Deep learning-based residual control chart for count data

IL DO HA

Abstract:

Statistical process control for count data has difficulty overcoming multicollinearity. In this
paper, we propose a new deep learning residual control chart based on the asymmetrical
count response variable when there are highly correlated explanatory variables. We implement
and compare different methods such as neural network, deep learning, principal component
analysis based Poisson regression, principal component analysis based negative
binomial regression, nonlinear principal component analysis based Poisson regression, and
nonlinear principal component analysis based negative binomial regression in terms of the
root mean squared error. Using two asymmetrical simulated datasets generated by the combined
multivariate normal, binary and copula functions, the neural network and deep learning
have a smaller mean, median, and interquartile range when compared to the principal
component analysis based Poisson regression, principal component analysis based negative
binomial regression, nonlinear principal component analysis based Poisson regression, and
nonlinear principal component analysis based negative binomial regression. We also compare
the deep learning and neural network based residual control charts in terms of the
average run length with the copula based asymmetrical simulated data and real takeover
bids data.