53 green belt course manual measure phase indian statistical institute sqc&or unit, bangalore

11

GREEN BELT GREEN BELT

COURSE MANUALCOURSE MANUAL

MEASURE PHASEMEASURE PHASE

INDIAN STATISTICAL INSTITUTEINDIAN STATISTICAL INSTITUTE

SQC&OR UNIT, BANGALORESQC&OR UNIT, BANGALORE

22

CONTENTSCONTENTS

S. No Topic Slide No.

1 Data Collection 55-98

2 Variation-Concepts 99-105

3 Measurement System Analysis 106-114

4 Descriptive Statistics 115-119

5 Control Chart 120-124

6 Looking into Data 125-141

7 Capability Evaluation 142-167

33

• What is Data ?

Data is a numerical expression of an activity.

Conclusions based on facts and data are necessary for any improvement.

-K. Ishikawa

If you are not able to express a phenomenon in numbers, you do not know about it adequately.

-Lord Kelvin

DATA GATHERINGDATA GATHERING

44

TYPES OF DATATYPES OF DATA

CONTINUOUS DISCRETE

Measurable

e.g. :Length, Temperature

Subjective Assessmente.g. :Score in a beautycontest

Countablee.g. :Number of defects

55

WHAT IS THE DIFFERENCE WHAT IS THE DIFFERENCE BETWEENBETWEEN

A SHAFT DIAMETER

THE NUMBER OF SHAFTS REJECTED FOR OVERSIZE

DIAMETER

The diameter of a

shaft can take any

value ever after the

decimal point e.g..

19.055, 19.0516

etc..

Data related to this

type of parameters

are called

Continuous data.

The number of shaft rejected has necessarily to be a whole number. e.g.. 0, 2, 7, 10 numbers rejected etc..

Data related to this type

of parameters are called

Discrete data.

66

WHICH OF THE BELOW ARE CONTINUOUS WHICH OF THE BELOW ARE CONTINUOUS AND DISCRETE DATA?AND DISCRETE DATA?

• Width of sheet

• No. of liners thinned

• Tubes rejected by Go- Nogo Gauge

• Diameter of Piston

• Height of a Man

• Sheet thickness

• Out of 100 sheets the numbers that meet the thickness 4 0.9

• Time taken to process a purchase order

• No. of bugs in a program

1717

FMEA

There are two primary flavors of FMEA:

Design FMEAs are used during process or product design and development.

The primary objective is to uncover problems that will result in potential failures within the new product or process.

Process FMEAs are used to uncover problems related to an existing process.

These tend to concentrate on factors related to manpower, systems, methods, measurements and the environment.

Although the objectives of design and process FMEAs may appear different, both follow the same basic steps and the approaches are often combined.

1919

FMEA drives systematic thinking about a product or process by asking and attempting to answer three basic questions:

What could go wrong (failure) with a process or system? How bad can it get (risks), if something goes wrong

(fails)? What can be done (corrective actions) to prevent things

from going wrong (failures)?

FMEA attempts to identify and prioritize potential process or system failures. The failures are rated on three criteria:

The impact of a failure - severity of the effects. The frequency of the causes of the failure - occurrence. How easy is it to detect the causes of a failure -

detectability.

FMEA

2020

Notice that only the causes and effects are rated - failure modes themselves are not directly rated in the FMEA analysis.

FMEA is cause-and-effect analysis by another name – avoid being hung up on the failure mode.

The failure mode simply provides a convenient model, which allows us to link together multiple causes with multiple effects.

It is easy to confuse failures, causes, and effects, especially since causes and effects at one level can be failures at a lower level.

Effects are generally observable, and are the result of some cause. Effects can be thought of as outputs.

FMEA

2121

Effects are usually events that occur downstream that affect internal or external customers.

Root causes are the most basic causes within the process owner’s control. Causes, and root causes, are in the background; they are an input resulting in an effect.

Failures are what transform a cause to an effect; they are often unobservable.

One can think of failures, effects, and causes in terms of the following schematic:

Root Causex

Failuref(x)

Effecty

FMEA

2222

Note that a failure mode can have numerous distinct effects, and that each effect has its own system of root causes.

With this in mind, another way to think of failures, effects, and causes is:

Causes - x's

Failure - f(x) Effect - y

FMEA

2323

Keep in mind that a single failure mode can have several effects, and that the cause-and-effect diagram on the previous slide should be repeated for each effect of the failure!!!

Failure Mode - f(x)

Effect 1 - y1

Effect 2 - y2

Effect n - yn

Cause Set 1 - x1's

Cause Set 2 - x2's

Cause Set n - xn's

.

.

.

.

.

.

FMEA

2424

The failures identified by the team in an FMEA project are prioritized by what are called Risk Priority Numbers, or RPN values.

The RPN values are calculated by multiplying together the Severity, Occurrence, and Detection (SOD) values associated with each cause-and-effect item identified for each failure mode.

Note: The failure mode itself is not rated and only plays a conceptual role in linking causes with their effects on the product, process, or system.

For a given cause-and-effect pair the team assigns SOD values to the effects and causes. Then an RPN is calculated for that pair: RPN = Severity x Occurrence x Detection.

Risk Priority Numbers

2525

Once the RPN values are assigned to each of the cause-and-effect pairs identified by the team, the pairings are prioritized.

The higher the RPN value, the higher the priority to work on that specific cause-and-effect pair.

The measurement scale for the SOD values is typically a 5 or 10 point Likert scale (an ordinal rating scale).

The exact criteria associated with each level of each rating scale is dependent upon either a company designed rating criteria or a specified rating criteria from an industry specific guideline.

We recommend the use of a 10 point Likert scale for each of the three rating criteria: Severity, Occurrence, and Detection.

FMEA

2626

Note: The 10 point scale facilitates the ability of the team to assign ratings in a timely fashion.

Too many levels can lead to a false sense of precision and a lot of agonizing over the exact rating to be assigned for each item.

The rating systems used should be developed to reflect the specific situation of interest.

Recall the example of the completed FMEA presented earlier.

