STATISTICAL PROCESS CONTROL (SPC) & STATISTICAL QUALITY CONTROL (SQC)

DEMMING'S 14 POINTS: Dr. Edward Demming, one of the famous quality advocates, summarized, in 14 points, what he believed to be necessary to obtain excellence within a corporation. These 14 points have gained world- wide acceptance.

1. Create constancy of purpose toward improvement of product and service.

2. Adopt the new philosophy. We are in a new economic age.

3. Cease dependence on inspection to achieve quality.

4. End the practice of awarding business on the basis of initial cost.

5. Improve constantly and forever every activity.

6. Institute training and education on the job, including management.

7. Institute leadership.

8. Drive out fear.

9. Break down barriers between departments.

10. Eliminate slogans and exhortations.

11. Eliminate work standards that prescribe numerical quotas.

12. Remove barriers that rob workers of their right to pride of workmanship.

13. Institute a vigorous program of education and self-improvement.

14. Put everybody in the company to work in teams to accomplish the transformation.

DEMMING'S THINKING:1. Management is responsible for improving the system.

2. Systems are complex: managers can't figure out all on their own the sources of problems.

3. Problems can be divided into two sources: local

Some workers, some of the time, … - also called Special Cause, Bias system

Continual, inherent within the process – also called Random, Common Cause

Managers first need to determine if a problem is local or system:

Managers must use the workers to determine this.

Workers and management must speak a common language for communicating this information. The common language is statistics and the type of problem can be identified using statistical process control.

GOALS OF SPC:understand the process

eliminate special cause variation

reduce common cause variation and maintain a process that is in "statistical control" and has high "process capability".

SPC FOR CHEMISTS1

DEFINITIONS:1. Statistics: a body of methods by which useful conclusions can be drawn from numerical

data. (Not simply facts stated as numbers.)

2. Process: a systematic series of actions directed to some end.

SPC: refers to controlling a process (e.g., chemical manufacture) based on responding to process data with statistical techniques and tools.SQC: refers to controlling the quality of a product based on responding to laboratory data with statistical techniques and tools.

3. Quality Assurance (Program): refers to a laboratory program that assures management, customers, government, etc. that the lab data is proven and of known quality. A lab may demonstrate quality control (and thereby give assurance to customers) as follows: a) include a standard of know concentration along with each batch of samples analyzed and

plot this result on a control chartb) calibrate instruments on a regular basis and retain proof of thisc) with every product shipment, retain samples that are properly labeled (e.g., analyst, date,

time, method number, instrument used) – these can be checked at a later date if neededd) demonstrate prevention of falsification of data (e.g., run blind samples, keep data

recorded in bound note books)

4. Blind Sample: refers to a sample of known concentration submitted as a routine sample without the analyst's knowledge

5. Accuracy: defines the difference between the measured value and the true value

6. Precision: is repeatability of a measurement. An analysis may yield precise results (repeatable) but be quite inaccurate.

Quantifying Accuracy: requires that the true value be known. The average ( ) of several measurements (xi) is reported as a percentage of the true value (T).E.g.: An analyst began with ‘0’ concentration of analyte and added measured amounts of a known standard. The data and accuracy might be reported as follows…

mg Ca+2 added mg Ca+2 recovered1 20 22

2 20 20

3 20 24

n = 3 xI = 66

The average % recovery on 3 analyses = 110%If the analyst repeated the procedure and obtained the following data, what is true about the accuracy and the precision with regard to the second set of data?

mg Ca+2 added mg Ca+2 recovered1 20 14

2 20 21

3 20 25

n = xI =

It is important to determine both accuracy and precision of a method.

SPC FOR CHEMISTS2

7. Error: like accuracy, is determined with reference to a true value, i.e., error = inaccuracy . In the previous example, the average % error could be reported as +10% in the first case and 0% in the second case.

