Multivariate Max-Chart

Abstract

A single control chart called Multivariate Maximum Control Chart (Max-Mchart) is proposed in this article that is capable of monitoring the process, with the quality of an item being determined by several correlated quality characteristics. This scheme simultaneously monitors the process location and process spread using only one chart. The chart quickly detects both small and large shifts in the process parameters and indicates the parameter that has shifted. Compared with other recently proposed single multivariate control charts, this chart quickly detects small shifts in the process mean and is also simple to use, as it applies the well known Shewhart control charts procedures to compute the average run lengths.

Max-Half-Mchart: A Simultaneous Control Chart Using a Half-Normal Distribution for Subgroup Observations

“…Let denote multivariate observations, with representing the subgroup order and representing the observation order in each group. In this research, Max-Mchart carries out the following transformations [14]:…”

“…The bivariate Max-Chart was developed by combining the Hotelling T 2 and Generalized Variance (GV) statistics [13]. Then, Thaga and Gabaitiri [14] extended The Bivariate Max-Chart [13] to the Maximum Multivariate chart (Max-Mchart) combined the Hotelling 2 and GV statistics using the normal standard distribution. Sabahno et al [15] expanded Max-Mchart using the gamma distribution in GV for monitoring process variability.…”

Bivariate semiparametric control charts for simultaneous monitoring of process mean and variance

“…Several univariate procedures have been properly extended to monitor multiple quality characteristics of a normally distributed process (see, for example, Cheng and Mao, Khoo, and Thaga and Gabaitiri). For additional multivariate CCs with memory, the interested reader is referred to the articles of Xie, Cheng and Thaga, Jeong and Cho, and Chen et al .…”

Identifying the time of a step change with multivariate single control charts

“…Following these ideas, the simultaneous monitoring approaches have been increasingly attractive in the literature. The existing literature includes the following studies: the traditional combination of the χ 2 and |S| control charts, Maximum Multivariate Exponentially Weighted Moving Average (Max-MEWMA) chart proposed by Chen et al, [6] Maximum Multivariate Control (Max-M) chart proposed by Thaga and Gabaitiri, [7] Maximum Multivariate Cumulative Sum (Max-MCUSUM) control chart proposed by Cheng and Thaga [8] and Multivariate Exponentially Weighted Likelihood Ratio (MELR) chart by Zhang and Wang. [9] The basic idea behind the max procedures, namely the Max-M, Max-MEWMA and Max-MCUSUM charts, is to transform the monitoring statistics for mean and covariance to standardized normal random variables, determine the maximum of these standard normal readings then apply a multivariate Shewhart procedure.…”

“…[9] The basic idea behind the max procedures, namely the Max-M, Max-MEWMA and Max-MCUSUM charts, is to transform the monitoring statistics for mean and covariance to standardized normal random variables, determine the maximum of these standard normal readings then apply a multivariate Shewhart procedure. According to Thaga and Gabaitiri, [7] these control charts are practical because the complex multivariate readings are transformed into standardized univariate scores and monitoring can proceed using the existing charts for univariate processes. Also the practitioners can monitor both the mean and variability using only a single control chart.…”