EWMA vs CUSUM usage

Question

Any advice or guidelines on when to use a CUSUM vs EWMA control charts?  I searched the net for a little while and couldn't find anything definitive on using one vs the other.

Also, any guidance on how to use them in a production setting when the data is a rolling date range?  And by that I mean the control limits, target and sigma would be set based upon an in control time period but a new set of data would be uploaded each day which would result in a days worth of data being dropped off.  Rolling time periods could be from as little as a week to as long as a quarter.

Thanks for any advice!!

Steve

statman · Answer

I apologize for my sophomoric response, but I want to make sure you understand the use of Shewhart's control chart method (X-MR charts are not diagnostic charts).  The purpose, as originally intended by Shewhart, was to compare sources of variation (components of variation) to determine which source has the greatest effect on the response variable (in control chart language, is the greatest source within subgroup or between subgroup?).  Of course, you are not limited to two layers of a sampling plan and each layer is correlated with a specific set of x's or components of variation. The sampling plan, which will be evaluated by control charts, is of utmost importance.  As you change subgroup sizes, you change what sources of variation are captured within subgroup.  As you change the frequency of taking the samples, you change the sources of variation captured (that can be influential) between subgroup.  Once the greatest source has been identified, continue to use sampling and control charts (or other tools like DOE) to further disaggregate the components and focus on the set of variables that should be investigated to reduce variation.

In order to accomplish the purpose, Shewhart first suggested the basis for comparison must be evaluated for consistency.  In other words, are the within subgroup sources of variation stable/consistent? (is the range chart "in-control"?)  If not, you should seek to understand why.  If those sources are consistent, then a comparison can be made.  The X-bar chart is a comparison chart.  It compares the sources of variation changing between subgroup (visualized as the averages plotted on the x-bar chart, FYI, they are biased to the between subgroup sources as a function of averaging) to the sources of variation captured within subgroup (as visualized by the control limits on the x-bar chart, A2*R-bar).  If the averages are within the control limits, then the within subgroup sources dominate, if there are signals of averages varying more than the within sources (e.g., points out-of-control), then the between sources dominate.  Rational subgrouping and sampling strategies are a key to this methodology working.

“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

The Shewhart control limits were empirically derived.  There is no normality assumption for the use of control charts! They were set to be a guide, possibly conservative, to decision making regarding which sources of variation are most influential.  There are, of course, the Western Electric patterns that can assist in the interpretation of "out-of-control" conditions which can help in the interpretation of which sources dominate.  Ultimately, you will be looking at the data graphically and deciding which sources you believe to dominate (with the assistance of statistics when those decisions are not obvious).

Your supposition of "the control limits, target and sigma would be set based upon an in control time period..."is non-sensical from a Shewhart control chart methodology approach.

Please read:

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

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

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

shampton82 · Answer

Hey @statman ,

I believe so! The goal is to be able to detect a smaller change in the process mean (less than 2 sigma) than can be identified in a timely manner by an I-MR chart.  The best I can tell is that you should use EWMA if the data has normality issues, you want to forecast the next data point, or you want have an indication of autocorrelation (using the residuals chart).  Otherwise a toss up? The data I pull for my control charts is set up to run daily but only for a fixed period of time which is different than all the examples that I read about that were based upon having all the data since the start of the process.

Hope this helps clear up my situation and appreciate any input!

Steve

statman · Answer

Steve, what is the purpose for using the control charts?  Are you intending to use them as they were intended to be used when invented by Shewhart?