The FMEA was developed by a team studying OS/390 online systems availability to end users.

On the following slides, we will see the ratings systems agreed upon by the team.

FMEA

2727

Severity rates the seriousness of the effect for the potential

failure mode - how serious is the effect if the failure did

occur?

The more critical the effect, the higher the severity rating.

FMEA

2828

Severity ratings for the online systems availability FMEA.

Severity Rank Criterion

None 1 No effect

Very Minor 2 No noticeable effect on production

Minor 3 Minor effect on production

Very Low 4 Very low effect on production

Low 5 Low effect on production

Moderate 6 Moderate effect on production

Significant 7 Noticeable effect on production

High 8 Production nearly halted

Very High 9 Production halted

Disaster 10 Implement Hotsite recovery

FMEA

2929

Occurrence, or frequency of occurrence, is a rating that describes the chances that a given cause of failure will occur over the life of product, design, or system.

Actual data from the process or design is the best method for determining the rate of occurrence. If actual data is not available, the team must estimate rates for the failure mode.

Examples:

The number of data entry errors per 1000 entries, or

The number of errors per 1000 calculations.

An occurrence value must be determined for every potential cause of the failure listed in the FMEA form.

FMEA

3030

The higher the likelihood of occurrence, the higher the

occurrence value.

Once again, occurrence guidelines can be developed and should

reflect the situation of interest.

FMEA

3131

Occurrence guidelines for the system availability FMEA:

Occurrence Rank Criterion Possible failure rate

Remote 1 Unklikely that cause occurs 1 in 15,00,000

Very low 2 Very low chance that cause occurs 1 in 1,50,000

Low 3 Few occurrences of cause likely 1 in 15,000

4 1 in 2000

5 1 in 400

6 1 in 80

7 1 in 20

8 1 in 8

9 1 in 3

10 1 in 2

Moderate Medium number of occurences of cause

Very High Very high number of occurrences of cause

High High number of occurrences of cause

FMEA

3232

The detection rating describes the likelihood that we will detect a cause for a specific failure mode.

An assessment of process controls gives an indication of the likelihood of detection.

Process controls are methods for ensuring that potential causes are detected before failures take place.

For example, process controls can include:

• Required fields or limited fields in electronic forms, • Process and/or system audits, and• “Are you sure” dialog boxes in computer programs.

If there are no current controls, the detection rating will be high. If there are controls, the detection rating will be low.

FMEA

3333

The higher a detection rating, the lower the likelihood we will detect a specific cause if it were to occur.

Detection guidelines developed for the system availability FMEA:Detection Rank Criterion

Almost certain 1 Cause obvious and easy to detect

Very High 2 Very high chance of detecting the cause

High 3 High chance of detecting the cause

Moderately High 4 Cause easily detected by inspection

Moderate 5 Moderate likelihood of detection

Low 6Low likelihood of detection

Very Low 7Very low likelihood of detection

Remote 8 Cause is hard to identify

Very Remote 9 Cause is very hard to identify

Almost impossible 10 Cause usually not detectable

FMEA

3535

Conducting an FMEA: Basic Steps

1. Define the scope of the FMEA.

2. Develop a detailed understanding of the current process.

3. Brainstorm potential failure modes.

4. List potential effects of failures and causes of failures.

5. Assign severity, occurrence and detection ratings.

6. Calculate the risk priority number (RPN) for each cause.

7. Rank or prioritize causes.

8. Take action on high risk failure modes.

9. Recalculate RPN numbers.

FMEA

3636

OBJECTIVES OF DATA COLLECTIONOBJECTIVES OF DATA COLLECTION• To know and quantify the status

• To monitor the process

• To decide acceptance or rejection

• To analyse and decide the course of action

HOW TO COLLECT DATA ?HOW TO COLLECT DATA ?

• Define the purpose

• Decide the type of analysis

• Define the period of data collection

• Is the the required data already available ?

3737

X = DirtD = DentS = ScratchB = Bubble

Hood Paint DefectsName: ____Date: ____Model: ____

DD D S

XXX B X

No. inspected: _____

LOCATION CHECK SHEETLOCATION CHECK SHEET

3838

STRATIFICATIONSTRATIFICATION• The method of grouping data by common points or

characteristics to better understand similarities and characteristics of data is called stratification.

• Such classification helps in obtaining vital information by distinguishing and comparing data in different class or strata.

• It also identifies the key strata to concentrate on.

• The stratification may be based on machines, operators, shifts or any other source of variation.

3939

STRATIFICATIONSTRATIFICATION

• The purpose of stratification is to ascertain the difference between different categories and to analyze the reasons behind abnormal distribution.

• Stratification of data is an effective method for isolating the cause of a problem.

• You can also stratify the data you collect by different QC tools such as graphs, Pareto diagrams, check sheets, histograms, scatter diagrams, and control charts.

4040

STRATIFICATION-AREA OF APPLICATIONSTRATIFICATION-AREA OF APPLICATION

• Raw Material Quantity supplied, Delivery time, Rejection % -

supplier wise and batch wise.

• Production Rejection percentage with respect to machine, shift, operator, raw material, tool, jig and so on.

• Engineering and designDraftsman wise drawing errors, Type of drawing wise.

4141

•The entire set of items is called the Population.

•The small number of items taken from the population to

make a judgment of the population is called a Sample.

•The numbers of samples taken to make this judgment

is called Sample size.

SAMPLE OF SIZE THREE

POPULATION

POPULATION AND SAMPLEPOPULATION AND SAMPLE

4242

POPULATION, SAMPLE AND DATAPOPULATION, SAMPLE AND DATA

POPULATION Sample DataRandom Sampling

Measurement / Observation

ACTION

NO ACTION

ISI, SQC UNIT, BANGALOREISI, SQC UNIT, BANGALORE SS-MEASURE PHASESS-MEASURE PHASE

Data Collection Plan Features


Data Collection Plan Features, cont.


