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1/8QUALITY PROGRESS I JUNE 2006 I 25

Use SPC forEveryday Work

Processesby Greg Gruska and Chad Kymal

tatistical quality control (SQC), also

known as control charting, started withWalter Shewharts work at the WesternElectric plant outside Chicago in the 1920s.

Since then, SQC has been reintroduced intoindustry every couple of decades or so and has

evolved into statistical process control (SPC) to

reflect the move away from product control to asystems focus.But why must SPC be periodically revitalized?

If it is all people say it was and is, shouldnt it beself-sustaining? Partly the problem is that if timesare good, management focuses not on economiccontrol but on volume control. So we see manyorganizations embracing SPC only during times oftrouble. When times are good, the attitude is Wedont have time for such luxuries.

Even organizations that implement SPC as part oftheir continual improvement efforts fail to sustain

its use, sometimes because the results of applyingSPC to processes have a variation model differentfrom the one shown in most books. It is a case ofusing the right toolbox but the wrong tool.

To help organizations use SPC tools the rightway, the Automotive Industry Action Groupssupplier requirements task force, representingGeneral Motors Corp., Ford Motor Co. andDaimlerChrysler, recently released a second edi-tion of its SPC Manual.1 The entire first chapterexplains the philosophy and use of SPC, main-taining it should not be applied to processes but

integrated into an organizations continualimprovement activities.

S

In 50 WordsOr Less

Theoretically, statistical process control (SPC)

is viewed as useful for economically producing

consistently acceptable products and services.

In practice, however, SPC isnt being used for

continually improving unique industrial

processes.

The right tools, such as advanced charts, can

make SPC effective in these situations.

STATISTICS

Use SPC forEveryday Work

Processes


2/8

The edition discusses a useful three-stageimprovement cycle for integration (see Figure 1):

1. Analyze the process.2. Maintain (control) it.3. Improve it.

Deployment Shortcomings

Despite the advantages of SPC, why have manyorganizational implementation efforts not beensuccessful or self-sustaining?

Many of the contributing causes have nothing todo with the underlying methodology but with theorganization and deployment. Some examples fol-low.

Constant change. SPC assumes the process con-trols maintain the common cause variation system.All too often this is not possible because there areongoing changes to the process resulting from:

Special causes of variation. Physical changes to the processwith the

intent of improving it. Administrative changes to the control activi-

ties for logisticalor whimsicalreasons. Changes in management direction regarding

what is desired or needed.Change is a necessary element of continual

improvement, but it must be within a plan-do-study-act cycle, not haphazardly applied withoutan understanding of its impact.

Right idea/wrong tool, or not understanding

the physics of the product and process. ApplyingSPC without understanding the physics of theproduct or process and the dominant sources ofvariation will lead to frustration among both oper-ators and management. Much of this happens

because most people have been exposed to onlybasic SPC control charts.

Although the four basic variable charts and fourbasic attribute charts are applicable to a wide vari-ety of processes, advanced charts are better suitedto many processes. The term advanced does notnecessarily imply the use of more sophisticated sta-tistics. Often, these charts are a modification of

basic charts for specific conditions of the process tooptimize the detection of special causes.2

If they use the wrong charts, the operators willnot see any benefit from the extra work necessaryfor the SPC implementation, and management willstill see inconsistencies in the process output.

Limited understanding. SPCs application isoften limited to processes similar to the examplesprovided in an SPC class. But SPC can be useful in

a wide variety of sectorsoutside manufacturing.Within healthcare, manyorganizations such as the

Joint Commission on Ac-creditation of HealthcareOrganizations and theInstitute for HealthcareImprovement have recog-nized the need to under-stand common and specialcauses of variation and theuse of SPC in process analy-sis. This goes beyond ad-ministrative processes toalso include clinical pro-cesses and improvementactions.3

Lack of patience. Evenwhen the SPC deploymentis the right idea using the

right tool, management andworkers seem to expect

26 I JUNE 2006 I www.asq.org

STATISTICS

SPC Improvement CycleFIGURE 1

1. Analyze the process Determine what the process

should be doing.

Determine what can go wrong.

Determine what the process is doing.

Achieve a state of statistical control. Determine capability.

2. Maintain the process Monitor process performance.

Detect special cause

variation and act on it.

3. Improve the process Change the process to better

understand common cause variation. Reduce common cause variation.

Plan Do

StudyAct

1

Plan Do

StudyAct

2

Plan Do

StudyAct

3



instant gratification. When they dont immediatelyobserve consistency and improvement, manage-ment may withdraw support or workers may notfollow through.

