Adaptive CUSUM procedures with Markovian mean estimation

Authors:
Lianjie Shu;Wei Jiang;Zhang Wu
Affiliations:
Faculty of Business Administration, University of Macau, Taipa, Macau;School of Systems & Enterprises, Stevens Institute of Technology, Hoboken, NJ 07030, United States;Division of Systems and Engineering Management, School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore
Venue:
Computational Statistics & Data Analysis
Year:
2008

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Abstract

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.