4646

SAMPLE SIZE RULES OF THUMBSAMPLE SIZE RULES OF THUMBStatistic or

ChartRecommended Minimum

Sample Size (n)

Frequency plot (Histogram)

50

Pareto chart 50

Scatter plot 24

Control chart 24

4747

• No two things in nature are alike. • This is also true for manufactured products. • This dissimilarity between two products for the

same characteristic is called variation.

• The variation may be or can be made to be so small so as to make the product SEEM similar.

• When we say that 2 things are similar we actually mean that it is not possible to measure the variation present within the accuracy of the existing measuring equipment.

• Variation between 2 products are compared for SIMILAR features or characteristics.

WHAT IS VARIATION ?WHAT IS VARIATION ?

4848

• Variations among pieces at the same time

• Variations across time

TYPES OF VARIATIONTYPES OF VARIATION

4949

This man wants to reach his work place by 6.55 a.m.. But he can not do so, exactly at 6.55 a.m. daily. Sometimes he reaches earlier (but almost never before 6.50 a.m.). Sometimes he reaches later (but almost never after 7.00 a.m.). WHY ?

6.50 6.55 7.00

6.55 a.m. 5 minutes.

5050

OF CERTAIN FACTORS WHICH• Affect the time he takes • He cannot control• Vary randomly

e.g. The traffic you encounter under normal course of travel

THE VARIATION THAT OCCURS DUE TO THESE KIND OF FACTORS IS CALLED INHERENT VARIATION OR COMMON CAUSE VARIATION OR WHITE NOISE.e.g.. m/c vibration,tool wear etc.

THIS IS BECAUSE....THIS IS BECAUSE....

5151

UNDER NORMAL SCHEME OF UNDER NORMAL SCHEME OF OPERATIONOPERATION

InherentVariability(white noise)

Aimed value

Minimum deviation

Maximum deviation

5252

6.30

TODAY HE IS EARLY !

WHY ?

PROBABLY BECAUSE :• His watch was running fast.• He got a lift.• His bus driver took a

shortcut.• He stayed over in the

colony.• He had some important work

to be finished before 7.30.These causes are characteristic of a specific circumstance and do not occur in the normal scheme of actions.

Variation due to these types of reasons is called assignable or special cause variation or black noise

5353

GRAPHICAL DISPLAY OF GRAPHICAL DISPLAY OF VARIABILITIESVARIABILITIES

InherentVariability

Assignable Variability


TOTAL VAR I A B I L I T Y



Aimed Value

CASE I

CASE II CASE III

(Black noise)

5454

COMMON PROBLEMS WITH MEASUREMENTSCOMMON PROBLEMS WITH MEASUREMENTS•Problems with the measurements themselves1. Bias or inaccuracy: The measurements have a different

average value than a “standard” method.2. Imprecision: Repeated readings on the same material vary

too much in relation to current process variation.3. Not reproducible: The measurement process is different

for different operators, or measuring devices or labs. This may be either a difference in bias or precision.

4. Unstable measurement system over time: Either the bias or the precision changes over time.

5. Lack of resolution: The measurement process cannot measure to precise enough units to capture current product variation.

5555

DESIRED MEASUREMENT CHARACTERISTICS DESIRED MEASUREMENT CHARACTERISTICS FOR CONTINUOUS VARIABLESFOR CONTINUOUS VARIABLES

Good accuracy if

difference is small

Standard value

Observed value

Data from repeated measurement of

same item

Good repeatability if variation is small *

1. AccuracyThe measured value has little deviation from the actual value. Accuracy is usually tested by comparing an average of repeated measurements to a known standard value for that unit.

2. RepeatabilityThe same person taking a measurement on the same unit gets the same result.

5656

3. ReproducibilityOther people (or other instruments or labs) get the same result you get when measuring the same item or characteristic.

Data from Part X

Data Collector 1

Data Collector 2

Good reproducibility if

difference is small *

Data from Part X


5757

4. StabilityMeasurements taken by a single person in the same way vary little over time.

Time 1

Time 2

Good stability if difference is

Small*

Observed value

Observed value


5858

5. Adequate Resolution

There is enough resolution in the measurement device so that the product can have many different values.

5.1 5.2 5.3 5.4 5.5X X

XXX

XXXXXX

XXX

XX


5959

MINITAB OUTPUTGage name:Date of study:

Reported by:

Tolerance:

Misc:

0

1

2

3

4

5Fred Joe Martha

Xbar Chart by reader

Sam

ple

Mea

n

X=3.531

3.0SL=4.824

-3.0SL=2.238

0

0

1

2

Fred Joe Martha

R Chart by reader

Sam

ple

Ran

ge

R=0.6875

3.0SL=2.246

-3.0SL=0.000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1

2

3

4

5

form

readerreader*form Interaction

Ave

rag

e

Fred

Joe Martha

Fred Joe Martha

1

2

3

4

5

reader

By reader

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1

2

3

4

5

form

By form

%Total Var%Study Var

Gage R&R Repeat Reprod Part-to-Part

0

50

100

Components of Variation

Per

cent

Gage R&R (ANOVA) for legibility s

6060

Gage R&R

Source %Contribution %Study Var Total Gage R&R 37.39 61.15 Repeatability 28.64 53.51 Reproducibility 8.75 29.59 reader 8.75 29.59 Part-To-Part 62.61 79.13 Total Variation 100.00 100.00

Number of Distinct Categories = 2

MINITAB OUTPUT

Acceptance criteria for MSA

1. Gage R & R < 10% Excellent

2. Gage R & R 10% to 30% Acceptable

3. Gage R & R > 30% Not acceptable

In addition: No. of Distinct categories 4

6161

Interpretation of MSA ResultsRepeatability error shall be low.

If it is high, then,

a. Instrument is improper

b. Method of measurement is not OK

c. System improvement is required

Reproducibility error shall be low.

If it is high, then,

a. Train the operator


c. Inspector skill not OK

6262

Interpretation of MSA Results

Part to Part variation shall be High.

If it is low, then,

a. Instrument is improper


6363

HISTOGRAMS: VARIATION FOR A PERIOD OF TIMEHISTOGRAMS: VARIATION FOR A PERIOD OF TIME

0

10

20

30

40

1 2 3 4 5 6 7 8

Number of Days for Approval

Num

ber

of O

ccur

renc

es

DEFINITION A Histogram shows the shape, or distribution, of the data by displaying how often different values occur.

