An adaptive exponentially weighted moving average-type control chart to monitor the process mean

Abstract

Exponentially weighted moving average (EWMA) control charts are typically used for faster detection of shifts in the process mean, relative to a Shewhart control chart, when the degree of shift is small. Normal guidelines suggest using a small (large) value of the weighting constant, λ, for detecting smaller (larger) shifts in the process mean. Prior research has suggested that the choice of λ should depend on the observed data and have considered the use of a weighting constant, that varies and adapts as monitoring continues and new data are collected. One such adaptive control chart, called the AEWMA chart, utilizes a rather computationally complex scheme to determine the weighting constant λ and it requires knowledge of the size of the shift, to specify whether it is “small” or “large”. A complex two-phase optimization scheme is then solved to yield “good solutions”. As an alternative, we propose an adaptive EWMA-type control chart that does not require knowledge of the degree of the shift. Further, the computational scheme is easier and completed in one stage. The performance of the proposed chart is studied using simulations, where the degree of the shift in the process mean is varied over a wide range of values. Based on the average run length (ARL), as a performance measure, the proposed chart is demonstrated to perform uniformly better than the traditional EWMA chart with a constant weight.The proposed chart also performs better than the AEWMA chart for moderate to large shifts.