Abstract
A residual (r) control chart of asymmetrical and non-normal binary response variable with highly correlated explanatory variables is proposed in this research. To avoid multicollinearity between multiple explanatory variables, we employ and compare a neural network regression model and deep learning regression model using Bayesian variable selection (BVS), principal component analysis (PCA), nonlinear PCA (NLPCA) or whole multiple explanatory variables. The advantage of our r control chart is able to process both non-normal and correlated multivariate explanatory variables by employing a neural network model and deep learning model. We prove that the deep learning r control chart is relatively efficient to monitor the simulated and real binary response asymmetric data compared with r control chart of the generalized linear model (GLM) with probit and logit link functions and neural network r control chart.
Highlights
Learning-Based Residual ControlThe COVID-19 pandemic started at the end of the year 2019
For the in-control case, the one-inflated case, and zero-inflated case, the expected lengths of the confidence interval on the deep learning regression model (DL) based on Bayesian variable selection (BVS), principal component analysis (PCA), nonlinear PCA (NLPCA), and whole data are shorter than in all other cases of Nnet in Tables 2–5 while, in terms of the coverage probability, the DL is keeping overall higher than the neural network regression model
In terms of the average run length (ARL), the coverage probability and the expected length of the confidence interval, we note that the r-chart based on the DL based on whole data for monitoring observations is about the same as the r-chart based on the DL based on BVS, PCA, and NLPCA
Summary
The COVID-19 pandemic started at the end of the year 2019. It has dramatically changed the social life of human activity since people fight against the spread of COVID-19 by covering their faces wearing masks and doing social distancing. Numerous multivariate control charts such as the Hotelling T 2 distribution [3], mulvariate CUSUM [4] and multivariate EWMA [5] have been proposed to monitor a process mean vector These multivariate control charts have a difficulty to handle non-normal and asymmetric data because of the estimation issue of the unknown covariance structure. We extend the single hidden layer neural network regression-based r control charts for binary asymmetrical data to a deep learning regression model with multiple hidden layers via Bayesian variable selection (BVS), principal component analysis (PCA) and nonlinear PCA (NLPCA) so that our r control chart can solve a multicollinearity problem among independent variables. Our deep learning r control chart will be evaluated with simulated data and Cleveland heart disease read data found in the UCI machine learning repository
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