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Keywords:

  • false position method;
  • integral equation;
  • Markov chain;
  • statistical process control

Abstract

Conventional control charts are often designed to optimize out-of-control average run length (ARL), while constraining in-control ARL to a desired value. The widely employed grid search approach in statistical process control (SPC) is time-consuming with unsatisfactory accuracy. Although the simulation-based ARL gradient estimators proposed by Fu and Hu [Manag Sci 45 (1999), 395–413] can alleviate this issue, it still requires a large number of simulation runs to significantly reduce the variance of gradient estimators. This article proposes a novel ARL gradient estimation approach based on integral equation for efficient analysis and design of control charts. Although this article compares with the results of Fu and Hu [Manag Sci 45 (1999), 395–413] based on the exponentially weighted moving average (EWMA) control chart, the proposed approach has wide applicability as it can generally fit into any control chart with Markovian property under any distributions. It is shown that the proposed method is able to provide a fast, accurate, and easy-to-implement algorithm for the design and analysis of EWMA charts, as compared to the simulation-based gradient estimation method. Moreover, the proposed gradient estimation method facilitates the computation of high-order derivatives that are valuable in sensitivity analysis. The code is written in Matlab, which is available on request. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 223–237, 2014