EXAMPLE “Number of Days for Approval”

6464

WHAT IS THE MEASUREWHAT IS THE MEASURE OF CENTRAL TENDENCY OF A OF CENTRAL TENDENCY OF A

SET OF NUMBERS? SET OF NUMBERS?

WHAT IS THE MEASUREWHAT IS THE MEASURE OF CENTRAL TENDENCY OF A OF CENTRAL TENDENCY OF A

SET OF NUMBERS? SET OF NUMBERS?

• There are three ways in which Central Tendency of Numbers can be measured.

• These are the 3 M’s

MEAN

MEDIAN

MODE

6565

MEASURES OF DISPERSIONMEASURES OF DISPERSIONMEASURES OF DISPERSIONMEASURES OF DISPERSION

The extent of the spread of the values from the mean value is called Dispersion.

The measures of Dispersions are– Range (R)– Standard Deviation (s)– Variance (s2)– Co-efficient of Variation (CV)

Standard deviation is the most commonly used measure of dispersion.

6666

Center of the bar

Smooth curve interconnecting

the center of each bar

Units of Measure

THE NORMAL CURVETHE NORMAL CURVE

6767

• If the frequency distribution of a set of values is such that :

– 68.26% of the values line within ±1s from the mean AND

– 95.46% of the values line within ±2s from the mean AND

– 99.73% of the values line within ±3s from the mean

Then the distribution is normal.

NORMAL DISTRIBUTION IS CHARACTERISED BY A BELL SHAPED CURVE.

NORMAL DISTRIBUTIONNORMAL DISTRIBUTION

6868

Is the process free of special cause variation?Is the process free of special cause variation?

On the shop floor this is a control chart…In reality it is a process behavior chart.

On the shop floor this is a control chart…In reality it is a process behavior chart.

6969

A Process is Sending a Signal if...A Process is Sending a Signal if...

7070

THE INDIVIDUAL X CHARTTHE INDIVIDUAL X CHART

When to Use:In situations where opportunities to get data are limited, such as low

production volume or testing.When sampling sizes greater than 1 simply do not apply, such as

accounting measures (overtime forecasting), sampling from homogeneous batches (contaminants in a clean room); or when samples have very small short-term variations (sheet metal stamping).

How: By plotting each individual measurement on an Individual X (IX) chart

Conditions:• Sample size of one.• Assumes normal distribution.

7171

PLOT POINT CALCULATION STEPS FOR PLOT POINT CALCULATION STEPS FOR IX CHARTIX CHARTSample IX

1 2 3 4 5 6 7 8 9 10

4.25 4.78 3.95 3.86 3.72 5.17 5.07 4.65 4.70 4.35

IX Plot Points

7272

0 1 2 3 4 5 6 7 8 9 10

3

4

5

6

Observation Number

Co

nce

ntra

tion

IX Chart for Concentration

Mean=4.45

UCL=5.620

LCL=3.280

THE INDIVIDUAL X CHARTTHE INDIVIDUAL X CHART

Conclusion: The process is in Statistical Control

7373

Checking Both Time Order and Distribution

In practice, if your data has a natural time order, you should always do a control chart as well as a frequency plot. Both give you different information.

In this case, there are no special causes that appear in the control chart (according to the Tests for Special Causes already taught), but the frequency plot clearly has a bimodal pattern and you’d want to investigate why.

7474

WORK SHEET: Interpreting Distribution and Time Order

•Objective: Gain an understanding of the different types of information provided by frequency plots and time plots, and how looking at the data from different perspectives can lead to different conclusions.•Instructions: Divide into pairs or small groups. Read the case study below and discuss your interpretation of the data shown in the back-to-back frequency plots. Then look at the time plot on the next page and discuss the questions shown there. Be prepared to discuss your answers with the class. Time: 10 min.

7575

Interpreting Distribution and Time Order

Supplier A 40 Deliveries

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5 Supplier B 40 Deliveries

Days from Target

This company was having trouble Scheduling the services delivered to its customers because of delays in receiving materials from their suppliers. They went into their computer records and recovered data from the past 40 weeks comparing promised delivery dates to actual delivery dates from their two main suppliers. Based on the frequency plots, which supplier would you recommend this company choose? Note: A negative number indicates

the delivery was early.

7676

•Now look at the time plot of the same data shown previously on the frequency plots.

•What is your interpretation now that you’ve seen both the time plot and frequency plot? Which supplier would you recommend using?

Interpreting Distribution and Time Order, cont.

Time Plot of Suppliers A and B Late Deliveries (40 weekly deliveries each)

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

=supplier A

=supplier B

7777

Answer•In the frequency plot, Supplier B looks far superior to Supplier A, having a much narrower distribution generally much nearer the target. In the time plot, however, it looks like Supplier A is making rapid strides in improving its ability to deliver on time. You would probably want to collect more data to make sure that Supplier A can sustain its current level of performance.

Supplier A 40 Deliveries

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5 Supplier B 40 Deliveries

Days from Target

Time Plot of Suppliers A and B Late Deliveries (40 weekly deliveries each)

–0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

=supplier A

=supplier B

7878

HISTOGRAM FROM MINITABHISTOGRAM FROM MINITABHISTOGRAM FROM MINITABHISTOGRAM FROM MINITAB

Make Sure the data window is active.

Choose GRAPH>HISTOGRAM (or) STAT > BASIC STATISTICS > DISPLAY DESCRIPTIVE STATISTICS

In X (or) Variables, enter the column containing the data, click OK (or) choose GRAPHS > HISTOGRAM OF DATA > OK.

You can choose Type of Histogram, No. of classes by clicking OPTIONS in GRAPH>HISTOGRAM menu.

You can use GRAPH>Dot plot to display the data

You can classify the source wise data to display the data in two different dot plots.

7979

DOT PLOT FROM MINITABDOT PLOT FROM MINITABDOT PLOT FROM MINITABDOT PLOT FROM MINITAB

Make Sure the data window is active.

