, ask the question Why did the process fail?

Keep in mind the following key phrase as a background thought in any 5 why exercise: "People do not fail, processesdo!"

HistoryThe technique was originally developed by Sakichi Toyoda and was later used within Toyota Motor Corporationduring the evolution of their manufacturing methodologies. It is a critical component of problem solving trainingdelivered as part of the induction into the Toyota Production System. The architect of the Toyota Production System,Taiichi Ohno, described the 5 whys method as "the basis of Toyota's scientific approach . . . by repeating why fivetimes, the nature of the problem as well as its solution becomes clear."[1] The tool has seen widespread use beyondToyota, and is now used within Kaizen, lean manufacturing, and Six Sigma.

5 Whys 32

TechniquesThere are two primary techniques used to perform 5 whys[2] : the fishbone (or Ishikawa) diagram, as well as atabular format[3] . These tools allow for analysis to be branched in order to provide multiple root causes for remedy.

CriticismWhile the 5 Whys is a powerful tool for engineers or technically savvy individuals to help get to the true causes ofproblems, it has been criticized by Teruyuki Minoura, former managing director of global purchasing for Toyota, asbeing too basic a tool to analyze root causes to the depth that is needed to ensure that the causes are fixed [4] .Reasons for this criticism include: − − −• Tendency for investigators to stop at symptoms rather than going on to lower level root causes.• Inability to go beyond the investigator's current knowledge - can't find causes that they don't already know.• Lack of support to help the investigator to ask the right "why" questions.• Results aren't repeatable - different people using 5 Whys come up with different causes for the same problem.• Tendency to isolate a single root cause, whereas each question could elicit many different root causes.

These can be significant problems when the method is applied through deduction only. On-the-spot verification ofthe answer to the current "why" question, before proceeding to the next, is recommended as a good practice to avoidthese issues.

References[1] Taiichi Ohno; foreword by Norman Bodek (1988). Toyota production system: beyond large-scale production. Portland, Or: Productivity

Press. ISBN 0-915299-14-3.[2] "An Introduction to 5-why" (http:/ / blog. bulsuk. com/ 2009/ 03/ 5-why-finding-root-causes. html). . Retrieved 6 March 2010.[3] "5-why Analysis using an Excel Spreadsheet Table" (http:/ / blog. bulsuk. com/ 2009/ 07/ 5-why-analysis-using-table. html). . Retrieved 25

December 2010.[4] "The "Thinking" Production System: TPS as a winning strategy for developing people in the global manufacturing environment" (http:/ /

www. toyotageorgetown. com/ tps. asp). . Retrieved 2011-02-02.

Whybecause analysis 33

Why–because analysisWhy–because analysis (WBA) is a method for accident analysis. It is independent of application domain and hasbeen used to analyse, among others, aviation-, railway-, marine- and computer related accidents and incidents. It ismainly used as an after the fact (or a posteriori) analysis method. WBA strives to ensure objectivity, falsifiability andreproducibility of results.

The result of a WBA is a why–because graph (WBG). The WBG depicts causal relations between factors of anaccident. It is a directed acyclic graph where the nodes of the graph are factors. Directed edges denote cause–effectrelations between the factors.

WBA in detailWBA starts with the question what the accident(s) in question is(are). In most cases this is easy to define. Nextcomes an iterative process to determine causes. When causes for the accident have been identified, formal tests areapplied to all potential cause-effect relations. This process can be iterated for the new found causes, and so on, until asatisfactory result has been achieved.

At each node (factor), each contributing cause (related factor) must have been necessary, and the totality of causesmust be sufficient: it gives the causes, the whole causes (sufficient), and nothing but the causes (necessary).

The formal testsThe counterfactual test (CT) – The CT leads back to David Lewis formal notion of causality and counterfactuals.The CT asks the following question: "If the cause had not been, could the effect have happened". The CT proves ordisproves that a cause is a necessary causal factor for an effect. Only if it is necessary for the cause in question then itis clearly contributing to the effect.

The causal sufficiency test – The CST asks the question: "Will an effect always happen if all attributed causeshappen?". The CST aims at deciding whether a set of causes are sufficient for an effect to happen. The missing ofcauses can thus be identified.

