Control Chart with subgroups entering the project at different times

[#1]

We are created a process across 9 different divisions. All the Divisions did not start at the same time. As other Divisions learned of the initial cohort success, they joined the project. In aggregate, by December 2023 we were consistently achieving 93% success. We created a control chart using the Numerators and denominators of all the Divisions participating in each month. Therein lies the run: that the addition of inexperienced Divisions along the journey introduces confounders that may show as special cause variation, where it was just each division catching up to the learning curve of the rest. Are there any ideas on how to present this aggregate data while still being statistically sound from a QI science standpoint? Thanks in advance for any thoughts!

[#2]

Hi @RatioMegalodon8,

Welcome in the Community !

Do the samples for each division were measured on a equivalent time, or do you have strong differences ? For example, division 1 has samples measured from January to October, whereas division 6 has sample measured from May to June.
Do each division has the same number of samples collected and measured ?

I would guess that with the information you provided, you would need to use an Xbar chart, where the average of measurements is displayed for each subgroup (division), as well as an indicator of the spread of the measurement for each subgroup (range of measurements).
You can see in JMP Help an example of an Xbar & R Control Chart and how to launch it.
In case of different groups sizes, there is also a dedicated example.

I still think that besides this control chart, it may also be interesting to dive into the results for each division (using a local data filter to filter results for one division at a time):

• You could run an Individual Measurement and Moving Range Chart (IMR control chart) for each division and check that their process is stable (no sudden big shift in the process).
• To detect small drift in the process for each division, you can use EWMA charts.

I hope this answer will help you,

[#3]

Thanks for the detailed response! Yes, you are correct in that start dates differed but end point for all divisions stayed the same. Sample size was unique to each division as well. We do have individual control charts to elucidate performance but were considering options for aggregate for presentation and system wide purposes. Other thoughts we had didn’t seem the best: starting the control chart when the last division entered w the centerline calculated by all divisions’ performance up that point (including 0’s for last entry since the process was not in place), a control chart that starts from first division entry but includes all divisions (including 0’s for all late arriving divisions until they actually had measurements). Neither are ideal.
Thanks again for anyone’s thoughts!

[#4 · Accepted solution]

Welcome to the community.  What are the objectives for using control charts?  How well do you understand control chart method as described by Dr. Shewhart?  

Control charts are used for 2 specific reasons:

1. To determine if the within subgroup variation (due to the sources of variation changing within subgroup) is consistent/stable therefore predictable, and if those sources are consistent, then

2. To determine which components of variation are most significant by comparing the between subgroup sources of variation (estimated by the averages) to the within sources of variation (the control limits).

Appropriate use of control chart method is completely dependent on rational subgrouping and sampling strategies.  Rational subgrouping and sampling requires the user to partition the sources of variation (components of variation) based on rational hypotheses. Changing subgroup size during the study renders the methodology useless as you are changing the basis for comparison (which x's are varying) during the study.

“The engineer who is successful in dividing his data initially into rational subgroups based on rational theories is therefore inherently better off in the long run. . .”

                                                                              Shewhart

Range charts are used to assess consistency/stability.  The only way to assess consistency is to compare something to itself over time. Hence the range chart assesses the within subgroup variation consistency.

X-bar charts are comparison charts.  They compare the sources of variation captured within subgroup to the sources of variation between subgroup and answer the question which sources have greater leverage on the charted parameter.

If you are not completely sure how the methodology "works", I suggest you read:

Shewhart, Walter A. (1931) Economic Control of Quality of Manufactured Product, D. Van Nostrand Co., NY

Wheeler, Donald, and Chambers, David (1992) Understanding Statistical Process Control, SPC Press (ISBN 0-945320-13-2)

Wheeler also has two papers that are easy to digest:

Wheeler, Donald (2015) “Rational Sampling”, Quality Digest

Wheeler, Donald (2015) “Rational Subgrouping”, Quality Digest

[#5]

Thanks for that thorough explanation. I appreciate your input and references.