Choose GRAPH> DOTPLOT

Enter the column containing the data, click OK

If you have source wise data, put the source variable (either Text or Numeric) in the next column. Click By Variable in the Dot Plot Menu, select the source column, click ok.

You get the Stratified Dot Plot on the same Graph.

8080

15 25 35 45 55 65 75 85 95 105

PRODUCTION

Dotplot for PRODUCTION

DAY

NIGHT

SHIFT

STRATIFIED DOT PLOT SHIFT WISE

8181

PARETO DIAGRAMPARETO DIAGRAM• The Pareto Principle is generally used to prioritize

quality improvement projects to get most returns for the resources invested.

• It is one of the most powerful tools and is widely used as means of attacking bulk of the problems with the optimal utilization of resources.

• The basic principle of Pareto is “Around 80% of overall effect is contributed by 20% of causes & vice versa”

8282

• To find out what the major problem is viz...

Quality Defects, Faults , Failures, Complaints, Repairs, Returned items etc.

Cost Amount of loss, Expenses

Delivery Stock, Shortages, Delay in delivery, Default in payment.

Safety Accidents, Breakdowns, mistakes.

PARETO CHART BY EFFECTPARETO CHART BY EFFECT

8383

• To find out what the major problem is Viz.

Operator Shift, Group,

Experience, Skill.

Machine Machines, Equipment, Tools

Raw material Manufacturer, Lot

Operational method Conditions, Order,

Method

PARETO CHART BY CAUSEPARETO CHART BY CAUSE

8484

HOW TO PREPARE A PARETO DIAGRAMHOW TO PREPARE A PARETO DIAGRAM Decide which item to be studied.

Stratify the problem according to sources (by defects, by supplier etc.) and tabulate the corresponding data.

Preferably data should be expressed in monetary terms rather than quantity or percentage.

Arrange the stratified items in descending order of value and draw a bar diagram.

Draw a curve showing the cumulative % above the bar chart starting from the greatest value.

8585

USES OF PARETO DIAGRAMUSES OF PARETO DIAGRAM

Find out the most important item/defect.

Ratio of each item to the whole.

Degree of improvement after remedial action in some limited area.

Improvement in each item/defect compared before and after correction.

8686

115 120 120 140 145 4301115 5.3 5.5 5.5 6.4 6.619.751.0

100.0 94.7 89.2 83.8 77.3 70.7 51.0

2000

1000

0

100

80

60

40

20

0

Defect

CountPercentCum %

Per

cent

Cou

ntPareto Diagram for Machine Stoppages (M/C No.14)

8787

26

50

70

87

97 100

0

20

40

60

80

100

120

140

FlightProblems

Baggage Service Refund Fares others

No

. o

f co

mp

lain

ts

010

203040

50607080

90100

Cu

m.

per

cen

tag

e

PARETO ANALYSIS OF PARETO ANALYSIS OF PASSENGER COMPLAINTS AT AN AIRPORTPASSENGER COMPLAINTS AT AN AIRPORT

8888

35

60

75

8593 98 100

0

20

40

60

80

100

120

140

160

180

200

Latedelivery

Missing orwrongitems

Fadingcolours

Stains Creased ButtonsMissing

Stretchedor torn

No.

of c

ompl

aint

s

0

10

20

30

40

50

60

70

80

90

100

PARETO ANALYSIS OF COMPLAINTS AT A LAUNDRYPARETO ANALYSIS OF COMPLAINTS AT A LAUNDRY

8989

PARETO DIAGRAM FROM PARETO DIAGRAM FROM MINITABMINITAB

PARETO DIAGRAM FROM PARETO DIAGRAM FROM MINITABMINITABOpen MINITAB Worksheet.

Put your data (no. of defects) in one column and the nomenclature in the other column.

Choose STAT > QUALITY TOOLS > PARETO CHART

Choose Chart Defects Table. In labels in: enter the nomenclature column and in frequencies in: enter the no. of defects column.

Enter the required Title.

9090

IMPORTANT SPC RATIOS IMPORTANT SPC RATIOS USEDUSED

This compares the requirement of the process output vis-a-vis the inherent variability of the process. Higher value than 1 implies that the process has got the capability to give the product within the set limits.

LSL x USL

- 3s + 3

s 6

LSL-USL

s 6

Tolerance

process of variation Normal

sticcharacteri ofrange allowable Maximum Cp

-3s +3s

9191

PROCESS POTENTIAL INDEX (Cp)PROCESS POTENTIAL INDEX (Cp)

Maximum Allowable Range of CharacteristicNormal Variation of Process

Cp =

The numerator is controlled by Design Engineering

The denominator is controlled by Process Engineering

9292

This gives us the positioning of the mean vis-a-vis the USL and the relationship between the two.

This gives us the positioning of the mean vis-a-vis the LSL and the relationship between the two.

Cpk - Process Performance Index. This is important

Cpk = Minimum of (Cpu and Cpl) ; for bilateral tolerances

= C pu ;for unilateral tolerance on upper side i.e..

= Cpl ;for unilateral tolerance on lower side i.e..

X+Y-O

X+O-Y

s3

X-USL Cpu

s3

LSLX Cpl

9393

These ratios help you in:

Predicting whether rejections will take place on the higher side or on the lower side.

Taking centering decisions.

Deciding whether to consider broadening of tolerances

Taking Decisions on whether to go in for new m/cs.

Deciding on the level of inspection required.

9494

LSL USL

Failure likely on lower side

LSL USL

LSL USL

CENTERING RELATED PROBLEMS

LSL USL

LSL USL

TOLERANCE OR NEW MACHINE DECISION

Failure likely on higher side

LSL USL

LSL USL

SOME SOME TYPESTYPESSOME SOME TYPESTYPES

9595

• Defect : Any non-conformity in a product or service– e.g. Late delivery or no. of tubes rejected

• Units : The nos. checked or inspected – 100 deliveries were monitored for being late, no. of units

are 100

– 1000 tubes were checked for oversize dia., no. of units are 1000

• Opportunity : Anything that you measure or check for.– Finished refrigerator is checked for 25 defects at final

inspection, the no. of opportunities is 25

A FEW TERMINOLOGIESA FEW TERMINOLOGIES

9696

WHAT IS A DEFECT?WHAT IS A DEFECT? A defect is any variation of a required

characteristic of the product (or its parts) or services which is far enough from its target value to prevent the product from fulfilling the physical and functional requirements of the customer, as viewed through the eyes of your customer.