Assumptions

W. Edwards Deming taught us the role of man-agement is to make predictions.4 The purpose ofSPC activities is to enable management to predictthe future state of a process by identifying andameliorating special causes of variation. For SPC to

be implemented effectively, some assumptionshold:

Variation and interdependencies exist in allthings.

Few systems and processes are constantly sta-ble.

When applying the basic control charts, real-ize the process being analyzed, monitored orcontrolled must be a purely random (or whitenoise stochastic) process.

A random process satisfies:

A common deviation from the standard assump-tions lies in processes with outputs correlated witheach other. Some include stamping, machining thatis tool wear dominant, chemical processing, thestock market and an individuals medical readings(for example, temperature, blood sugar level and

blood pressure).

These processes are called stationary processesand satisfy:5

This is also called an autoregressive process or aprocess with autocorrelated data.

The Shewhart chart control limits and the stan-

dard calculations for capability indexes depend onthe assumption of a white noise process. Stationary

E [ t ] = x t = x for allt.

t

kt 1

with the correlation between xand x equals .

tx for allt.Var ( ) = 2t =

2

E [ t ] = t = for allt.

t t kis uncorrelated with for all k.

for allt.V (t) = 2t =

2ar

is not enough. It sometimes can be difficult to dis-tinguish between a white noise and a merely sta-tionary processin fact, the white noise process isoften called a weakly stationary process.

Several charts can monitor and control a station-ary process:

Autoregressive charts. These include the autore-gressive, and autoregressive and moving averagemodels. This approach seeks to model the underly-ing relationships among the process output valuesand use this knowledge to better identify otherspecial causes of variation.

Cumulative sum (CUSUM) and exponentially

weighted moving average charts (EWMA).

Although the CUSUM and EWMA were devel-oped to detect small shifts in the mean in randomprocesses, they are robust enough to handleprocesses with minor autocorrelation.

Individuals (I) and moving range (MR) charts.

If the within subgroup variation is less than orequal to the discrimination of the measurementsystem appropriate for the process, an I and MRchart may be a suitable way to control the processvariation. However, very strong autocorrelationmay still display itself in a nonrandom pattern.

Structured samples. If the source of the autocor-relation is a consistent and predictable specialcause, the selection of the sampling quantity andfrequency should reflect this dominant source ofvariation. For example, if the process is material

Upper specification limit

Lower specification limit

Time

Rapidly Drifting Process CenterFIGURE 2


4/828 I JUNE 2006 I www.asq.org

dominant, the sampling should occur wheneverthe material changesfor example, with thechange of coils.

Structured charting. If the source (special cause)of the autocorrelation is predictable, it is possible

to control the process by segregating the withinsubgroup variation from the between subgroupvariation on separate charts. The between-withinchart uses an I and MR chart approach and the typ-ical range chart:

The I chart plots the subgroup averages asindividuals against the control limits based onthe moving ranges.

The MR chart plots the between subgroupvariation using the moving ranges based onthe subgroup averages.

The rangeor standard deviationchartplots the within subgroup variation (commoncause variation).

How Common Are Common Causes?

Shewhart charts require the center of the processto remain constant over time and the variation dueto only common causes for process behavior to bepredictable.

However, one type of special cause is not part ofthe common cause variation but, within bounds, ispredictable. This type of cause is often called aneconomically allowable special cause (EC), becauseonly minor cost benefit results from its elimination.Another name for this type is environmental cause.

If the EC has a consistent and predictable behav-ior, the behavior of the total process variation canalso be predicted within bounds. If the EC is incon-sistent or exhibits chaotic behavior, the controlmethods in the example that follows will not beeffective.

A classic example of a process with an EC is ascrew machine. In this process, the tool wear israpid. Figure 2 (p. 27) is an example of a rapidlydrifting process center, often evident within thespan of a single shift. Because of this EC, the processcan have additional variation caused by setup varia-

tion.Organizations often use conventional control

limits, with the process center forced to be at themidpoint of the specification limits. This can resultin overcontrol and decreased productivity.

A screw machine is used to manufacture smallshafts. The shafts are produced continuously onthe same machine by two shifts per day, six daysper week. The measurement under study is the flatwidth of the shaft spindle.

The process center m increases rapidly as themachine tools wear. The process may run for an

entire eight-hour shift before tool maintenance isrequired. The process standard deviation, !X,remains fairly constant during the course of a toolwear cycle.

Once the effect of tool wear is removed, there isstrong evidence the product measurements are

being generated by a white noise process.The objectives of the control plan are: Keep tool change time to a minimum. Minimize operator overcontrol. Maximize the length of the tool wear cycle. Ensure the process remains in control once the

tool wear variation has been taken intoaccount.

