A uniformly most powerful cumulative sum scheme based on symmetry

Abstract

The V-mask cumulative sum (CUSUM) or its corresponding tabular form is known to be optimal for detecting a shift in mean of magnitude 2k. It is also known that the optimality of the CUSUM is not uniform against other alternatives. This has prompted quality improvement practitioners to propose various modifications of the V-mask. Some of these modifications are somewhat ad hoc. We propose a parabolic mask which is based on a uniformly most powerful test. We compare the performance of the proposed parabolic mask with the various V-mask modifications. The results show that a CUSUM with parabolic mask is better in detecting a shift in mean across a wider range.