A defect is also anything that causes the processor or the customer to make adjustments.

ANYTHING THAT DISSATISIFIES YOUR CUSTOMER

9797

An 'unit' may be as diverse as a:

Piece of equipment Line of software Order Technical manual Medical claim Wire transfer Hour of labour Billable dollar Customer contact

DEFINING AN UNITDEFINING AN UNIT

9898

• Every possibility of making an error is called an opportunity• The total opportunities available for an error to take place are

Nos.Chkd. x Opp• If there are more than 1 opp. The sigma can be calculated by finding

DPMO.• Knowing DPMO we refer to the Normal Dist. Table to get the Sigma

value • One could inflate the opp. and hence get an enhanced Sigma But the

opp.are limited to what exactly is checked for.E.g. a sheet is checked for thickness, length & width and can be

rejected for either.Hence the opp. is 3

THE CONCEPT OF OPPORTUNITYTHE CONCEPT OF OPPORTUNITY

9999

No. of opportunities = No. of points checked

If you don’t check some points then it becomes a

passive opportunity. We should take only active

opportunities into our calculation of d.p.o., and

Sigma level.

100100

TOP = NO. OF UNITS CHECKED x

NO. OF OPPORTUNITIES OF FALIURE

TOP = NO. OF UNITS CHECKED x

NO. OF OPPORTUNITIES OF FALIURE

e.g. If in final inspection 100 refrigerators, each having 25 opportunities are checked

TOP = 25 x 100 =2500

TOTAL OPPORTUNITY (TOP)TOTAL OPPORTUNITY (TOP)

101101

DPO = DEFECTS

TOP

e.g. If in the above e.g. there were found 25 defects DPO = 25 = 0.01 2500

DEFECTS PER OPPORTUNITY (DPO)DEFECTS PER OPPORTUNITY (DPO)

102102

DPU = NO. OF DEFECTS

NO. OF UNITS CHECKED

e.g. In the above example DPU = 25 = 0.25 100

DEFECTS PER UNIT (DPU)DEFECTS PER UNIT (DPU)

103103

DPMO = NO. OF DEFECTS x 106

NO. OF UNITS x OPP.

e.g. In the above example DPMO = 25 x 106 = 10000

100 x 25

DPMODPMO

104104

CATEGORY DEFECTS UNITS OPP TOP DPU DPMO

TYPE1TYPE2TYPE3TYPE4TYPE5

COMPOSITE

1002222516??

21532

??

10001500130025003000

?? ?? ?? ??

DPMO = DEFECTS x 106

TOP

DPMO = DEFECTS x 106

TOP

Units x Opp.) Should not be taken in the denominator as in the normal case

HOW WOULD YOU ESTABLISH THE SIGMA FOR THE BELOWHOW WOULD YOU ESTABLISH THE SIGMA FOR THE BELOW

105105

ATTRIBUTE DATAATTRIBUTE DATA

Step 1: Examine a sample of size ‘n’ units

Step 2: Count the number of defectives/defects as per defect

definition

Step 3: Calculate

DPU or DPO = No. of Defectives (or defects) / Total no. of

Units (or total no. of opportunities)

Preferred no. of opportunities= 1

Step 4: DPMU or DPMO = DPU ( or DPO) x 106 in ppm.

Step 5: Refer the ppm to Sigma rating conversion table

106106

EXAMPLEEXAMPLE

We checked 500 Purchase Orders (PO) and PO had 10 defects then,

d.p.u. = d/u = 10/500 = 0.02

In a P.O. we check for the following:a) Supplier address/approvalb) Quantity as per the indentc) Specifications as per the indentd) Delivery requirementse) Commercial requirements

Then there are 5 opportunities for the defects to occur. Then, The total no. of opportunities = m u = 5x500 = 2500

107107

EXAMPLEEXAMPLE

Defects per opportunity, d.p.o. = d/(m u) = 10/2500 = 0.004

If expressed in terms of d.p.m.o. (defects per million opportunities) it becomes

d.p.m.o . = d.p.o. x 106 = 4000 PPM

Refer Sigma conversion table and read the value of Sigma Rating

108108

• For a 100% inspection process, 10000 units are produced. Each can be rejected for 8 different reasons. 100 were rejected. What is the DPU, TOP, DPMO & DPO.

• For the above the next day 20 units were rejected such that 2 units had 3 defects & 1 unit had 2 defects rest all had 1 defect. Find the DPU,TOP, DPMO & hence DPO.

• 20000 Items are supplied by a vendor. 5% of these are to be checked as per the sampling plan for 5 characteristics. 100 defects were found. Find the Sigma rating of the process.

EXERCISE EXERCISE

109109

CONTINUOUS DATACONTINUOUS DATAStep 1: Ensure Gauge R&R (if the CTQ is measured using an

instrument) < 30%. Otherwise improve measurement

system

Step 2: Collect the data (Minimum of 50 readings) on the

CTQ’s as per the data collection plan.

Step 3: Check for trend or special cause using individual

control chart

Step 4: Plot Histogram (Follow MINITAB steps. GO TO: Stat

> Basic Statistics > Display Descriptive Statistics >Enter

Variables > ‘Click’ Graphs > ‘Tick’ Graphical

Summary>OK>OK

110110

CONTINUOUS DATACONTINUOUS DATAStep 5: Read mean & standard deviation and interpret the

data as coming from Normal distribution if p > 0.05,

otherwise treat the data as non-normal.

