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Level IV

CUSUM Control Chart Comparison to “n out of k+n points” as a New User Rule Option (2019-US-EPO-202)

Level: Intermediate


Daniel Sutton, Statistician - Innovation, Samsung Austin Semiconductor


    The CUSUM Control Chart has been shown to be sensitive to small shifts compared to standard WECO (Western Electric Co) rules and Nelson rules, in particular Rule 2: “9 points in a row on a single side of the center line” [1]. Some examples of CUSUM control charts show the CUSUM technique will pick up a signal in a sequence of 9 or more points, where just one point is barely on the other side of the center line, and so Rule 2 is not triggered in that particular sequence. Question: is the SPC chart missing the signal because we do not allow for the one point on the other side of the center line? The alternative for Rule 2 of “n out of n+k points” is re-visited. Control charts in JMP and other software are hard-coded for Rule 2 “n points in a row on a single side of the center line”. This might require updating the Control Chart Builder options for Customize Tests to allow this configuration for the user, so that one platform, the Control Chart Builder, can continue to be used for all SPC analysis.

     Utilizing JMP software’s built in reports of Process Screening, Control Chart Builder, and CUSUM, JMP scripts were created that could quickly generate random normal data and example signals, analyze combinations of varying k and n for the “n out of n+k” rule, and at the same time compare to traditional tests and CUSUM. The scripts extracted when tests were triggered, determined how many signals were detected, and how many false positives and false negatives occurred. Examples for different scenarios were compared.

     The results show that CUSUM is better for both false positives and detects small shifts faster than even “n out of n+k” rules. Rules 1,2,5,6 do better for short duration signals. A drawback of the CUSUM chart is that it does not display the actual data points. It is recommended that the CUSUM chart be added to Control Chart Builder, as an option along side the standard SPC charts, for graphical interpretation in a single window for the user. If the CUSUM chart cannot be easily added to the Control Chart Builder, the alternative of adding a user configurable “n out of n+k” rule is also recommended for the Control Chart Builder platform.