STATISTICS

68

64

60

56

520 10 20 30 40 50 60 70 80 90 100

Averageforsample

Sample number

Sample AveragesFIGURE 3

Allow the operator to stay as

close as possible to traditional

Shewhart procedures.



Minimize the probability of producing a non-conforming part.

The first step in trying to meet these objectives isto realize once again the fundamental equation ofprocess control must be revised in this situation toread:

Total variation = common cause variation + toolwear variation + other special cause variation.

Isolate and measure tool wear variation sepa-rately from other sources of variation. Understandthe trade-off between long tool wear cycles and theneed to deal with fussy tool change problems.Allow the operator to stay as close as possible totraditional Shewhart procedures.

How To Do It Right

The first step in dealing with toolwear trends is to collect the right kindof data. For this process the approachselected is:

Draw samples of size three onceevery 675 pieces, which keeps thesampling frequency close to itsoriginal value of a sample onceevery hour.

Use a pan holding approximately

675 pieces to determine when asample needs to be drawn.The values from the first 101 samples are

shown in Figure 3. Each dot represents the averagefor a sample of size three.

It is difficult to see tool wear cycles in these data.Examination suggests tool wear trends in the firstpart of the data. These trends can be highlighted byremoving the lines connecting the last point in onecycle with the first point in the next cycle.

Extensively annotated control charts providedby the operators helped identify individual cycles.

It was determined most of the later data were notcollected under the proper conditions and couldnot be used for estimating tool wear.

Tool wear patterns lurking in the data emergeonce extraneous lines and dots are removed (seeFigure 4).

The first step is to determine whether the tool(the special cause) is consistent over time (tool-to-tool variability is predictable). To find a common

60

62

58

56

54

520 1 2 3 4 5 6 7

Averagevalueof

subgroupreading

Sample number (675 pieces per pan)

Slope = 0.7962

Superimposed Patterns WithRegression Line and X-bar ChartFIGURE 5

Subgroupaverage

Subgroup or time

Random SampleFIGURE 6

68

64

60

56

520 10 20 30 40 50 60 70 80 90 100

Averagevalueof

subgroupreading

Sample number

Sample DataFIGURE 4



trend in the various tool wear patterns, all cycleswere superimposed and a single simple linearregression model was fit to the entire collection oftool wear trends (see Figure 5, p. 29).

The regression model explained 77% of thedatas variation. The unexplained variation

exhibited the properties of white noise.The tool wear slope of 0.7962 was estimated

using a simple linear regression model. This regres-sion model also estimated a standard error of0.0571 for the slope coefficient. Three standarderror tool wear growth limits can be calculated by

(3 x .0571) applied to the expected aver-age line.

When someone is manually controllingprocesses with a tool, he or she can lay atransparency of Figure 6 (p. 29) on top ofthe control chart.

The control limits in Figure 5 (p. 29) arethe same as those in a conventional X-barchart except they follow the average toolwear line rather than a horizontal center-line. This approach requires the specialcausetool wearto exhibit a predictableand consistent behavior, which requirescontrol by the supplier and purchasing.

The second step is to verify and quanti-fy the tool wear behavior over time bystudying a random sample of tools overtheir life (see Figure 6). This may require100% sampling if the tool life is short.

This analysis must determine whetherthe expected tool life pattern and commoncause variation are consistentand thuspredictable. Then this information should

be used to establish process control chartsto control the process variation and toolwear variation (see Figure 7).

As confidence is gained in the process,the diagonal control charts can be replaced

by I charts monitoring specific tool life fea-tures (see Figure 8):

Setup control. Ensures the setupthestarting point of the process trendofeach tool is consistent. This, with thechange control, also determines thecapability indexes of the process.

Wear control. Ensures there is nochange in the tool life model.

Change control. Ensures the usefullife of the tool has been reached andthe end life model of the tool has notchanged. This, with the setup control,

also determines the capability indexesof the process.

STATISTICS

Subgroupaverage

Subgroup or time

Control ChartFIGURE 7

Change control

Wear control

Setup control

Features

Controlling FeaturesFIGURE 8

Change control

Expected number of parts

Setup control

Controlling FeaturesContinual Improvement

FIGURE 9



As confidence in the process andtooling increases, monitoring can usethe tool life or number of parts before arequired change (see Figure 9).

In this stage of the continual improve-ment process, there is confidence thetooling wear trend will be consistent andacceptable due to the actions of the sup-pliers of the tooling and materials. Theneed for redundant inspection can beeliminated.