Step 6: Do the process capability analysis as follows.1. Stat > Quality Tools > Capability Analysis (Normal) > Enter Variable

> Sample Size = 1 > Enter Specification Limits ( L/ U/ or both) > Go to

Options>Remove the tick from Within subgroup analysis>OK>Stamp

> Use Variable (if the date/ Time/ Batch no. to be incorporated) > OK

> OK

2. Read Expected performance in PPM if the data is normal

3. Read Observed performance if the data is non-normal.

4. In either case go to PPM – Sigma conversion table and find the Sigma

rating.

111111

EXAMPLE (Normal)EXAMPLE (Normal)

8765432

USLLSL

Process Capability Analysis for Dia.

PPM Total

PPM > USL

PPM < LSL

PPM Total

PPM > USL

PPM < LSL

Ppk

PPL

PPU

Pp

Cpm

StDev (Overall)

StDev (Within)

Sample N

Mean

LSL

Target

USL

848771.69

410672.19

438099.50

780000.00

400000.00

380000.00

0.05

0.05

0.08

0.06

*

1.04820

1.06439

50

4.96330

4.80000

*

5.20000

Exp. "Overall" Performance Observed PerformanceOverall Capability

Process Data

Within

Overall

PPM = 848771.67 Sigma Level = 0.47

112112

EXAMPLE (Non-Normal)EXAMPLE (Non-Normal)

-10 0 10 20 30

LSLUSL

Process Capability Analysis for Data

USL

Target

LSL

Mean

Sample N

StDev (Overall)

Pp

PPU

PPL

Ppk

Cpm

PPM < LSL

PPM > USL

PPM Total

PPM < LSL

PPM > USL

PPM Total

4.10000

*

2.90000

3.92903

50

4.52914

0.04

0.01

0.08

0.01

*

480000.00

280000.00

760000.00

410133.41

484943.80

895077.22

Process Data

Overall Capability

Observed Performance Expected Performance

PPM = 760000 Sigma Level = 0.80

113113

Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO0.01 931888 0.26 892512 0.51 838913 0.76 770350 1.01 687933 1.26 594835 1.51 496011 1.76 3974320.02 930563 0.27 890651 0.52 836457 0.77 767305 1.02 684386 1.27 590954 1.52 492022 1.77 3935800.03 929219 0.28 888767 0.53 833977 0.78 764238 1.03 680822 1.28 587064 1.53 488033 1.78 3897390.04 927855 0.29 886860 0.54 831472 0.79 761148 1.04 677242 1.29 583166 1.54 484047 1.79 3859080.05 926471 0.30 884930 0.55 828944 0.80 758036 1.05 673645 1.30 579260 1.55 480061 1.80 3820890.06 925066 0.31 882977 0.56 826391 0.81 754903 1.06 670031 1.31 575345 1.56 476078 1.81 3782810.07 923641 0.32 881000 0.57 823814 0.82 751748 1.07 666402 1.32 571424 1.57 472097 1.82 3744840.08 922196 0.33 878999 0.58 821214 0.83 748571 1.08 662757 1.33 567495 1.58 468119 1.83 3707000.09 920730 0.34 876976 0.59 818589 0.84 745373 1.09 659097 1.34 563559 1.59 464144 1.84 3669280.10 919243 0.35 874928 0.60 815940 0.85 742154 1.10 655422 1.35 559618 1.60 460172 1.85 3631690.11 917736 0.36 872857 0.61 813267 0.86 738914 1.11 651732 1.36 555670 1.61 456205 1.86 3594240.12 916207 0.37 870762 0.62 810570 0.87 735653 1.12 648027 1.37 551717 1.62 452242 1.87 3556910.13 914656 0.38 868643 0.63 807850 0.88 732371 1.13 644309 1.38 547758 1.63 448283 1.88 3519730.14 913085 0.39 866500 0.64 805106 0.89 729069 1.14 640576 1.39 543795 1.64 444330 1.89 3482680.15 911492 0.40 864334 0.65 802338 0.90 725747 1.15 636831 1.40 539828 1.65 440382 1.90 3445780.16 909877 0.41 862143 0.66 799546 0.91 722405 1.16 633072 1.41 535856 1.66 436441 1.91 3409030.17 908241 0.42 859929 0.67 796731 0.92 719043 1.17 629300 1.42 531881 1.67 432505 1.92 3372430.18 906582 0.43 857690 0.68 793892 0.93 715661 1.18 625516 1.43 527903 1.68 428576 1.93 3335980.19 904902 0.44 855428 0.69 791030 0.94 712260 1.19 621719 1.44 523922 1.69 424655 1.94 3299690.20 903199 0.45 853141 0.70 788145 0.95 708840 1.20 617911 1.45 519939 1.70 420740 1.95 3263550.21 901475 0.46 850830 0.71 785236 0.96 705402 1.21 614092 1.46 515953 1.71 416834 1.96 3227580.22 899727 0.47 848495 0.72 782305 0.97 701944 1.22 610261 1.47 511967 1.72 412936 1.97 3191780.23 897958 0.48 846136 0.73 779350 0.98 698468 1.23 606420 1.48 507978 1.73 409046 1.98 3156140.24 896165 0.49 843752 0.74 776373 0.99 694974 1.24 602568 1.49 503989 1.74 405165 1.99 3120670.25 894350 0.50 841345 0.75 773373 1.00 691462 1.25 598706 1.50 500000 1.75 401294 2.00 308538

Sigma and DPMO conversion table

114114

Sigma and DPMO conversion tableSigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO

