Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection

Ishaq Adeyanju Raji,Mu’Azu Ramat Abujiya,Nasir Abbas,Muhammad Riaz

doi:10.3390/math9212772

Ishaq Adeyanju Raji, Mu’Azu Ramat Abujiya + Show 2 more

Open Access

https://doi.org/10.3390/math9212772

Copy DOI

Journal: Mathematics	Publication Date: Nov 1, 2021
Citations: 1	License type: CC BY 4.0

Affiliation: King Fahd University of Petroleum and Minerals

Abstract

While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a robust multivariate control chart based on the Stahel-Donoho robust estimator (SDRE), whilst the process parameters are estimated from phase-I. Through intensive Monte-Carlo simulation, the study presents how the estimation of parameters and presence of outliers affect the efficacy of the Hotelling T2 chart, and then how the proposed outlier detector brings the chart back to normalcy by restoring its efficacy and sensitivity. Run-length properties are used as the performance measures. The run length properties establish the superiority of the proposed scheme over the default multivariate Shewhart control charting scheme. The applicability of the study includes but is not limited to manufacturing and health industries. The study concludes with a real-life application of the proposed chart on a dataset extracted from the manufacturing process of carbon fiber tubes.

Highlights

IntroductionOutliers are those observations at both extremes, which do not follow the majority of observations pattern in a dataset
This paper evaluated the in-control performance of the multivariate
Shewhart control chart when chart the parameters estimated from phase-Ifrom samples that samples were prone

Summary

Introduction

Outliers are those observations at both extremes, which do not follow the majority of observations pattern in a dataset. Outlier detection is of concern in data analysis and scientific areas, of which statistical process control (SPC) is not an exemption [1]. This is because outliers have a major influence on any statistical analysis as they increase the error variance, reduce the power of statistical tests, and cause bias in estimation, leading to incorrect inferences and conclusions, and sometimes, ending with deadly decisions, take the health sector as an example. The art of outlier detection is a prominent and important aspect of data analysis, even more so that more and more data are being analyzed simultaneously, such as with multivariate control charting

Objectives

Methods

Results

Conclusion