One-Sided and Two One-Sided Multivariate Homogeneously Weighted Moving Charts for Monitoring Process Mean

Abstract

Multivariate memory-type control charts that use information from both the current and previous process observations have been proposed. They are designed to detect shifts in both upper and downward directions with equal precision when monitoring the process mean vector. The absence of directional sensitivity can limit the charts' application, particularly when users are interested in detecting variations in one direction than the other. This article proposes one-sided and two one-sided multivariate control charts for monitoring shifts in the process mean vector. The proposed charts are presented in the form of the multivariate homogeneously weighted moving average approach that yields efficient detection of shifts in the mean vector. We provide simulation studies under different shift sizes in the process mean vector and evaluate the performance of the proposed charts in terms of their run length properties. We compare the average run length (ARL) results of the charts with the conventional charts as well as the onesided and two one-sided multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) charts. Our simulation results show that the proposed charts outperform the existing charts used for the same purpose, particularly when interest lies in detecting small shifts in the mean vector. We show how the charts can be designed to be robust to non-normal distributions and give a step-by-step implementation efficient application of the charts when their parameters are unknown and need to be estimated. Finally, an illustrative example is provided to show the application of the proposed charts.INDEX TERMS Average run length; multivariate homogeneously weighted moving average; one-sided control charts; two one-sided control charts, robustness, estimation.

Homogeneously Weighted Moving Average Control Charts: Overview, Controversies, and New Directions

“…Malela-Majika et al [35] corrected the variance used in the HHWMA X chart design proposed by [51]. For more details regarding the parametric DHWMA and HWMA charts for monitoring the location parameter, readers are referred to Alevizakos et al [22,23,56,65].…”

“…Their performance analysis revealed that the MHWMA T 2 chart outperforms its multivariate counterparts under known and estimated process parameters. Later, Adegoke et al [56] proposed one and two one-sided MHWMA charts for monitoring small shifts in the process mean vector, denoted as the OMHWMAI and OMHWMAII, respectively. The OMHWMAI chart is a one-sided chart for monitoring upward shifts by transforming the observation X i into positive values.…”

A New Nonparametric Multivariate Control Scheme for Simultaneous Monitoring Changes in Location and Scale

“…Control schemes have been frequently used for fault detection in quality control with products and health-care monitoring [10][11][12][13][14]. A process should be monitored using statistical means to determine whether a shift occurs, and action should be taken once the process is considered out-of-control (OC) [15][16][17][18]. Many researchers have discussed and proposed many useful charts, such as Shewhart charts [19,20], cumulative sum (CUSUM) charts [21][22][23][24][25][26][27][28][29][30], and exponentially weighted moving average (EWMA) charts [31][32][33][34][35][36][37][38], to detect whether there is a change in quality characteristics in a process.…”