One-sided Adaptive Truncated Exponentially Weighted Moving Average X¯ Schemes for Detecting Process Mean Shifts

Abstract

One-sided type schemes are known to be more appropriate for monitoring a process when the direction of a potential mean shift can be anticipated. Furthermore, if the magnitude of the potential mean shift is unknown, it is desired to design a control chart to perform well over a wide range of shifts instead of only optimizing its performance in monitoring a particular mean shift level. The one-sided adaptive truncated exponentially weighted moving average (ATEWMA) X scheme recommended in this paper is a control chart that combines a Shewhart X scheme and a new one-sided EWMA X scheme together in a smooth way for rapidly detecting the upward (or downward) mean shifts. The basic idea of the recommended one-sided ATEWMA X scheme is to truncate the observations (i.e., the sample means X) first, and then to dynamically weight the past observations according to a suitable function of the current prediction error. This helps to improve the sensitivity of the proposed one-sided ATEWMA X scheme for detecting both small and

Probability‐type, Shewhart‐type and EWMA control charts for individual observations from the two‐parameter Lindley distribution

“…A lot of work has been done on optimal design of control charts in literature [e.g. Capizzi and Masarotto, 34 , Castagliola et al., 35 Khoo et al., 36 Castagliola et al., 37 Saha et al., 38 Yeong et al., 39 Chong et al., 40 Tang et al., 41 Xie et al., 42 Yeong et al 43 …”

“…A lot of work has been done on optimal design of control charts in literature [e.g. Capizzi and Masarotto, 34 , Castagliola et al, 35 Khoo et al, 36 Castagliola et al, 37 Saha et al, 38 Yeong et al, 39 Chong et al, 40 Tang et al, 41 Xie et al, 42 Yeong et al 43 ] based on minimizing the out-of-control value of various performance criteria. Since all the study here has been based on ARL (which is the most commonly used performance criterion) the optimal design of the EWMA control chart will be done by minimizing the ARL.…”