8. Variation: like precision, deals with repeatability of data and also stability of a process, i.e., variation = instability = imprecision

Errors and variation can arise from two kinds of causes:

1. Special Causes: (assignable, bias, local variation), error/variation results in one direction (either + or -) and can be traced to an assignable, special cause, e.g., miscalibrated instrument. It can be detected by running known standards and recalibrating.

2. Common Cause: (random, system variation) error/variation results randomly (without bias) in both directions (+ and -) and in varying magnitude – due to unknown causes. Random variation is chronic (continual), e.g., normal fluctuations in instruments, natural variation in raw materials.

Statistics is more applicable to measuring and controlling variation from common cause (random) than from special causes. (bias).

Exercise Identify the following causes of variation as Special or Common

a) spectrophotometer calibration off _______

b) spectrophotometer unsteady _______

c) forgot to add one reagent to all samples and standards _______

d) it is unusually humid during analysis and samples are hydroscopic _______

e) temperature gauge on distillation column is reading 5 low _______

f) sloppy analytical technique _______

% Recovery is a measure of ……………………………….

Calculate the average % recovery and average % error in the following analysis

mg Cr+3 added mg Cr+3 recovered1 50 57

2 50 55

3 50 50

n = xI =

Match the following….

1 precision A imprecision2 variation B closeness to true value3 error C repeatability4 accuracy D inaccuracy

SPC FOR CHEMISTS3

STATISTICS FOR SPCVariation (imprecision, instability, degree of repeatability) is described in statistics by the standard deviation

If a large homogeneous sample is analyzed many times (say ‘n’ times), all results will not be identical but will vary over a ‘range’.

Range = [highest value – lowest value].

Normally the values will cluster about the ‘average value’.

Average = =

ExerciseCalculate the average and range of the following measurements.

a) 1.31, 1.32, 1.30, 1.36, 1.37

b) 1.30, 1.41, 1.36, 1.35, 1.32

c) 1.29, 1.36, 1.37, 1.30, 1.33

d) 1.34, 1.30, 1.30, 1.38, 1.36

When every part is measured, the arithmetic average ( ) is called the Mean (), pronounced ‘mu’.

The majority of the values will be very close to the average ( ) and fewer values will be far from . If the values are plotted as a frequency distribution (a plot of number of times a value is obtained versus the value itself), the plot will approximate that shown below and is called a ‘Normal Distribution’, ‘Gaussian Curve’ or a ‘Bell Curve’.

SPC FOR CHEMISTS4

2% 2%14% 14%

# of times

xI

occurs

magnitude of xi

Normal Distribution

-2 2 3-3 -1 10

34%34%

The most useful measure of dispersion is not range but rather standard deviation.

Standard deviation:

Think of standard deviation as being the average range or average deviation from the mean.

When all parts are measured, the standard deviation calculation becomes…

When the sample size, n, is large (n > 30), both formulas give approximately the same value.

Regarding the Normal Distribution: 68.26% of all data points lie within 1 of the mean 95.46% of all data points lie within 2 of the mean 99.73% of all data points lie within 3 of the mean

Thus for data which closely follows the normal distribution:Any single analytical result has a 68% probability of being within 1 standard deviation of the mean.Any single analytical result has a 95.5% probability of being within 2 standard deviations of the mean.Any single analytical result has a 99.7% probability of being within 3 standard deviations of the mean.

ExerciseDuring her shift, a chemist measured 20 viscosity readings (shown below) on a large sample of solution.

365.3 365.7 366.0 366.0 366.0366.3 366.0 365.3 363.0 365.3364.3 366.3 365.0 365.0 365.3364.0 366.0 361.3 365.7 363.3

Use the data to calculate …

a) the sample average

b) the range of the data

c) the standard deviation

d) Within what limits (range) will

SPC FOR CHEMISTS

n = number of data points in the sample(xi - ) is the difference between an individual datum and the sample averagesx is the standard deviation of the sample

n = number of data points (usually called the population, ‘N’) = average (usually called the population mean, ‘’)

x = standard deviation of the population (pronounced sigma)

5

68% of the data lie?

95% of the data lie?

