The Effect of Non-Normality on the Performance of CUSUM Procedures

(Thomas P. Ryan and Belinda J. Faddy)

Abstract


Cumulative sum (CUSUM) procedures are a superior alternative to Shewhart control charts because they have better average run length (ARL) properties, especially in regard to detecting small parameter changes. The most commonly used CUSUM procedures are based on the assumption of normality. Curiously, there is no published, comprehensive study of the effect of non-normality on CUSUM procedures. Accordingly, we consider the effect of skewed distributions and heavy-tailed distributions on normality-based procedures. We consider not only a basic CUSUM scheme, but also Shewhart-CUSUM and fast initial response (FIR) CUSUM procedures. We use a Markov chain approach to approximate the in-control ARLs and show that even moderate non-normality has a strong effect on the in-control ARL of CUSUM procedures, especially a Shewhart-CUSUM procedure. Lastly, we consider the difficult task of designing robust CUSUM procedures.

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