The Robustness and Performance of CUSUM Control Charts Based on the Double-Exponential and Normal Distributions

Abstract

We investigate the effects of non-normality on the statistical performance of cumulative sum (CUSUM) control charts for monitoring the process mean μ Our objective is to maintain tight control of the process so that detecting both small and large shifts in μ is important. We consider the standard CUSUM chart, which is based on the normal distribution, and a second CUSUM chart, which is based on the heavy-tailed doubleexponential distribution. We also investigate the issue of whether it is preferable from the perspective of statistical performance to base these control charts on samples of n > 1 observations or on individual observations ( n = 1). We assume that the sampling rate in terms of the number of observations per unit time is fixed, so using n = 1 means that samples can be taken more frequently than when n > 1. We show that using n > 1 in either chart does not give a significant improvement in in-control robustness, compared to using n = 1. We also show that, unlike the double-exponential CUSUM chart, for n = 1, the standard CUSUM chart can be designed to be highly robust to non-normality and very effective at detecting shifts of all sizes, even for highly skewed and extremely heavy-tailed process distributions. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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