99% of the data lie?

Understanding Standard Deviation:The standard deviation of a group of data is one sixth (1/6) of the total range of data that were measured. For example:a) An analyst reports the concentration of PO4

-3 in a sample as = 50.0 ppm; sx = 1.0 ppmThus, the average result was 50.0 units1/6 of the total range of data was 1.0 unitThe total range of data was 50.0 3.0 units, i.e., 47 53 ppm.

b) Analysis of Fe+3 yielded = 10.0 ppm, sx = 0.1 ppmThus the average result was 10.0 units1/6 of the total range of data was 0.1 unitsThe total range of data was 10.0 0.3 units, i.e., 9.7 10.3 ppm

Quantifying Precision (Relative Standard Deviation):It is important for chemists to quantify the degree of precision in their work. This is done when various methods of analysis are being evaluated and compared. It might also be used to compare the work of two different analysts performing the same method.In the previous data for PO4

-3 and Fe+3 analysis, which analytical test gave greater precision?In a) the sx = 1.0 on an average of 50.0In b) the sx = 0.1 on an average of 10.0To quantitatively compare precision of methods, calculate sx as a percentage of .

For a) we have For b) we have

The result indicates that method b) is twice as precise as method a). The calculated values (2% and 1%, respectively) are called relative standard deviation (RSD).

RSD gives the sx as if the average ( ) were 100 units. RSD is used in validating new laboratory analytical methods and in Round Robin studies. In Round Robins, a large homogenous sample is divided in portions. Portions are sent to different labs and tested by different analysts. The chemists performing the analysis do not know the correct concentration of analyte. All results are collected and laboratory performance is evaluated.

ExerciseYou have just analyzed a product storage tank in order to certify this material for shipment to a customer. All parameters are well within specification except PO4

-3, which is measured at the specification limit of 50 ppm. Based on past analysis (and method validations) the RSD of this method is 4.0%. Is this product ‘on spec’? Hint: Use the established RSD to determine the concentration range within which the true value will lie.

Standard Deviation for Multiple Samples:Statistically it is true that the average ( i ) of a set of samples (xi ) will be closer to the true value (true population mean) than only 1 sample.

SPC FOR CHEMISTS6

Therefore the standard deviation of a number of averages (s i ) will be lower than the standard deviation of a number of single samples (sxi).S I can be calculated as follows:

In the last exercise, by only analyzing 1 sample of the storage tank (x I = 50 ppm), you must report that the true value lies in the range of 50 6 ppm ( 3), i.e., between 44 and 56 ppm.

If you resample the storage tank and, for example, if the average of the 2 samples is also 50 ppm, you can now use s to calculate the range, as follows.

Now after averaging 2 sample results, the true value lies in a smaller range, i.e., [50 3()] = [50 3(1.4)] = [50 4.2] = 45.8 54.2 ppm

ExerciseAs an extension of the PO4

-3 analysis in the storage tank, calculate the range within which the true value lies for the following cases…a) n = 4, = 50.0, sx = 2b) n = 9, = 50.0, sx = 2

Confidence Limits:On a given day you may run a single analysis on a process sample using a proven method for which you have already calculated the standard deviation of the method. It would be correct to say that your single value has a 95% probability of being within 2 of the true value. This is called the 95% confidence limit.For example, with = 1 unit and a single measurement of 100 units, we can state with 95% confidence that the true concentration is 100 2 units (2), i.e., 98 to 102 unitsWe can also state with 99% confidence that the true concentration is 100 3 units (3), i.e., 97 to 103 units.If we make such statements many times, we will be wrong about 5 times per 100 (at 95% confidence limit) or only about 1 time per 100 (at the 99% confidence limit)

ExerciseYour established analytical method has = 0.5 ppm and you obtain a single measurement of 8.0 ppm. How would you report to your boss the true concentration of the sample using the 95% and 99% confidence limits?

