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Abstract
Control charts are widely used in industries to monitor a process for quality improvement. Evaluation of the average run length (ARL) or average time to signal (ATS) plays an important role in the design of control charts and performance comparison. In this paper, we review several basic and popular procedures, including the Markov chain and integral equation methods for computing ARL, ATS and associated run length distributions for cumulative sum charts, exponentially weighted moving average charts and combined control charts, respectively. Some important references and key formulations are provided for practitioners.
Acknowledgements
The authors are grateful to the Editor and the anonymous referee for their valuable comments that have improved this paper vastly. This paper is supported by the National Natural Science Foundation of China Grants 11001138, 11071128, 11131002, 11101306, and 11201246, the RFDP of China Grant 20110031110002 and the Fundamental Research Funds for the Central Universities 65010731 and 65012231.