Only if for all causal relations the CT is positive and for all sets of causes to their effects the CST is positive theWBG is correct: each cause must be necessary (CT), and the totality of causes must be sufficient (CST): nothing isomitted (CST: the listed causes are sufficient), and nothing is superfluous (CT: each cause is necessary).

Whybecause analysis 34

Example

Partial Why–because graph of the capsizing of the Herald of Free Enterprise

External links• Why-Because Analysis [1] (WBA)

References[1] http:/ / www. rvs. uni-bielefeld. de/ research/ WBA/

Eight Disciplines Problem Solving 35

Eight Disciplines Problem SolvingEight Disciplines Problem Solving is a method used to approach and to resolve problems, typically employed byquality engineers or other professionals.

D0: The Planning Phase: Plan for solving the problem and determine the prerequisites.

D1: Use a Team: Establish a team of people with product/process knowledge.

D2: Define and describe the Problem: Specify the problem by identifying in quantifiable terms the who, what,where, when, why, how, and how many (5W2H) for the problem.

D3: Developing Interim Containment Plan Implement and verify Interim Actions: Define and implementcontainment actions to isolate the problem from any customer.

D4: Determine and Identify and Verify Root Causes and escape points: Identify all applicable causes that couldexplain why the problem has occurred. Also identify why the problem has not been noticed at the time it occurred.All causes shall be verified or proved, not determined by fuzzy brainstorming. One can use 5Whys or IshikawaDiagram to map causes against effect/Problem identified.

D5: Choose and verify Permanent Corrections (PCs) for Problem/Non Conformity: Through pre-productionprograms quantitatively confirm that the selected correction will resolve the problem for the customer.

D6: Implement and validate PCAs: Define and Implement the best corrective actions.

D7: Prevent recurrence/Corrective Actions: Modify the management systems, operation systems, practices, andprocedures to prevent recurrence of this and all similar problems.

D8: Congratulate your Team: Recognize the collective efforts of the team. The team needs to be formally thankedby the organization.[1] [2]

8D has become a standard in the Auto, Assembly and other industries that require a thorough structured problemsolving process using a team approach.

HistoryFord Motor Company developed a method, while the military also developed and quantified their own processduring World War II. Both of these methods revolve around the Eight Disciplines.

Ford's PerspectiveThe development of a Team Oriented Problem Solving strategy, based on the use of statistical methods of dataanalysis, was developed at Ford Motor Company. The executives of the Powertrain Organization (transmissions,chassis, engines) wanted a methodology where teams (design engineering, manufacturing engineering, andproduction) could work on recurring problems. In 1986, the assignment was given to develop a manual and asubsequent course that would achieve a new approach to solving tough engineering design and manufacturingproblems. The manual for this methodology was documented and defined in "Team Oriented ProblemSolving"(TOPS), first published in 1987. The manual and subsequent course material was piloted at WorldHeadquarters in Dearborn, Michigan. Many changes and revisions were made based on feedback from the pilotsessions. This has been Ford's approach to problem solving ever since. It was never based on any military standard orother existing problem solving methodology. The material is extensive and the 8D titles are merely the chapterheadings for each step in the process. Ford also refers to their current variant as G8D (Global 8D).

Eight Disciplines Problem Solving 36

Military UsageThe US Government first standardized a process during the Second World War as Military Standard 1520'Corrective Action and Disposition System for Nonconforming Material' .[3] This military standard focused onnonconforming material and the disposition of the material.

The 8D Problem Solving Process is used to identify, correct and eliminate recurring problems. The methodology isuseful in product and process improvement. It establishes a permanent corrective action based on statistical analysisof the problem. It focuses on the origin of the problem by determining Root Causes.

This 'Determine a Root Cause' step is a part of the military usage of the 8D's but was not a reference in thedevelopment of the 8D problem solving methodology and is not referenced or included in the TOPS manual orcourse.

UsageMany disciplines are typically involved in the "8D" process, all of which can be found in various textbooks andreference materials used by Quality Assurance professionals. For example, an "Is/Is Not" worksheet is a commontool employed at D2, and a "Fishbone Diagram" or "5 Why Analysis" are common tools employed at step D4.

