A novel gradient approach for optimal design and sensitivity analysis of EWMA control charts

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

A Control Chart for Exponentially Distributed Characteristics Using Modified Multiple Dependent State Sampling

“…In this section, the efficiency of the proposed t-chart under MMDS sampling is evaluated compared to the t-chart under the MDS and GMDS sampling schemes. In many studies, a simulation approach is extensively employed to demonstrate the performance and effectiveness of control charts [27][28][29][30][31]. Using simulated data is convenient and is usually done when exact statistics of the proposed process are not available.…”

A Control Chart for Gamma Distribution using Multiple Dependent State Sampling

“…This simulation approach is commonly used when the exact form of the mean and other measures of the proposed process is not available. Many researchers have used the simulation approach for the effectiveness of control charts including among others Santos (2009), Abbasi and Miller (2013), , , Chananet et al (2014), Shu et al (2014), , Azam et al (2015) and Aslam (2016).…”

Improved EWMA schemes for monitoring the ratio of two normal random variables

“…According to the research of Shu et al., 26 the EWMA scheme is considered one of the most important tools to detect small or moderate changes. In recent years, different modifications of EWMA schemes have been developed in the SPC literatures, such as the adaptive EWMA (AEWMA) (Capizzi and Masarotto 27 ), the new AEWMA (Haq and Khoo 28 ), the improved one‐sided EWMA without‐ and with VSI (Hu et al 29 …”