Statistical Methods and Control Charts

Analysis, Statistics, Control Charts, Statistical Methods

Question:
My question is regarding a threading process.  There is 100% inspection for go/no go check and about 5% rejection/rework.  The batch size is 5,000 nos and is completed in 3 days of production. Two such batches are produced in a month.

What type of control chart should be used to monitor the process? How should the process capability be calculated in this case?

Answer:
The type of control chart first depends on what type of data you are measuring.  If you are doing go/no go then you are limited to a “P” chart or a “C” chart.  A “P” chart looks at % good (or bad).  A “C” chart looks at the number of defects found.

If you are measuring thickness or strength, (something that can be measured), then you can use a X-bar/R chart or an X-bar/S chart depending on many samples are taken.

That is the simple answer; part of this depends on how you are taking samples and how often.  If samples are taken at the start and the finish, then I would probably recommend the “P” chart.

If you can measure throughout the manufacturing process, and you look at the type of defects, then I recommend a “C” chart.

Ideally, if you can get measurement data, you are better off with the X-bar/R or the X-bar/S charts.  These tend to be better predictors and it is easier to calculate capability.

With the capability for the go/no go data, you can get % defective, (or % good) and multiply that by 1,000,000 to get your capability estimate in defects per million.

Jim Bossert
SVP Process Design Manger, Process Optimization
Bank of America
ASQ Fellow, CQE, CQA, CMQ/OE, CSSBB, CSSMBB
Fort Worth, TX


Additional ASQ resources:

ASQ Learn About Quality- Control Charts

The Shewhart p Chart for Comparisons
by Marilyn K. Hart and Robert F. Hart

Control Chart to Analyze Customer Satisfaction Data

Control chart, data, analysis

Q: Let’s assume we have a process that is under control and we want to monitor a number of key quality characteristics expressed through small subjective scales, such as: excellent, very good, good, acceptable, poor and awful. This kind of data is typically available from customer satisfaction surveys, peer reviews, or similar sources.

In my situation, I have full historical data available and the process volume average is approximately 200 deliveries per month, giving me enough data and plenty of freedom to design the control chart I want.

What control chart would you recommend?

I don’t want to reduce my small scale data to pass/fail, since I would lose insight in the underlying data. Ideally, I’d like a chart that both provides control limits for process monitoring and gives insight on the repartition of scale items (i.e., “poor,” “good,” “excellent”).

A: You can handle this analysis a couple of ways.  The most obvious choice and probably the one that would give you the most information is a Q-chart. This chart is sometimes called a quality score chart.

The Q-chart assigns a weight to each category. Using the criteria presented, values would be:

  • excellent = 6
  • very good =5
  • good =4
  • acceptable =3
  • poor =2
  • awful=1.

You calculate the subgroup score by taking the weight of each score and multiply it by the count and then add all of the totals for the subgroup mean.

If 100 surveys were returned with results of 20 that were excellent, 25 very good, 25 good, 15  acceptable, 12 poor, and 3 awful, the calculation is:

6(20)+5(25)+4(25)+3(15)+2(12)+3(1)= 417

This is your score for this subgroup.   If you have more subgroups, you can calculate a grand mean by adding all the subgroup scores and dividing it by the number of subgroups.

If you had 10 subgroup scores of 417, 520, 395, 470, 250, 389, 530, 440, 420, and 405, the grand mean is simply:

((417+ 520+ 395+ 470+ 250+ 389+ 530+ 440+ 420+ 405)/10) = 4236/10 =423.6

The control limits would be the grand mean +/- 3 √grand mean.  Again, in this example, 423.6 +/-3√423.6 = 423.6 +/-3(20.58).   The lower limit is  361.86 and the upper limit is 485.34. This gives you a chance to see if things are stable or not.  If there is an out of control situation, you need to investigate further to find the cause.

The other choice is similar, but the weights have to total to 1. Using the criteria presented, the values would be:

  •  excellent = .3
  • very good = .28
  • good =.25
  • acceptable =.1
  • poor=.05
  • awful = .02.

You would calculate the numbers the same way for each subgroup:

.3(20)+.28(25)+.25(25)+.1(15)+.05(12)+.02(1)= 6+7+6.25+1.5+.6+.02=21.37

If you had 10 subgroup scores of 21.37, 19.3, 20.22, 25.7, 21.3, 17.2, 23.3, 22, 19.23, and 22.45, the grand mean is simply ((21.37+ 19.3+ 20.22+ 25.7+ 21.3+ 17.2+ 23.3+ 22+ 19.23+ 22.45)/10)= 212.07/10 =21.207.

The control limits would be the grand mean +/- 3 √grand mean.  Therefore, the limits would be 21.207+/-3 √21.207= 21.207+/-3(4.605).  The lower limit is  7.39 and the upper limit is 35.02.

The method is up to you.  The weights I used were simply arbitrary for this example. You would have to create your own weights for this analysis to be meaningful in your situation.  In the first example, I have it somewhat equally weighted. In the second example, it is biased to the high side.

I hope this helps.