In the late 1990s, Ford developed a revised version of the 8D process, that they call "Global 8D" (G8D) which is thecurrent global standard for Ford and many other companies in the automotive supply chain. The major revisions tothe process are as follows:

• Addition of a D0 (D-Zero) step as a gateway to the process. At D0, the team documents the symptoms thatinitiated the effort along with any Emergency Response Actions (ERAs) that were taken before formal initiationof the G8D. D0 also incorporates standard assessing questions meant to determine whether a full G8D is required.The assessing questions are meant to ensure that in a world of limited problem-solving resources, the effortsrequired for a full team-based problem-solving effort are limited to those problems that warrant these resources.

• Addition of Escape Point to D4 through D6. The idea here is to consider not only the Root cause of a problem, butequally importantly, what went wrong with the control system in allowing this problem to escape. Global 8Drequires the team to identify and verify this Escape Point (defined as the earliest control point in the controlsystem following the Root Cause that should have detected the problem but failed to do so) at D4. Then, throughD5 and D6, the process requires the team to choose, verify, implement, and validate Permanent CorrectiveActions to address the Escape Point.

Recently, the 8D process has been employed significantly outside the auto industry. As part of Lean initiatives andContinuous Improvement Processes it is employed extensively within Food Manufacturing, High Tech, and HealthCare industries.

External links• Society of Manufacturing Engineers: SME, [4]• The 8 Disciplines (8D) Process [5]

• Laurie Rambaud (2006), 8D Structured Problem Solving: A Guide to Creating High Quality 8D Reports, PHREDSolutions [6], ISBN 0-9790553-0-X

• Eight Disciplines (8D) Problem solving [7]

• Difference between containment, corrective and preventive actions in 8D Report [8]

Eight Disciplines Problem Solving 37

References[1] http:/ / www. siliconfareast. com/ 8D. htm[2] http:/ / www. 12manage. com/ methods_ford_eight_disciplines_8D. html[3] http:/ / www. everyspec. com/ MIL-STD/ MIL-STD+ (1500+ -+ 1599)/ MIL_STD_1520C_NOT_1_1407[4] http:/ / www. sme. org/ cgi-bin/ get-newsletter. pl?LEAN& 20030116& 1&[5] http:/ / www. siliconfareast. com/ 8D. htm[6] http:/ / www. phredsolutions. com[7] http:/ / elsmar. com/ 8D/[8] http:/ / www. 8dreport. com/ articles/ difference-between-containment-corrective-and-preventive-actions-in-8d-report/

Article Sources and Contributors 38

Article Sources and ContributorsSeven Basic Tools of Quality  Source: http://en.wikipedia.org/w/index.php?oldid=452577720  Contributors: 1ForTheMoney, Bwpach, Cristianrodenas, Cybercobra, DanielPenfield, Dweias,P7lejo, Pdcook, QCforever, RSStockdale, Sin-man, Sspecter, 4 anonymous edits

Ishikawa diagram  Source: http://en.wikipedia.org/w/index.php?oldid=456509121  Contributors: -Midorihana-, -nothingman-, 0x845FED, Abmac, AbsolutDan, Ajivarges, Alansohn, Alant,Allmightyduck, Ancheta Wis, Ap, Arthena, At Large, Attilios, AugPi, Babrahamse, Bharatmoorthy, Biglovinb, Boogachamp, Briansun, Burt Harris, Capi, CarrotMan, Charles Matthews, ChuckieB, Closedmouth, CommonsDelinker, Craigwb, Cybercobra, DanielPenfield, Darkwind, Destynova, DoomProof, Dysprosia, Eaefremov, Egaal, ElationAviation, EncycloPetey, Ettrig, Exitcreative,Faizdiro, Filippof, Findbecca, Gaius Cornelius, Gav Newman, Gch42, Gianvittorio, GraemeL, Greudin, Greyskinnedboy, Hayvac, Imroy, Infinoid, Ixuscane, Jaromil, Jsifoni, Jsong123, KShiger,Karn-b, Kedarg6500, Kkwright88, Kumioko, Letranova, Liberal Saudi, Ligulem, LilHelpa, Logicalgregory, Manop, Martin451, Mdd, Mendaliv, Metacomet, Michael Hardy, Minimac, N419BH,Nbarth, Noveltyghost, PHermans, Pgr94, Phil Bridger, Philip Trueman, PietroSavo, Pikesway, Pinkadelica, Poeloq, Quorn3000, Rlsheehan, Robert Thyder, Ronz, Russeltarr, Santtus,SarahAlSaleh, Saxifrage, Sbwoodside, Slashme, SueHay, Taffykins, Techieb0y, Thequality, ThreeVryl, Tide rolls, Tom W.M., Tomjenkins52, Unfree, Utcursch, Utuado, Vcornelius, Vinchem,Vrenator, Was a bee, Wasell, Wavelength, Weeman com, Weetjesman, Wikid77, 187 anonymous edits