SPC FOR CHEMISTS

s i = standard deviation of averages of subgroups (sets) of sampless xi = standard deviation of a group of single samplesn = number of samples in the subgroup

7

QUALITY CONTROL CHARTSWhere Control Charts are Used: incoming raw materials, e.g., assay, delivery time, errors in orders the process itself, e.g., concentration of impurities, production rates maintenance, e.g., repair time, corrosion/wear rate of tanks marketing/sales, e.g., customer complaints, product delivery time laboratory, e.g., concentration of secondary standards, recovery on spikes/standards every where in manufacturing and research industries

Types of Variation:Special Causes (bias)temporary, assignable, fixable, e.g., seasonal effects instrument calibration is off ‘off-spec’ raw material

Common Cause (random)continual, chronic, system, e.g., poorly trained worker fluctuations in machinery normal variation of ‘on-spec’ raw material

How to Reduce Variation:Fundamental Point: Special causes and random causes of variation are treated differently.Juran’s 85% Rule: 85% of variation is random error in the system and can only be remedied by management make changes to the system. 15% of variation is special cause and is fixable by the worker.

Steps in an SPC Program:1. Identify the cause of variation in order to remedy it. This is not always obvious; often it is

elusive because manufacturing operations are complex - many interrelated variables. Statistical Control Charts distinguish between Common causes and Special causes of variation.

2. Remove special causes, e.g., recalibrate the instrument, store standards to minimize deterioration, etc. Once a process is free of special causes, it is said to be STABLE even though it still has variation due to random causes.

3. Estimate the Process Capability.4. Establish and carry out a plan to monitor, improve and assure the quality of the process, e.g.,

charting, maintenance, training and record keeping, in order to constantly and forever reduce variation.

Usefulness of Control Charting:1. detects special causes of variation2. measures and monitors common causes of variation3. know when to look for problems and adjust or when to keep hands off4. know when to make a fundamental change.

Setting up an Xi Chart (Individuals Chart):It is generally recommended that one standard (xi) be run with each batch of samples or if large batches are run simultaneously, one standard for each 10 - 20 samples. When 20 - 25 analyses of standards have been gathered, calculate and sx.On suitable graph paper (or a predesigned SPC chart) construct a chart with the y-axis as concentration and the x-axis numbered sequentially (sample #'s or dates)Draw horizontal lines across the chart as follows…

SPC FOR CHEMISTS8

1. a solid line at y = (mean)2. a dashed line at y = + 3sx (upper limit of xI values, called Upper Control Limit, UCL)3. a dashed line at y = - 3sx (lower limit of xI values, called Lower Control Limit, LCL)After calculating UCL and LCL ( 3sx), see if any points exceed these limits. They should not be included in constructing the Xi chart limits as these points due to special causes (not common) and will skew the chart. Discard these out of control points and calculate new values for , sx, UCL and LCL. This is not cheating.Again check the data to ensure that all data lies within the new UCL and LCL. If not repeat the discarding and recalculating of data until all points are within UCL and LCL.If you repeatedly cannot draw a control chart with all data within the limits, it indicates that the process is out of control, plagued with special causes of variation and you cannot utilize a control chart until you eliminate these special causes. Recall that only 1 result per 100 should lie beyond the control limits, i.e., >99% of all data lies within 3sx if random variation is the cause. Such a process (or data set) is said to be IN CONTROL.If data exceeds the control limits more frequently, this is due to special causes of variation and the process (or data set) is said to be OUT OF CONTROL.

Using and Interpreting Xi Charts:1. Continue to plot new data on the Xi chart in real time (as the data is measured/collected).2. Circle any data points that are out of control (out of the limits). Any out-of-control point

should be immediately suspect for special causes of variation and investigation undertaken.3. Check for special causes (bias) if…

a) 7 or more consecutive points are on the same side of b) 7 or more consecutive points are rising or falling

Periodically calculate the and sx for a new set of data (minimum 25 points). If it differs from the values first calculated, draw new lines for , UCL and LCL forward from that point.

