Multioutput least square SVR-based multivariate EWMA control chart: The performance evaluation and application

Hidayatul Khusna,Suhartono Suhartono,Muhammad Ahsan,Dedy Dwi Prastyo,Muhammad Mashuri,Yibing Li

doi:10.1080/23311916.2018.1531456

Abstract

Autocorrelation leads to a bias estimator of standard control charts. It is important to develop control chart that allows autocorrelation and to evaluate its performance. The objective of this paper is to evaluate the performance of multioutput least square support vector regression (MLS-SVR)-based multivariate exponentially weighted moving average (MEWMA) control chart for monitoring multivariate autocorrelated data. For first order of vector autoregressive (VAR) and first order of vector moving average data, the proposed control chart tends to yield stable in-control average run length at about 200. The proposed control chart becomes more insensitive due to the increase of MEWMA smoothing parameter. In the real application, the proposed method is successfully applied to monitor water turbidity and chlorine residual data in the drinking water manufacturing process.

Highlights

Traditional control chart usually assumes that variables are statistically independent over time
One of the multivariate control charts for monitoring autocorrelated data named multioutput least square support vector regression (MLS-support vector regression (SVR))-based multivariate exponentially weighted moving average (MEWMA) control chart is evaluated based on two types of linear time series data
Böhm and Hackl (1996) derived close form approximation of in-control average run length (ARL) to evaluate the effect of autocorrelation on the performance of cumulative sum (CUSUM) control chart

Summary

Introduction

Traditional control chart usually assumes that variables are statistically independent over time. One of the multivariate control charts for monitoring autocorrelated data named MLS-SVR-based MEWMA control chart is evaluated based on two types of linear time series data. Böhm and Hackl (1996) derived close form approximation of in-control ARL to evaluate the effect of autocorrelation on the performance of cumulative sum (CUSUM) control chart Both Shewhart and CUSUM charts become less sensitive to detect small shift in the mean when applied to the residual of autocorrelated process (Runger, Wlllemain, & Prabhu, 1995). Mashuri, Suhartono, Prastyo, and Ahsan (2018) proposed MLS-SVR-based MEWMA control chart and evaluated its ability to detect the presence of both additive and innovative outliers in the simulation data which follow vector autoregressive and moving average model with order (1,1).

MLS-SVR-based MEWMA control chart

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Conclusions and future research