Check sheet  Source: http://en.wikipedia.org/w/index.php?oldid=454256255  Contributors: 10metreh, AugPi, Boxplot, C Saretto, Cesium 133, Conscious, DanielPenfield, Ed!, Hsz, Kingturtle,Metacomet, Space Pirate 3000AD, 7 anonymous edits

Control chart  Source: http://en.wikipedia.org/w/index.php?oldid=457451039  Contributors: AbsolutDan, Adoniscik, Alansohn, AugPi, Blue Kitsune, Boxplot, Buzhan, Cherkash, Chris Roy,ChrisLoosley, Cutler, DARTH SIDIOUS 2, DanielPenfield, Ed Poor, Epbr123, Eric Kvaalen, Evolve2k, Facius, Fangmail, Fedir, G716, Gaius Cornelius, Gareth.randall, Gideon.fell, Giftlite,Gloucks, HongKongQC, ImZenith, Italian Calabash, J04n, Jayen466, KKoolstra, Kedarg6500, Kevin B12, King Lopez, Leaders100, MarkSweep, Martijn faassen, Mdd, Melcombe, Mendaliv,Metacomet, Michael Hardy, Michaelcbeck, Nfitz, NorwegianBlue, Oleg Alexandrov, Oxymoron83, Peter Grey, Phreed, QualitycontrolUS, Qwfp, Rich Farmbrough, Ride the Hurricane,Rlsheehan, Ronz, Rupertb, SGBailey, Shoefly, Skunkboy74, Spalding, Statnerd, Statwizard, SueHay, Taffykins, Thetorpedodog, Thopper, Trisweb, Versus22, Xsmith, 118 anonymous edits

Histogram  Source: http://en.wikipedia.org/w/index.php?oldid=456560203  Contributors: 160.5.82.xxx, 2D, 5 albert square, ABF, Aastrup, AbsolutDan, Aitias, Ajraddatz, Alansohn, AlekseyP,Asterion, AugPi, Auldglory, Aushulz, Avenged Eightfold, Avenue, AxelBoldt, Baa, Bart133, Barticus88, BartlebytheScrivener, BenFrantzDale, Bettia, Bkell, BlaiseFEgan, Bobo192, Bogey97,Bongwarrior, Borgx, Boxplot, Calvin 1998, Capt. James T. Kirk, Catalin Bogdan, Charles Matthews, Chester Markel, Chris the speller, Chris53516, Chuunen Baka, Conversion script,Cristianrodenas, Ctbolt, Cyclopia, DVD R W, DanielPenfield, DarthVader, Deep316, Demus Wiesbaden, Den fjättrade ankan, Disavian, Djeedai, Dkkicks, DmitTrix, Donarreiskoffer, Ecov,Ehrenkater, Eng.ahmedm, Enviroboy, Epbr123, Evgeny, Faithlessthewonderboy, Fatka, FayssalF, FreplySpang, Furrykef, G716, Garglebutt, Gary King, Gc1mak, Gcjblack, GeordieMcBain,Giftlite, Glane23, Glen, Hadleywickham, HenningThielemann, Hgberman, Hooperbloob, Hu12, Hydrogen Iodide, IGeMiNix, Immunize, Indon, Irishguy, Iwaterpolo, J.delanoy, JRSP, James086,Jamesootas, Japanese Searobin, Jerry teps, Jiminyjimjim, Jni, Johan1298, JohnManuel, Josemiotto, Jusdafax, KGasso, Karol Langner, Kierano, Kjetil1001, Kku, KnightRider, Kuru, Lara bran,Lathrop, LeaveSleaves, Leonam, Liberio, Liftarn, Ligulem, Lindmere, Luna Santin, MBlakley, Macrakis, Magog the Ogre, Male1979, Manop, Martarius, Master of Puppets, Mathstat, Mattopia,Meekywiki, Melcombe, Mendaliv, Metacomet, Mhym, Michael Hardy, Mihoshi, Moreschi, Mr coyne, Mwtoews, N5iln, Naravorgaara, Nbarth, NeilN, Neko-chan, Nield, Nijdam, Noctibus, Nsaa,Ohnoitsjamie, Onionmon, P.B. Pilhet, Pathoschild, Paul August, PaulTheOctopus, Philip Trueman, Phill779, Piano non troppo, Plantphoto, Prumpa, Pyrrhus16, Qwfp, RJaguar3, RichFarmbrough, Richjwild, Rjwilmsi, Robert P. O'Shea, RodC, Ronhjones, Ronz, Rufous, SE7, Saxbryn, Sbwoodside, Schutz, Seraphim, Shimazaki, Shoeofdeath, Smith609, Spaz4tw, Specs112,Staticshakedown, Steven J. Anderson, Steven Zhang, Straif, SuperHamster, Surya21, Taffykins, Tangent747, The Thing That Should Not Be, The wub, TheNewPhobia, Theswampman, ThomasArnhold, Tide rolls, Tombrazel, Tomi, Tommy2010, Undisputedloser, Velella, Voice In The Wilderness, Vrenator, Wile E. Heresiarch, Woohookitty, Wwwwolf, Xftan, YUL89YYZ,Yamaguchi先 生 , Yurik, Zach1994, Zaharous, Zheric, Zhou yi777, Zondox, ZooFari, Zr40, Zvika, 412 anonymous edits

