An efficient adaptive EWMA control chart for monitoring the process mean

Abstract

In recent years, the memory‐type control charts—exponentially weighted moving average (EWMA) and cumulative sum (CUSUM)—along with the adaptive and dual control‐charting structures have received considerable attention because of their excellent ability in providing an overall good detection over a range of mean‐shift sizes. These adaptive memory‐type control charts include the adaptive exponentially weighted moving average (AEWMA), dual CUSUM, and adaptive CUSUM charts. In this paper, we propose a new AEWMA chart for efficiently monitoring the process mean. The idea is to first design an unbiased estimator of the mean shift using the EWMA statistic and then adaptively update the smoothing constant of the EWMA chart. The run length profiles of the proposed AEWMA chart are computed using extensive Monte Carlo simulations. Based on a comprehensive comparative study, it turns out that the proposed AEWMA chart performs better than the existing AEWMA, adaptive CUSUM, dual CUSUM, and Shewhart‐CUSUM charts, in terms of offering more balanced protection against mean shifts of different sizes. An example is also used to explain the working of the existing and proposed control charts.

A survey on multivariate adaptive control charts: Recent developments and extensions

“…Haq and Kho investigated an adaptive multivariate EWMA (MAEWMA HK ) control chart in which the mean shift magnitude is estimated at each sampling point. This scheme was originally investigated in the univariate case by Haq et al in the univariate case. According to Haq and Kho, the MAEWMA HK chart outperforms the MAEWMA chart proposed by Mahmoud and Zahran, and provides overall good detection over a range of mean shift magnitudes.…”

Application of EWMA chart for monitoring process mean in paper industry

“…The exponentially weighted moving average (EWMA) control chart is a good alternative to the Shewhart control chart (Schilling & Nelson, 1976;Shewhart, 1931;Wheeler, 1996;Liu et al, 2007) when we are interested in detecting small shifts (Braimah et al, 2014;Costa & Rahim, 2016). The performance of the EWMA control chart is approximately equivalent to that of the cumulative sum control chart (Haq et al, 2018;Simões et al, 2010;You & Khoo, 2015) and in some ways it is easier to set up and operate (Jones et al, 2001). The exponentially weighted moving average is defined as zi = xi + (1)zi1 where 0 <   1 is a constant and the starting value (required with the first sample at I = 1) is the process target, so that z0 = 0.…”

A new adaptive EWMA control chart for monitoring the process dispersion

“…Since and for θ >0 and θ <0, respectively, we suggest considering when estimating | θ |. Using the sequence { Y t }, the plotting statistic of the proposed AEWMA chart for monitoring increases or decreases in the process dispersion is implemented by recursively computing the following AEWMA statistic (cf, Haq et al): where M 0 =0 and is a function of , defined by the following: …”

“…Recently, Haq et al have designed a new AEWMA chart for efficiently monitoring small‐to‐moderate or small‐to‐large shifts in the process mean. On similar lines, we design a new AEWMA dispersion chart for monitoring different kinds of shifts in the process variance.…”