The computation of average run length and average time to signal: an overview.

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. [ABSTRACT FROM PUBLISHER]