Pareto chart  Source: http://en.wikipedia.org/w/index.php?oldid=455440289  Contributors: A. B., AbsolutDan, Anonymous Dissident, AugPi, BlckKnght, Boxplot, Celique, Ck lostsword,Cootha, Craigwb, DanielPenfield, Dashuler@gmail.com, DylanW, Elbac14, Feureau, Gribeco, Hu12, Imroy, Irishguy, Kormie, LilHelpa, MBlakley, MdG, Melcombe, Metacomet, MichaelHardy, NajaB, NawlinWiki, Nbarth, Nlskrg, Noe, Nubiatech, ParetoDaddy, PhilKnight, Pm master, Pscott22, Ronz, Rupertb, Seav, Srleffler, Stevegallery, Stillnotelf, SueHay, T-turtle, Taffykins,Takahashi J, Top Jim, Tuyvan, Verne Equinox, Waycool27, WoodenBooks, 87 anonymous edits

Scatter plot  Source: http://en.wikipedia.org/w/index.php?oldid=456709727  Contributors: 28421u2232nfenfcenc, Acroterion, Ad1024, Alansohn, Alexius08, AndrewHowse, AugPi, Bento00,Bjoram11@yahoo.co.in, BoomerAB, CaAl, CardinalDan, Catalin Bogdan, Chris24, Claygate, Conscious, Cosmicfroggy, Courcelles, Crissov, Cryptic, Curtixlr8, Cyclopia, DVdm,DanielPenfield, Den fjättrade ankan, Dimitrees, DoubleBlue, Downtown dan seattle, Dude1818, Epbr123, Epim, Eskimospy, Faithlessthewonderboy, Fangfufu, FelixKaiser, Funandtrvl, G716,Giftlite, Glenn macgougan, Gogo Dodo, Hgberman, Hooperbloob, Hu12, Hut 8.5, Ishikawa Minoru, Itai, JForget, Joefromrandb, Kadoo, Karnesky, Lambiam, Llygadebrill, Loodog, Lord SpringOnion, Mack2, Marianika, Martarius, Mathstat, McSly, Mdd, Melcombe, Mendaliv, Metacomet, Michael Hardy, Michael Snow, Micropw, Mitch Ames, Mmmmmmmmmm korn, Moorsmur,NawlinWiki, Nezzadar, Nigelovich, NightwolfAA2k5, Nishkid64, Nwstephens, Oleg Alexandrov, OnePt618, Orphan Wiki, Ph.eyes, Philip Trueman, Piotrus, Qwfp, RabidZombie,Rathinavelpec, Reyk, RodC, Roland Longbow, Ryk, Sbwoodside, ScaldingHotSoup, Snigbrook, Steinsky, Stevertigo, Sturm55, SueHay, TKD, Talgalili, Tedernst, VinceBowdren, VisFan,Watersidedoc, Whosasking, 171 anonymous edits