Charts:When standards (or samples) are analyzed in replicate (duplicate, triplicate, etc.) each time period (day, shift, etc.) an chart is constructed. This is the same as an X i chart except that each point ( I) plotted on the chart is the average of several data points (called a subgroup). one point per period is a subgroup size of n = 1 (this generates an Individuals (XI) chart) two points per period is a subgroups size of n = 2 three points per period is a subgroup size of n = 3, etc.

is simply the average of all subgroup averages ( I)

UCL and LCL for charts are calculated as 3 , where = average standard deviation. That is, for each subgroup of data (e.g., each day's data) a standard deviation is calculated (sx). The average standard deviation ( ) is the arithmetic average of sx for all subgroups.

A simpler method for constructing XI and charts is discussed later.

Range Charts (R charts):Range is the difference between the highest and lowest data points in a group.

SPC FOR CHEMISTS9

Control charts are constructed with a range chart immediately below the Xi or chart.When more than 1 data point per day is analyzed and I values are plotted on an chart, the range is the difference between the highest and lowest xI in that period (subgroup).When only 1 data point (xI) per period is plotted on the Xi chart then a 'moving range' can be plotted on a moving range chart. The moving range is the absolute value of the difference between (usually) two consecutive xI values, e.g., between today's reading and yesterday's reading. Moving range charts will have one less point than the corresponding Individuals chart.

Constructing an R Chart:

1. Calculate the arithmetic average of the ranges & draw it as a solid horizontal line

2. UCLR can be calculated as 3sR (like UCLx) but more often it is calculated using a formula derived from the normal distribution, i.e., UCLR = D4 , where D4 is a factor obtained from tables used in constructing control charts. UCLR is drawn as a dotted line on R charts.

3. LCL is often not used for range charts, rather the zero line serves as LCL.

R Charts:Advantages:Range charts can be used when no XI or chart can be constructed for example, when standards are unavailable or too unstable to retain and analyze repeatedly. Instead the actual unknown samples are split and analyzed in replicate and the range (xlargest - xsmallest), R values, and UCLR are calculated and plotted on an R chart.Disadvantage:Range charts do not detect bias (special cause variation) because this is cancelled out when the difference between analysis is calculated, leaving only random (common) causes of variation. The range chart shows the precision of the values.

Constructing Control Charts - The Shortcut Method:In order to simplify control chart construction (avoid calculating standard deviation) various factors can be used. For example, for an and R chart, the following calculations apply.UCLx = + A2 UCLR = D4LCLx = - A2 LCLR = D3

and are the arithmetic averages you calculate from your data sets.A2, D3, and D4 are read from tables (see SPC manual)Select A2, D3, and D4 according to the subgroup size (n) of the data set and the type of chart being prepared. For example, duplicate standard analysis each day corresponds to a subgroup size of n = 3 and in this case an chart can be prepared using the following factors…for n = 3: A2 = 1.693 D4 = 2.574 D3 = no valueNote that factors A2, D3, and D4 are calculated from a perfect Gaussian distribution. UCL and LCL calculated from these factors will exactly match those calculated from 3 only when the data is also normally distributed, randomly sampled and many data points are averaged. Otherwise some differences will occur. In most cases the differences will be negligible.

ExerciseThe tabulated data are measurements of Fe content (ppm) in anhydrous HF. The subgroup size n = 3. Use the data to perform the following tasks.a) Calculate the control limits for an and chart.

SPC FOR CHEMISTS10

b) If there are any out of control points assume they are related to special causes and recalculate the limits.

c) What happened to the control limits as out-of-control points were removed?d) Plot a control chart of the data once all of the points are in control.

Subgroup Average Range Subgroup Average Range1 298 34 11 251 802 282 40 12 250 83 211 127 13 258 1004 220 81 14 286 1105 233 95 15 255 936 319 33 16 223 1327 380 219 17 285 1348 214 60 18 292 2369 275 90 19 255 8710 182 55 20 298 45

a) A2 = …………. D3 = ……………. D4 = ………………

= …………. UCLx = ………… LCLx = ………………

= ………… UCLR = ………… LCLR = ……………..

