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

For more information on this topic, please visit ASQ’s website.

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

For more on this topic, please visit ASQ’s website.

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

For more on this topic, please visit ASQ’s website.

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

For more on this topic, please visit ASQ’s website.