Stratified sampling  Source: http://en.wikipedia.org/w/index.php?oldid=457662240  Contributors: 1Rabid Monkey, Aldis90, Anand Karia, Antonrojo, Avenue, CDN99, Canthusus, Conversionscript, Den fjättrade ankan, Dick Beldin, Edison, Enlil Ninlil, Everyking, Evil saltine, G716, Giftlite, Gilliam, Graham87, Henrygb, Ian13, Inseeisyou, Jeremysolt, Jfitzg, Jitse Niesen, Johnkarp,KerathFreeman, Kiefer.Wolfowitz, Kku, Lachoneus84, Larry_Sanger, Lilac Soul, LordDarkPhantom, Lou.weird, M1ss1ontomars2k4, Mbhiii, McSly, Melcombe, Michael Hardy,Mydogategodshat, Narcher01, Ninjakannon, Oleg Alexandrov, Orderud, Pinethicket, Proteus, Qwfp, Rich Farmbrough, Robert Merkel, Rossami, Ruodyssey, Saam 1, Sabrown100, Saittam,ShakingSpirit, Stotr, Tangotango, Trontonian, Uksh, Votemania, Wikieditor06, Wser, Xndr, Xp54321, Yunshui, Zginder, 141 anonymous edits

Root cause analysis  Source: http://en.wikipedia.org/w/index.php?oldid=456689321  Contributors: AbsolutDan, Abualfad, AdjustShift, Ancos, Anoopkzm, Anthonyrenda, Astral, Bachrach44,Bobanni, Bugpower, Canderson1494, Causeeffect, Charlesbaldo, Cranders7, Crasshopper, Credible58, Dalechadwick, Dchristle, Deangano, Deichmans, Discospinster, DrBillCorcoran,Drjamesaustin, EoGuy, Excirial, Fedkad, FinalRapture, Firebird, Free Bear, Giliev, Hagerman, Harrias, IceCreamAntisocial, Inwind, JK August, Jamelan, Jruderman, Karada, Kedarg6500, Kku,Kurtaotto, Loren.wilton, Luigi30, Mannuthareja, Marcusmccoy, Mausy5043, Michael Devore, Michael Hardy, Mysterychopper3027, Ngocnb, NineInchNachos, Obankston, Orange Suede Sofa,Peterlewis, Phil Bridger, Philip Trueman, PietroSavo, Prainog, Raj Vimal Dev, RedWolf, Rich Farmbrough, RichardF, Ronz, RustySpear, Samwaltersdc, Sdayal, Seraphimblade, Slashme,Slightsmile, Spikebailey666, Starazagora, Tbonnema, The Anome, Thequality, Tnxman307, Utuado, Velella, WhatamIdoing, William Flower, Ygfperson, 185 anonymous edits

5 Whys  Source: http://en.wikipedia.org/w/index.php?oldid=453649654  Contributors: AbsolutDan, Amalas, Aremith, Bdoserror, BenAveling, BlackBeast, Cebess, Charlesbaldo, Corza,Credible58, Darp-a-parp, Deborah new, DonNorman, Dwlegg, Eivind F Ø yangen, Enchanter, Euchiasmus, Everything counts, Firebird, Forerunner411, Goliadkin, Gwinkless, Harda, Hu12,Hyacinth, J.delanoy, Jbreazeale, Jchyip, Jonverve, KimBecker, LeaW, Linforest, MartinsB, MattieTK, Misbeliever, MrOllie, Nick Number, Nlaverdure, Ofol, PM800, PetterEkhem, Pm master,Ronz, Saxifrage, Septagram, Shadowjams, Spalding, Takethemud, The Anome, Utuado, Vikom, YippyEyeO, Yunipo, ZimZalaBim, 97 anonymous edits

Why–because analysis  Source: http://en.wikipedia.org/w/index.php?oldid=452140651  Contributors: AllTheCoolNamesAreAlreadyTaken, Andreas Kaufmann, Bender235, Bilbo1507, Edward,Gh5046, Matthew Yeager, Michael Hardy, Nbarth, Otto4711, Pomte, Srnec, The Anome, Tony1, Trivialist, WhaleWey, 6 anonymous edits