2.01 305026 2.26 223627 2.51 156248 2.76 103835 3.01 65522 3.26 39204 3.51 22216 3.76 119112.02 301532 2.27 220650 2.52 153864 2.77 102042 3.02 64256 3.27 38364 3.52 21692 3.77 116042.03 298056 2.28 217695 2.53 151505 2.78 100273 3.03 63008 3.28 37538 3.53 21178 3.78 113042.04 294598 2.29 214764 2.54 149170 2.79 98525 3.04 61780 3.29 36727 3.54 20675 3.79 110112.05 291160 2.30 211855 2.55 146859 2.80 96801 3.05 60571 3.30 35930 3.55 20182 3.80 107242.06 287740 2.31 208970 2.56 144572 2.81 95098 3.06 59380 3.31 35148 3.56 19699 3.81 104442.07 284339 2.32 206108 2.57 142310 2.82 93418 3.07 58208 3.32 34379 3.57 19226 3.82 101702.08 280957 2.33 203269 2.58 140071 2.83 91759 3.08 57053 3.33 33625 3.58 18763 3.83 99032.09 277595 2.34 200454 2.59 137857 2.84 90123 3.09 55917 3.34 32884 3.59 18309 3.84 96422.10 274253 2.35 197662 2.60 135666 2.85 88508 3.10 54799 3.35 32157 3.60 17864 3.85 93872.11 270931 2.36 194894 2.61 133500 2.86 86915 3.11 53699 3.36 31443 3.61 17429 3.86 91372.12 267629 2.37 192150 2.62 131357 2.87 85344 3.12 52616 3.37 30742 3.62 17003 3.87 88942.13 264347 2.38 189430 2.63 129238 2.88 83793 3.13 51551 3.38 30054 3.63 16586 3.88 86562.14 261086 2.39 186733 2.64 127143 2.89 82264 3.14 50503 3.39 29379 3.64 16177 3.89 84242.15 257846 2.40 184060 2.65 125072 2.90 80757 3.15 49471 3.40 28716 3.65 15778 3.90 81982.16 254627 2.41 181411 2.66 123024 2.91 79270 3.16 48457 3.41 28067 3.66 15386 3.91 79762.17 251429 2.42 178786 2.67 121001 2.92 77804 3.17 47460 3.42 27429 3.67 15003 3.92 77602.18 248252 2.43 176186 2.68 119000 2.93 76359 3.18 46479 3.43 26803 3.68 14629 3.93 75492.19 245097 2.44 173609 2.69 117023 2.94 74934 3.19 45514 3.44 26190 3.69 14262 3.94 73442.20 241964 2.45 171056 2.70 115070 2.95 73529 3.20 44565 3.45 25588 3.70 13903 3.95 71432.21 238852 2.46 168528 2.71 113140 2.96 72145 3.21 43633 3.46 24998 3.71 13553 3.96 69472.22 235762 2.47 166023 2.72 111233 2.97 70781 3.22 42716 3.47 24419 3.72 13209 3.97 67562.23 232695 2.48 163543 2.73 109349 2.98 69437 3.23 41815 3.48 23852 3.73 12874 3.98 65692.24 229650 2.49 161087 2.74 107488 2.99 68112 3.24 40929 3.49 23295 3.74 12545 3.99 63872.25 226627 2.50 158655 2.75 105650 3.00 66807 3.25 40059 3.50 22750 3.75 12224 4.00 6210

115115

Sigma and DPMO conversion tableSigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO Sigma DPMO

4.01 6037 4.26 2890 4.51 1306 4.76 557 5.01 224 5.26 85 5.51 30.4 5.76 10.24.02 5868 4.27 2803 4.52 1264 4.77 538 5.02 216 5.27 82 5.52 29.1 5.77 9.84.03 5703 4.28 2718 4.53 1223 4.78 519 5.03 208 5.28 78 5.53 27.9 5.78 9.44.04 5543 4.29 2635 4.54 1183 4.79 501 5.04 200 5.29 75 5.54 26.7 5.79 8.94.05 5386 4.30 2555 4.55 1144 4.80 483 5.05 193 5.30 72 5.55 25.6 5.80 8.54.06 5234 4.31 2477 4.56 1107 4.81 467 5.06 185 5.31 70 5.56 24.5 5.81 8.24.07 5085 4.32 2401 4.57 1070 4.82 450 5.07 179 5.32 67 5.57 23.5 5.82 7.84.08 4940 4.33 2327 4.58 1035 4.83 434 5.08 172 5.33 64 5.58 22.5 5.83 7.54.09 4799 4.34 2256 4.59 1001 4.84 419 5.09 165 5.34 62 5.59 21.6 5.84 7.14.10 4661 4.35 2186 4.60 968 4.85 404 5.10 159 5.35 59 5.60 20.7 5.85 6.84.11 4527 4.36 2118 4.61 936 4.86 390 5.11 153 5.36 57 5.61 19.8 5.86 6.54.12 4397 4.37 2052 4.62 904 4.87 376 5.12 147 5.37 54 5.62 19.0 5.87 6.24.13 4269 4.38 1988 4.63 874 4.88 362 5.13 142 5.38 52 5.63 18.1 5.88 5.94.14 4145 4.39 1926 4.64 845 4.89 350 5.14 136 5.39 50 5.64 17.4 5.89 5.74.15 4025 4.40 1866 4.65 816 4.90 337 5.15 131 5.40 48 5.65 16.6 5.90 5.44.16 3907 4.41 1807 4.66 789 4.91 325 5.16 126 5.41 46 5.66 15.9 5.91 5.24.17 3793 4.42 1750 4.67 762 4.92 313 5.17 121 5.42 44 5.67 15.2 5.92 4.94.18 3681 4.43 1695 4.68 736 4.93 302 5.18 117 5.43 42 5.68 14.6 5.93 4.74.19 3573 4.44 1641 4.69 711 4.94 291 5.19 112 5.44 41 5.69 14.0 5.94 4.54.20 3467 4.45 1589 4.70 687 4.95 280 5.20 108 5.45 39 5.70 13.4 5.95 4.34.21 3364 4.46 1538 4.71 664 4.96 270 5.21 104 5.46 37 5.71 12.8 5.96 4.14.22 3264 4.47 1489 4.72 641 4.97 260 5.22 100 5.47 36 5.72 12.2 5.97 3.94.23 3167 4.48 1441 4.73 619 4.98 251 5.23 96 5.48 34 5.73 11.7 5.98 3.74.24 3072 4.49 1395 4.74 598 4.99 242 5.24 92 5.49 33 5.74 11.2 5.99 3.64.25 2980 4.50 1350 4.75 577 5.00 233 5.25 88 5.50 32 5.75 10.7 6.00 3.4

53 green belt course manual measure phase indian statistical institute sqc&or unit, bangalore

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