Residual Control Chart for Binary Response with Multicollinearity Covariates by Neural Network Model

Jong-Min Kim,Yumin Liu,Kayoung Park,Ning Wang

doi:10.3390/sym12030381

Abstract

Quality control studies have dealt with symmetrical data having the same shape with respect to left and right. In this research, we propose the residual (r) control chart for binary asymmetrical (non-symmetric) data with multicollinearity between input variables via combining principal component analysis (PCA), functional PCA (FPCA) and the generalized linear model with probit and logit link functions, and neural network regression model. The motivation in this research is that the proposed control chart method can deal with both high-dimensional correlated multivariate data and high frequency functional multivariate data by neural network model and FPCA. We show that the neural network r control chart is relatively efficient to monitor the simulated and real binary response data with the narrow length of control limits.

Highlights

The current available quality control research has focused on symmetrical data having the same shape with respect to left and right
For the in-control and the one-inflated cases, the average run length (ARL) based on principal component analysis (PCA) are smaller than the ARLs based on functional PCA (FPCA) but, for zero-inflated case, the ARLs based on FPCA are smaller than the ARLs based on PCA
We have presented the binary response regression model-based statistical process control r-charts for dispersed binary asymmetrical data with multicollinearity among input variables

Summary

Introduction

The current available quality control research has focused on symmetrical data having the same shape with respect to left and right. In order to monitor a process mean vector, there have been a number of multivariate control charts including Hotelling T 2 distribution [1], mulvariate CUSUM [2] and multivariate EWMA [3] These current available multivariate control charts have limitations to handle high-dimensional data because of the complexity of the covariance structure. Neural network based methods have been applied to quality control research areas, but there is no research available for residual (r) control charts for binary asymmetrical data with highly correlated multivariate covariates by using neural network regression model. The first one is that the proposed control chart method can deal with high-dimensional correlated multivariate data by neural network model and the second one Symmetry 2020, 12, 381; doi:10.3390/sym12030381 www.mdpi.com/journal/symmetry

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Conclusion