As confidence in the process andtooling further increases, monitoringcan use the tool life and periodic sys-tems audits (see Figure 10).

Based on process knowledge gained,there is confidence the tooling weartrend and life will be consistent andacceptable due to the actions of thesuppliers of the tooling and materials.The need for redundant inspection can

be eliminated.In the final stages, setup control

moves offline, and control uses thetool life or block tool change (seeFigure 11).

In this stage of the continual improve-ment process, there is confidence:

The tooling wear trend and lifewill be consistent and acceptabledue to the actions of the suppliersof the tooling and materials.

The variation caused by the machine will beconsistent and acceptable due to preventivemaintenance.

Setup consistency will be controlled by offlinesetup activities.

The need for any online inspection can be elimi-nated. This does not eliminate the need for period-ic system and product audits to verify the processcontrols are still valid or ensure an unknown spe-cial cause hasnt crept into the process.

At any stage, the controlling cycle must restart if: The tooling exhibits erratic behavior. A different vendor begins to supply the tool-

ing or material.

Other Types of Control Charts

The new edition of SPC Manual discusses the

need to understand the underlying model of vari-ation and physics of the process. To enable thereader to select the appropriate tool for a specificprocess model, the manual includes sections onthe following charts:6

Probability based charts. Short run control charts. Charts for detecting small changes. Non-normal charts. Multivariate charts. Regression control charts. Residual charts. Autoregressive charts.The manual describes and identifies the use of

each and provides references for further study butprovides how-to instructions only for the basiccharts.


Setup control

Controlling FeaturesFurther Continual Improvement

FIGURE 10


Offline

setup control

Controlling FeaturesContinualImprovement Final Stage

FIGURE 11



STATISTICS

Warnings

It is important to understand the real meaningof random. Selecting a random sample requiresspecific techniques.

In practice, many people think blind selectionis random selection. In reality, this may be hap-hazard or convenience sampling. Using haphaz-ard or convenience sampling when randomsampling is required can lead to biased andtherefore erroneous conclusions.

SPC is useful and necessary for continualimprovement, but many applications do notrealize its full benefit because they lack knowl-edge of the tools and the processes to be ana-lyzed, maintained and improved.

Although basic control charts, covered in allintroductory SPC courses, have a wide applica-tion to random processes, there also are manystationary processes or ones with predictableECs that need advanced charts or the applicationof a basic chart in a manner reflecting the actualprocess nature.

If the goal is to eliminate the need for chartingby building knowledge of and confidence in theprocess, SPC charts need to be used so organiza-tions can increase their understanding of thecommon causes and special causes affecting theirprocesses. Then they can replace SPC charts withrobust policies and techniques governing processcontrol.

REFERENCES AND NOTES

1. SPC Manual, second edition, Automotive Industry

Action Group, 2005.

2. The SPC Manual, second edition, includes discussion

and references to many of these advanced charts.

3. Improving Heart Failure Care Through

Education, www.ihi.org/ihi/topics/improvement/

improvementmethods/improvementstories/

improvingheartfailurecarethrougheducation.htm.

4. W.E. Deming, The New Economics: For Industry,

Government, Education, second edition, MIT Press, 2000.

5. There are several classifications of stochastic

stationary processes. This example is just one type.

6. The manual does not maintain these are all the

possible charts that can be used. The ones discussed do

cover the majority of situations.

GREG GRUSKA, a Fellow of ASQ, is the vice president of

product development for Omnex Systems and a principal

consultant in performance excellence and a Six Sigma Master

Black Belt for Omnex, Ann Arbor, MI. He directed the devel-

opment and initial implementations of Comprehensive

Process Control Planning, a book published by Omniface

Corp. Gruska is a writing member of the measurement sys-

tems analysis, SPC and failure mode and effects analysis

manual subcommittees of the Automotive Industry Action

Group supplier quality requirements task force, which is part

of the international task force governing ISO/TS 16949. Withmasters degrees in mathematics and engineering from Michi-

gan State University and Wayne State University, Gruska is

also an ASQ certified quality engineer. He has been a mem-

ber of the board of examiners and a judge for the Michigan

Quality Leadership Award since 1994.

CHAD KYMAL, an international trainer and consultant, is

chief technical officer and founder of Omnex Inc. He wrote

the ISO/TS 16949:2002 Implementation Guide and the

Auditor Handbook to ISO/TS 16949:2002A Guideto the Automotive Process Approach to Audits, both

published by Paton Press. He has served on the Malcolm

Baldrige National Quality Award board of examiners and

as an RABQSA certified lead auditor. Kymal has a masters

degree in industrial and operations engineering and an

MBA, both from the University of Michigan.

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