Eight Disciplines Problem Solving  Source: http://en.wikipedia.org/w/index.php?oldid=455486393  Contributors: Ankur3020, Corza, Credible58, Cybercobra, Elonka, Fwbeck, Gejigeji, Hmoul,Jayron32, Kesal, Leuko, LilHelpa, Malcolma, Michael Hardy, Mm40, Nae'blis, Neilbeach, Ofol, Parends, Peterlewis, Pvosta, Quorn3000, RSStockdale, Starasinicb, Surv1v4l1st, Tctwood,Wbbeardie, YippyEyeO, Ynhockey, 32 anonymous edits

Image Sources, Licenses and Contributors 39

Image Sources, Licenses and ContributorsImage:Cause and effect diagram for defect XXX.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Cause_and_effect_diagram_for_defect_XXX.svg  License: Creative CommonsAttribution-Sharealike 3.0  Contributors: DanielPenfieldFile:Ishikawa Fishbone Diagram.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Ishikawa_Fishbone_Diagram.svg  License: GNU Free Documentation License  Contributors:FabianLange at de.wikipediaImage:Check sheet for motor assembly.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Check_sheet_for_motor_assembly.svg  License: Creative Commons Attribution-Sharealike3.0  Contributors: DanielPenfieldImage:Quality_Control_Checksheet_Example.GIF  Source: http://en.wikipedia.org/w/index.php?title=File:Quality_Control_Checksheet_Example.GIF  License: GNU Free DocumentationLicense  Contributors: Carterdriggs, Ken Gallager, Space Pirate 3000AD, 1 anonymous editsImage:Xbar chart for a paired xbar and R chart.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Xbar_chart_for_a_paired_xbar_and_R_chart.svg  License: Creative CommonsAttribution-Sharealike 3.0  Contributors: DanielPenfieldImage:ControlChart.svg  Source: http://en.wikipedia.org/w/index.php?title=File:ControlChart.svg  License: Public Domain  Contributors: Original uploader was DanielPenfield at en.wikipediaImage:Histogram of arrivals per minute.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Histogram_of_arrivals_per_minute.svg  License: Creative Commons Attribution-Sharealike3.0  Contributors: DanielPenfieldImage:Black cherry tree histogram.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Black_cherry_tree_histogram.svg  License: Creative Commons Attribution-ShareAlike 3.0Unported  Contributors: Mwtoews, 2 anonymous editsImage:Travel time histogram total n Stata.png  Source: http://en.wikipedia.org/w/index.php?title=File:Travel_time_histogram_total_n_Stata.png  License: Creative CommonsAttribution-Sharealike 3.0  Contributors: Qwfp (talk)Image:Travel time histogram total 1 Stata.png  Source: http://en.wikipedia.org/w/index.php?title=File:Travel_time_histogram_total_1_Stata.png  License: Creative CommonsAttribution-Sharealike 3.0  Contributors: Qwfp (talk)Image:Cumulative vs normal histogram.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Cumulative_vs_normal_histogram.svg  License: Creative Commons Attribution-Sharealike3.0  Contributors: KieranoImage:Pareto chart of titanium investment casting defects.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Pareto_chart_of_titanium_investment_casting_defects.svg  License:Creative Commons Attribution-Sharealike 3.0  Contributors: DanielPenfieldFile:Pareto.PNG  Source: http://en.wikipedia.org/w/index.php?title=File:Pareto.PNG  License: Public Domain  Contributors: Original uploader was Metacomet at en.wikipediaImage:Scatter diagram for quality characteristic XXX.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Scatter_diagram_for_quality_characteristic_XXX.svg  License: CreativeCommons Attribution-Sharealike 3.0  Contributors: DanielPenfieldImage:oldfaithful3.png  Source: http://en.wikipedia.org/w/index.php?title=File:Oldfaithful3.png  License: Public Domain  Contributors: Anynobody, Maksim, Mdd, Nandhp, Oleg Alexandrov,WikipediaMaster, 6 anonymous editsImage:Scatter plot.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Scatter_plot.jpg  License: Public Domain  Contributors: UCRLImage:Herald of Free Enterprise WBG.png  Source: http://en.wikipedia.org/w/index.php?title=File:Herald_of_Free_Enterprise_WBG.png  License: Public Domain  Contributors:AllTheCoolNamesAreAlreadyTaken, AnonMoos, CarrotMan, Mdd, Razorbliss, 1 anonymous edits

License 40

LicenseCreative Commons Attribution-Share Alike 3.0 Unported//creativecommons.org/licenses/by-sa/3.0/