An optimal design of cumulative sum control chart based on median run length

Abstract

Designs of cumulative sum (CUSUM) control charts have traditionally been based on the average run length (ARL). However,interpretatios based on the ARL can be misleading as the in-control run length distribution of a CUSUM chart is highly skewed. Any meaningful interpretation based on the ARL is complicated by the fact that the form of the ren length distribution changes according to the shift in the process mean, and for certain shifts, the run length distributions are almost symmetric. For a run length distribution which can vary from a bighly skewed distribution to an almost symmetric distribution with respect to the sift, the median run length (MRL) is a more meaningful quantity to depend on since interpretation based on the MRL is more readily understood. An important reason for the wide sqread and easily. On the other hand, the MRL and in general, percentage points of run length distribution of a CUSUM chart can be computed accurately and easily. On the other hand, the MRL and in general, percentage points of run length distribution of a CUSUM chart are much harder to compute. Two methods of computing the MRL of a CUSUM chart are examined with emphasis given to the numerical accuracy. An optional design of CUSUM chart based on the MRL is proposed and graphs are provided such that the chart parameters of an optimal CUSUM chart can be determined easily, A normal process is assumed.

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