Deep learning-based residual control chart for count data

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.

Keywords:

• Average run length
• count data
• deep learning: residual control chart

Additional information

Funding

The authors would like to thank the editor and the two anonymous respected referees for their suggestions, which have greatly improved the paper. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2020R1F1A1A01056987).

Notes on contributors

Jong-Min Kim

Jong-Min Kim is Full Professor at the Statistics Discipline, University of Minnesota at Morris, Morris, Minnesota, USA. He received his BS from the Department of Mathematics Education, Cheongju University in 1994; MS from the Department of Mathematics, Chung-Ang University in 1996; and PhD from the Department of Statistics, Oklahoma State University, Oklahoma, USA, in 2002. His current research interests include copula, time series analysis, and survey sampling.

Il Do Ha

Il Do Ha is a Full Professor at the Department of Statistics, Pukyong National University, Busan, South Korea. He received his PhD from the Department of Statistics, Seoul National University, Seoul, South Korea in 1999. His current research interests include hierarchical likelihood approach for multivariate survival data, random effect models, medical statistics and machine learning.