Don't know enough about this process to say for sure if it is appropriate, but another alternative is to use a three-way chart as described in Donald Wheeler's book "Understanding Statistical Process Control".

Agree with the previous post, that 3 way charts (within/between) are a good way to monitor two sources of variation (e.g. within cavity, between cavity).

Also regardless of the presence of other sources of variation between subgroups, individuals charts will always be less sensitive to detecting process changes than will be xbar charts.  Smaller shifts are detectible as the sample size increases.  The inherent potential Type II errors found in Individuals charts seesm to be rarely discussed (assuming we are using SPC to detect small process changes when they occur).

Thanks for your comments:

1. Three-way control charting is applied, for example, when there is variability within a part and several parts are selected within subgroups that are tracked over time using a control chart. This was not the case in the example described; however, the three-way control chart does use an individuals chart of subgroup means, which is similar to the described 30,000-foot-level reporting.

2. Agree that the hypothesis of normality from the probability plot would be rejected for this data set; hence, the estimates of non-compliance will have some associated error because of this. However, even for this extreme example, where there are two distinct distributions, the probably plot does not look as bad as one might initially think from being a straight line; hence, we can still provide a rough estimate of the percentage not conforming. In all likelihood, this non-normality topic would not have been brought up if the capability statement were presented in the article using Minitab’s capability analysis routine, which does not include a normality assessment when providing its process capability reporting. The probability plot non-conformance result noted in the article is the same as what could have been reported using Minitab’s capability analysis routine output "PPM total". Also, the 30,000-foot-level charting approach would lead to the appropriate behavior – understanding what could be done to improve the process.

3. Agreed that the next step that one would take when attempting to reduce the amount of non-conformance in the 30,000-foot-level charting would be to create hypotheses to test out various theories. One theory might create a hypothesis test for assessing variability between days relative to within days, which would be significant. This could then lead to investigation why this is occurring and what might be done to reduce the source of this between subgroup variability. If an improvement were made, the 30,000-foot-level control chart would transition to a new level of stability that had a reduced rate of non-conformance shown in the probability plot. Note how this behavior is quite different than addressing all the special cause conditions that were created using traditional control charts, which could have led to much firefighting.

4. A control charting of standard deviation could have been made without a transformation. The standard deviation would have been in control for this set of data; however, zero would have been within the control limits. Since standard deviation cannot physically be below zero, this leads us to a dilemma. We could have moved the control limit on the lower side to zero; however, there would have been no way to detect if the within-subgroup variability reduced because of a change. A more general approximate approach to address this situation is to take the log of standard deviation. Transformations should be made only when they make physical sense. Since standard deviation can never get below zero, the log-normal distribution is a general, easy to use, transformation that fits fairly well and makes physical sense for this situation.

5. Subgrouping is very important. With 30,000-foot-level reporting, we need to have all common-cause input variability to occur between subgroups.

6. Relative to the type II error comment, the primary goal of a 30,000-foot-level assessment is to not detect small changes but describe at a high level how the process is performing relative to stability and customer needs. When our common-cause variability from this high-level view is not providing what we desire then process improvements are needed. Improvements to the process are then demonstrated when the 30,000-foot-level chart transitions to a new, improved level of stability. Note, this is different than traditional control charting which has a primary intent of identifying when special cause occurs so that these problems can be addressed in a timely fashion.

I wonder wether USA is an acronym for Using Statistical A ...: if Statistix were an effective Tool, its so much intensive use should have resulted in a better World, whatever the meaning of this Statement. Which is not; for many reasons; may be the root cause - or reason - is that Statisitix is like the mythical Panacea - just a myth. Thank you.