Process Capability (Capability Index):Process capability (Cp) is simply the ability of a process to meet a customer's product specification (assuming the process is centered on target). A process must be in control (random variation only) before Cp can be calculated.

= the standard deviation established from previous shipments (the process history).

6 = the range of concentrations which included 99.7% of all previous shipments.

If the process is not centered (on target), the process output will be less than its ‘capability’ indicates. It is possible to have an excellent Cp but produce 100% NC product.

ExerciseA customers specs for hydrofluoric acid = 70.0 - 72.0 % HF. Previous product shipments averaged 71.0% with a = 0.333. Calculate the process capability for meeting the customer's specification.

If Cp = 1, then the supplier can meet the customer's specification on 99.7% of the shipments.

If Cp < 1, then the supplier can produce off spec. material (more than 0.3% of the shipments).

If Cp > 1.33, then the process can demonstrate 99.999% conformance to customer specs.

SPC FOR CHEMISTS11

North American auto makers generally require that their suppliers maintain a Cp of 1.33

Capability Ratio: (CR) is simply the inverse of Process Capability. For example, a Cp of 1.33 is equivalent to a CR of 1/1.33 = 0.75. A Capability Ratio of 0.75 means that the process spread occupies 75% of the tolerance. The lower the CR the more capable the process.

CPU, CPL and Cpk:

CPU is the ‘Upper Process Capability’, i.e., the process capability to meet the upper spec. limit.

CPL is the ‘Lower Process Capability’, i.e., the process capability to meet the lower spec. limit.

Cpk is equal to the lower of CPU and CPL. Cpk is a better measure of process capability than Cp of CR since Cpk takes into account the actual process center compared to the target.

For 1-sided specifications: Calculate CPU for specifications which are maximums and calculate CPL for specifications which are minimums. In such cases, both CPU and CPL may be referred to as Cpk since they are numerically equal.

One-sided specifications are common in the chemical industry where a customer's specification is a maximum impurity (spec. = 25 ppm As) or minimum assay (spec. = 50 % NaOH).

ExerciseCalculate the process capability for the following data.

1. Arsenic determinations on past shipments average 19.0 ppm with = 2.0. The customer's specification is 25 ppm max. Calculate the capability of the process in meeting the spec.

2. NaOH assay of past shipments averaged 51.0% with sx = 0.50. The customer's spec. is 50.0% min. Calculate the capability of the process in meeting the spec.

SPC FOR CHEMISTS12

PRINCIPLES FOR CONTROL CHARTING IN A CHEMICAL PROCESS/LABORATORY:Suggestions for what should be charted: Chart the concentration of key reagents (those used to certify product shipments), i.e.,

secondary standards, e.g., 1.0N NaOH for acidimetric titration. Normality is routinely checked against primary standard (e.g., KHP). Normality changes of stock reagent are posted and causes for change are investigated, e.g., different analyst (different technique), deterioration of reagent (NaOH absorbs CO2 - Nitrogen pad NaOH reagents)

Known standards are run with each batch of product samples. Of course this is done for calibration of spectrophotometers, etc., however the instrument reading (e.g., Absorbance) of the standard is also plotted on a control chart. This may reveal trends or fluctuations in method, technique or instrumentation which can be investigated and rectified. The R chart will show the common cause variation of the method and the chart will reveal special cause problems. Charting shows trends that are not apparent from raw data.

Chart analysis of a finished product. This will allow determination of Cp or Cpk. This also gives the range of the assay of the product. Customers want this info. You must decide which parameter to plot. A typical product certification may have 8 to 10 parameters (specifications). You probably don't have time to plot all parameters. Discuss with the customer/management which parameters are critical, e.g., concentration of main component and certain impurities (H2O, As, Fe, SO4

-2, PO4-3, H2SiF6, grease, color, particle size distribution, etc., etc.)

