A new adaptive CUSUM control chart for detecting the multivariate process mean

• Published in: Quality and reliability engineering international Vol. 27; no. 7; pp. 877 - 884
• Main Authors: Dai, Yi, Luo, Yunzhao, Li, Zhonghua, Wang, Zhaojun
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.11.2011
• Subjects: Adaptive control systems; average run length; Chains; Computation; Control charts; Estimates; exponentially weighted moving average; multivariate CUSUM; multivariate mean; Operators; Optimization; Reliability engineering; statistical process control
• ISSN: 0748-8017; 1099-1638; 1099-1638
• DOI: 10.1002/qre.1177

We propose a new multivariate CUSUM control chart, which is based on self adaption of its reference value according to the information from current process readings, to quickly detect the multivariate process mean shifts. By specifying the minimum magnitude of the process mean shift in terms of its non‐centrality parameter, our proposed control chart can achieve an overall performance for detecting a particular range of shifts. This adaptive feature of our method is based on two EWMA operators to estimate the current process mean level and make the detection at each step be approximately optimal. Moreover, we compare our chart with the conventional multivariate CUSUM chart. The advantages of our control chart detection for range shifts over the existing charts are greatly improved. The Markovian chain method, through which the average run length can be computed, is also presented. Copyright © 2010 John Wiley & Sons, Ltd.