Jim Bossert
SVP Process Design Manger, Process Optimization
Bank of America
ASQ Fellow, CQE, CQA, CMQ/OE, CSSBB, CSSMBB
Fort Worth, TX

Related Resources from the ASQ Knowledge Center:

Find more open access articles and resources about control charts in ASQ Knowledge Center search results:

Learn About Quality: Control Charts

The control chart is a graph used to study how a process changes over time. Data  are plotted in time order. A control chart always has a central line for the  average, an upper line for the upper control limit and a lower line for the lower control limit. These lines are determined from historical data. Read the full overview and download a free control template here.

Should Observations Be Grouped for Effective Process Monitoring? Journal of Quality Technology

During process monitoring, it is assumed that a special cause will result in a sustained shift in a process parameter that will continue until the shift is detected and the cause is removed.

In some cases, special causes may produce a transient shift that lasts only a short time. Control charts used to detect these shifts are usually based on samples taken at the end of the sampling interval d, but another option is to disperse the sample over the interval. For this purpose, combinations of two Shewhart or two cumulative sum (CUSUM) charts are considered. Results demonstrate that the statistical performance of the Shewhart chart combination is inferior compared with the CUSUM chart combination. Read more.

The Use of Control Charts in Health-Care and Public-Health Surveillance (With Discussion and Rejoinder), Journal of Quality Technology

Applications of control charts in healthcare monitoring and public health surveillance are introduced to industrial practitioners. Ideas that originate in this venue that may be applicable in industrial monitoring are discussed. Relevant contributions in the industrial statistical process control literature are considered. Read more.

Browse ASQ Knowledge Center search results for more open access articles about control charts.

Find featured open access articles from ASQ magazines and journals here.

Capability Analysis

 

Pharmaceutical sampling

Q: Why is a standard capability analysis determined to be best represented by 30 pieces?

I have answered this question by explaining it best represents a normal distribution. But I wonder if this is traceable to an industry standard?

A: You are right that most people associate 30 pieces with the conventional quantity for performing a capability study.  Although I don’t know the origin of this number, I can tell you the following:

  • The number 30 has nothing to do with whether or not the population is normally distributed.
  • In many applications, the number 30 is insufficient to properly model the process.  For example, automotive industry standards published by the Automotive Industry Action Group (AIAG) in their statistical process control (SPC) and production part approval process (PPAP) documents define 100 pieces as the appropriate sample size for an initial capability study (based on 20 subgroups of five or 25 subgroups of four).

I hope you find this helpful.

Denis J. Devos, P.Eng
A Fellow of the American Society for Quality
Devos Associates Inc.
London Ontario
www.DevosAssociates.com

Related Content:

Statistics in Pharmaceutical Development and ManufacturingJournal of Quality Technology,  open access

An overview is given of the use of statistical thinking and methods in the research and development and manufacturing functions in the pharmaceutical industry. Four case studies illustrate how these issues work in real life settings. A synopsis of these issues concludes that the technical nature of pharmaceutical development and manufacturing offers opportunities for the effective use of statistical methods leading to both process-development understanding and product-quality improvement.

Build a Usable Process Capability Database, Six Sigma Forum Magazine, Open Access

Design for Six Sigma requires that designs meet customer needs without sacrificing quality. A number of statistical tools can be used to produce process capability data to enable development teams to design products that can be produced at reasonable cost on existing equipment. However, setting up and using a process capability database is poorly understood and as a result, it is seldom used. To create a successful database, it is necessary to get management support, build the right data structure, collect the right data, and use the data correctly. A correctly designed database will allow the product development team to focus its efforts only on those tolerances in which the capability is unclear or in which function or cost improvements can be achieved.

Visual Fill Requirements

Pharmaceutical sampling

Q: I work for a consumer products company where more than 60% of our products have a visual fill requirement. This means, aside from meeting label claim, we must ensure the fill level meets a visual level.

What is the industry standard for visual fills?

We just launched Statistical Process Control (SPC), and we notice that our products requiring visual fills show significant variability.

A: This is an interesting question. The NIST SP 1020-2 Consumer Package Labeling Guide and the Fair Packaging and Labeling Act, along with any other industry standards, regulate how you must label a product “accurately.” However, it appears you have been burdened with a separate, and somewhat conflicting requirement —  a visual fill requirement.

In most cases, you probably cannot satisfy both requirements without variability. The laws and standards will direct labeling requirements with regard to accuracy, and your company is liable for that. If you choose to use visual fill standards for “in-process” quality assurance, then you would need a fairly broad range between the upper and lower acceptance limits.

Personally, I would use weights and measures as needed to meet customer and legal requirements. These are the data I would use for SPC records.

If your company has a need (or a desire) to use visual fill levels for a gage, then generating a work instruction telling employees where a caution level is would be a way to start. In other words, “If the visual level is above point A or below point B, immediately notify management.” If you are to remain compliant with what you put on a label, visuals will change from run to run. Using them as a guide for production personnel can be a helpful tool, but not as a viable SPC input.

Bud Salsbury
ASQ Senior Member, CQT, CQI

Editor’s Pick: Hear how Procter & Gamble developed a solution for setting appropriate targets for product filling processes in Setting Appropriate Fill Weight Targets—A Statistical Engineering Case Study from the April 2012 Issue of Quality Engineering.