Chemical process operators will chart variables of the chemical process, e.g., furnace temperature, reboiler temperature on the distillation column, pressure on carbonating tower, etc. With modern computer-controlled processes pressure, temperature and flow readings are continuously fed to data processing software which immediately plots and displays data in control charts for the process operators. By monitoring the process (not just the product) quality control is achieved by prevention rather than detection. Operators can distinguish between common causes and special causes of variation. They are quickly alerted to special problems and can begin to investigate and adjust the process. In response to random variation an operator will know when to just allow the system to fluctuate naturally. It avoids a common operations error called 'over controlling'.

Who Decides and Who Does the Charting?:Ultimately management is responsible for the QC system. However, management will involve employees representing many areas of the process. Often a company will establish a quality team made up of key members such as an internal quality assurance officer, an SPC specialist, a process engineer, a laboratory foreman, a process operator, a maintenance foreman, etc. This group will usually make key decisions as to where charting would be most valuable. The process operators must have significant input into what measurements will be taken (how often and when) since the operators are usually the ones to take measurements and plot the data. The operator must be trained to interpret the control chart so they can respond to the chart results and improve the process.

Some Benefits of Control Charting:It is often found that control charting gives operators greater better process control, increased accountability to management, greater pride in his/her work. It gives credibility to the operator's recommendations to management re: the need for repairs.Many industries must be able to demonstrate process capability in order to win and keep customer contracts. The ISO and QS standards have gained world-wide recognition in recent years and as a result many companies have invested considerable resources toward QA/QC (training, quality specialist positions, and equipment).

SPC FOR CHEMISTS13

TOOLS FOR QUALITY IMPROVEMENT:Organizational:1. Flow chart2. Cause and Effect (fishbone, Ishikawa) diagram3. Check Sheet 4. Pareto chart

Statistical:5. Time-ordered plot (run chart)6. Histogram (dot plot)7. Statistical control charts (variables & attribute charts)8. Scatter plot

Flow Charts:Purpose: show parallel and sequential operations in a logical figure and show a graphical representation of dependencies.

They are commonly used in manufacturing processes to show the flow of material through a plant. They may also be used to track paper work and action sequences associated with delivery of a service, e.g., delivery of a product, delivery of a certificate of analysis to a customer, etc.

Operations are classed as either bottleneck or non-bottleneck

A bottleneck operation can have less than or equal to capacity

A non-bottleneck operation has capacity that exceeds demand

Flow chart principles:

1. The cost of operating a bottleneck is equal to the cost of operating the whole system, since time lost at a bottleneck is time lost to the whole system.

2. Increased productivity for the bottleneck is increased productivity for the whole system

3. Time wasted or lost at a non-bottleneck is of no consequence, since, short of a completed and total breakdown, it will have absolutely no impact upon the throughput of the system.

4. Time saved at a non-bottleneck is worthless since it does not translate into increased productivity for the system as a whole.

(Source: Wheeler & Chambers: Understanding Statistical Process Control, 1986)

Conventions used in drawing flow charts:

circle = starting point

box = action taken

diamond = decision point

trapezoid = end of process

rectangle with rounded sides = discussion point, meeting, phone call, etc.

Draw a flow diagram for getting to work in the morning.

SPC FOR CHEMISTS14

Cause and Effect Diagrams: (Fishbone/ Ishikawa diagrams)

Most people are overwhelmed by the number of factors that are possible problem causes. Dr. Kaoru Ishikawa used a ‘fault tree’ approach to organize information.

Procedure:

Brainstorm: gather together many different people closely associated with the process Everyone is encouraged to contribute No discussion, evaluation or criticism of suggestions at this stage Suggestions not limited to factors in participants own work area Concentrate on eliminating the problem; don’t excuse the problem

After a list is generated, like items are combined in separate lists, redundant items are eliminated and voting is carried out to prioritize the remaining items.

