A Complete Control Chart Decision Tree

[leaning]

Hello. Depending on what I look at the information is different.

P charts: fixed sample size? varying sample size? both?
X-bar and R: 2-9 subgroups? 2-7? 2-5?
X-bar and S: >7, >9, >10 subgroups?
etc.

Is there a EC-vetted decision chart that captures all or most of the control charts and is more accurate especially with respect to subgroup information: X-bar, Xbar-sub-d, R, r-sub-d, X-bar&R, IX, IX-sub-d, S, MR, I&MR, CUSUM, EWMA, MACC, g charts, run chart, trend chart, etc.?


Thanks for your help!

Regards,
leaning

 

[Miner]

Re: A Complete Control Chart Decision Tree?

P charts: fixed sample size? varying sample size? both? It was designed for varying sample sizes, but will work for both. np charts will only work in theory on fixed sampled sizes, although they will "work in practice" if the sample sizes vary within relatively narrow limits.

X-bar and R: 2-9 subgroups? 2-7? 2-5? X-bar and S: >7, >9, >10 subgroups?etc. Wheeler addresses this in Myth 1 of the linked paper. See page 15 for his summary. In short, it makes no difference whether you use the range or the standard deviation, regardless of the subgroup size. Shewhart used standard deviation before using range, but opted for range because it was easier to calculate on the factory floor. He also recommended smaller subgroup sizes. See Wheeler's latest article.

If by EC, you mean Elsmar Cove, I do not recall a "vetted" decision tree. Why not construct one yourself and submit it here for comment? We would be happy to provide feedback.

 

[AMIT BALLAL]

Re: A Complete Control Chart Decision Tree?

Miner, thanks for the post. It really helped.
I had prepared a comparison chart during an Inhouse training, please have a look and give your comments.



Thanks,
Amit

 

[Miner]

Re: A Complete Control Chart Decision Tree?

Amit,

Your table would match what 95% of quality practitioners and consultants would state.

• Some might quibble over the subgroup size used to prefer r over s. I have seen anywhere from 5 to 10 used as this demarcation. However, I tend to agree with Wheeler's article where the use of XbarR vs XbarS is really a matter of preference, and that the subgroup size is irrelevant.

• The P and C charts will work for varying or constant sample size. np and U charts are simplified versions that are limited to constant sample sizes.
  However, in practice both will work effectively where the sample sizes vary slightly about a constant.

• The I chart (from I-MR) can be used alone. The MR chart adds very little.
  Also, this chart works well with count data once the counts are large enough for the normal approximation to the Poisson distribution to kick in (although Wheeler would probably say that is unnecessary). It also seems to work well with binomial data provided the rates are not close to 0 or 1. It is easy to tell whether the I chart will work on these data types by observing the data plots within the limits. As long as the data do not hug the center line or oscillate wildly outside the limits, it will often work quite well.

 

[AMIT BALLAL]

Re: A Complete Control Chart Decision Tree?

Thanks Miner for your reply. I have some beliefs regarding following concepts, please correct me if I'm wrong, this will help me to improve my understanding of SPC. I didn't know how to use multiquote, therefore identified your quotes and my comments using different formatting.

• Some might quibble over the subgroup size used to prefer r over s. I have seen anywhere from 5 to 10 used as this demarcation. However, I tend to agree with Wheeler's article where the use of XbarR vs XbarS is really a matter of preference, and that the subgroup size is irrelevant.

If we are using a smaller subgroup size, range is good measure of variation. But when sample size is increased, range doesn't show variation accurately because it includes only two extreme values (i.e. Maximum - Minimum) excluding other values. And in this case, standard deviation is more accurate, since it considers all values in a subgroup.

• The P and C charts will work for varying or constant sample size. np and U charts are simplified versions that are limited to constant sample sizes.
  However, in practice both will work effectively where the sample sizes vary slightly about a constant.

Agreed. If the sample size is not varying by large amount, both charts can be used.

 

[Miner]

Re: A Complete Control Chart Decision Tree?

• Some might quibble over the subgroup size used to prefer r over s. I have seen anywhere from 5 to 10 used as this demarcation. However, I tend to agree with Wheeler's article where the use of XbarR vs XbarS is really a matter of preference, and that the subgroup size is irrelevant.

If we are using a smaller subgroup size, range is good measure of variation. But when sample size is increased, range doesn't show variation accurately because it includes only two extreme values (i.e. Maximum - Minimum) excluding other values. And in this case, standard deviation is more accurate, since it considers all values in a subgroup.

From a purely statistical perspective, you are correct. However, Shewhart control charts (and the I-MR chart) are not based purely upon statistics. They were based upon empirical studies and economic decisions that balanced the cost of missing a true signal that the process had changed vs. the cost of chasing a false signal when the process had not changed. Shewhart had considered 2 sigma limits but decided the cost of chasing false alarms was too high and opted for 3 sigma limits (engineers love round numbers).

Wheeler follows in this same tradition by arguing that I-MR charts may be used for non-normal data because despite violating statistical principles, THEY STILL WORK. In the same vein, using range or standard deviation STILL WORKS regardless of the sample size.

The bottom line is that control charts are remarkably robust tools that will continue to work despite violation of the statistical rules that have been imposed by "statisticians" that came along years after the original tools had successfully worked without those requirements.

Non statistical choices such as your choice of how to subgroup have a much greater impact on how successful your chart is than the statistics.