Adaptive CUSUM procedures with Markovian mean estimation

This paper proposes using a Markovian-type mean estimating procedure in the conventional cumulative sum (CUSUM) control scheme to update its reference value in an adaptive way. This generalizes a class of Markovian adaptive CUSUM (ACUSUM) schemes to achieve the aim of providing an overall good performance over a range of future expected but unknown mean shifts. A two-dimensional Markov chain model is developed to analyze the run length performance of the new scheme. A comparison of run length performance of the proposed ACUSUM scheme and other control charts is shown favorable to the former.