Construction of Diagram:

1. Choose the problem. Write it at the end of a horizontal arrow2. List all factors that influence the effect3. Arrange and stratify factors: use principal factors as branches. Consider the main

categories of variation in a process, i.e., machinery, materials, methods, measurement, environmental factors, and people

4. Draw stems to branches for various sub-factors5. Check diagram to see that it is complete.

Diagram Analysis: - For each factor…

1. Is there any record of this cause2. Is the factor directly/indirectly controllable3. Is there a control chart4. Is the factor variable or attribute5. Does it affect bias or precision6. Has the factor been standardized (Is there a quantified relationship between the factor &

the product quality)7. Does it interact with other factors

Summary: A framework for collective efforts and for tracking progress.

Draw a cause-and-effect diagram for reasons for poor grades in organic chemistry course.

The Check Sheet: (e.g., product shipment problems)

This simple tool allows one to gather data needed for various decision tools. Commonly, the vertical axis is the problem(s) encountered and the horizontal axis is a time scale. Inserting a check mark each time the problem appears gives the frequency of the problem.

SPC FOR CHEMISTS15

Mon. Tue. Wed. Thurs. Fri.

Product off spec.

Low Production

Pareto Chart: - When several causes of NC’s are identified, which should be remedied first?

Focuses attention on problems offering greatest potential for improvement, i.e., separates the ‘vital few’ from the ‘trivial many’

Such focus is necessary due to money/manpower limitations Helps eliminate distractions, individual agendas Must also apply common sense. In some cases, the most frequent problem may not be the

most costly or most critical, e.g., solving one or two customer complaints may have greater payoff than solving the most frequent problem.

Construction: Constructed like a dot plot or histogram: Y-axis is number of occurrences, X-axis is various

causes. Is basically a vertical bar graph Easily drawn using spreadsheet software, e.g., MS Excel – bar graph Occasionally drawn as a pie chart.

SPC FOR CHEMISTS16

CAUSES

NU

MB

ER O

F O

CC

UR

REN

CES

REASONS FOR BEING LATE TO CLASS

PIE CHART

Time-ordered Plots (Run Charts):Simple plots of data in the order taken can often reveal trends and/or shifts that are not apparent form tabular data. Data trends, shifts, cycles become apparent. Often the time at which a problem appeared is identified.

Dot Plot or Histogram:Reveal the type of distribution, e.g.,, normal, skewed, bimodal, other.

This distribution appears normal. Special causes of variation are probably not present.

SPC FOR CHEMISTS17

ppm

PO

4-3

DATE

PO4-3 MIDPOINT

FREQ

UEN

CY

Statistical Control Charts: Variables charts: X & R, X & s, individuals and moving range, median charts

Attributes charts: p chart (proportions faulty), np chart (number faulty), q chart (proportion good), c & u charts (faults per unit)

These are covered elsewhere in the notes or the Big 3 SPC manual

Useful in operating a process, signaling presence of special causes of variation, and assessing process capability. They do not identify the cause of the variation. Other tools are needed.

Scatter Plots:These plots reveal interrelated effects. They may help identify the cause of a variation. For example, you are trying to determine why the absorbance of your 10ppm standard solution varies from day to day over a long period of time. Plot absorbance values vs. suspected causes.

SPC FOR CHEMISTS18

Abs

orba

nce

1.2

1.0

1.4

.8

.6

Abs

orba

nce A vs. Analyst

Tom Pat Jim Joe

The scatter plots reveal no clear relationship between absorbance variation and any particular analyst or shift, however a strong relationship is indicated between lab temperature and absorbance of the 10 ppm standard.Linear regression may also be used for quantitative data. After entering data (x,y values) into the 2-variable stats mode of your calculator, display the ‘r’ value, i.e.,. the correlation coefficient. This will be a value between –1 and +1. r = +1 indicates a perfect direct

(positive) correlation r = -1 indicates a perfect inverse

(negative) correlation r = 0 indicates no correlation

1.2

1.0

1.4

.6

A vs. Shift

Days Afternoons Nights

.8

Abs

orba

nce A vs. Lab Temperature

22 24 262018

Lab Temp. ( C )

1.4

1.2

1.0

.8

.6