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

Rumaisa Kruba,Muhammad Mashuri,Dedy Dwi Prastyo

doi:10.1109/access.2021.3100078

Rumaisa Kruba, Muhammad Mashuri + Show 1 more

Open Access

https://doi.org/10.1109/access.2021.3100078

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Abstract

A Simultaneous control chart is a well-known tool for monitoring the process mean and process variability with a single chart. In recent decades, many researchers have been interested in developing simultaneous control charts. The Shewhart chart is the most common and simple simultaneous control chart. The Multivariate Maximum control chart (Max-Mchart) is a type Shewhart chart that simultaneously monitors the process of multivariate data. This paper proposes a new transformation using a half-normal distribution to improve the Max-chart performance for subgroup observations. The new proposed chart is called Max-Half-Mchart. The Average Run Length (ARL) results show that the proposed Max-Half-Mchart outperforms the Max-Mchart. Additionally, in real data scenarios, the proposed Max-Half-Mchart is consistent with the statistic in the Hotelling T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> chart and the Generalized Variance (GV) chart.

Highlights

A simultaneous chart is a single chart that simultaneously monitors the process mean and process variability
This paper proposes different calculations of the Upper Control Limit (UCL), since the statistics of the proposed Max-Half-Mchart have an unknown specific distribution
The Average Run Length (ARL) of the proposed Max-Half-Mchart decreases significantly when there is a shift in the covariance matrix, while the mean vector remains in-control

Summary

INTRODUCTION

A simultaneous chart is a single chart that simultaneously monitors the process mean and process variability. Chen and Thaga[7] developed the Maximum Cumulative Sum (Max-CUSUM) control chart for autocorrelated data. The Maximum Multivariate CUSUM (MaxMCUSUM) was introduced by Cheng and Thaga [11] using a standardized mean vector and the covariance matrix for the statistics. Thaga and Gabaitiri [14] extended The Bivariate Max-Chart [13] to the Maximum Multivariate chart (Max-Mchart) combined the Hotelling T 2 and GV statistics using the normal standard distribution. R. Kruba et al.: Max-Half-Mchart: Simultaneous Control Chart Using Half-Normal Distribution effective only when detecting large shifts. Kruba et al.: Max-Half-Mchart: Simultaneous Control Chart Using Half-Normal Distribution effective only when detecting large shifts To overcome this issue and improve the Max-Mchart’s performance during the monitoring process, this paper proposes an improvement on Max-Mchart [14] using a half-normal distribution in terms of transformation. This paper proposes different calculations of the Upper Control Limit (UCL), since the statistics of the proposed Max-Half-Mchart have an unknown specific distribution

NEW SIMULTANEOUS CONTROL CHART

Compare CiH with the UCLh for the proposed

APPLICATION TO REAL DATA

CONCLUSION