A generalized multiple dependent state sampling chart based on ridge penalized likelihood ratio for high-dimensional covariance matrix monitoring

Saemian, Maziar; Salmasnia, Ali; Maleki, Mohammad Reza

doi:10.24200/sci.2022.60169.6640

A generalized multiple dependent state sampling chart based on ridge penalized likelihood ratio for high-dimensional covariance matrix monitoring

Articles in Press

Document Type : Research Article

Authors

Maziar Saemian ¹

Ali Salmasnia ²

Mohammad Reza Maleki ³

¹ Department of Industrial Engineering, University of Eyvanekey, Semnan, Iran

² Assistant Professor

³ Industrial Engineering Group, Golpayegan College of Engineering, Isfahan University of Technology, Golpayegan

10.24200/sci.2022.60169.6640

Abstract

Online monitoring of high-dimensional processes variability in which the number of variables is larger than the sample size is a challenging issue for quality practitioners because the sample covariance matrix is not invariable. To deal with this challenge, a generalized multiple dependent state sampling (GMDS) chart based on ridge penalized likelihood ratio (RPLR) statistic is developed for Phase II monitoring of multivariate process variability under high-dimensional setting. The developed control chart benefits from three advantages: (1) departing from the conventional covariance matrix charts, it can be efficiently employed for both spars and non-spars covariance matrices; (2) it is able to detect spars shift patterns in which only a few covariance matrix elements are deviated from their nominal values; and (3) it outperforms the detectability of the RPLR chart in terms of average run length (ARL) and standard deviation of run length (SDRL). The performance of RPLR, MDS-RPLR, and GMDS-RPLR charts are compared using extensive simulation studies by considering different diagonal and/or off-diagonal covariance matrix disturbance. Moreover, sensitivity analysis are provided to analyze how the number of process variables and GMDS parameter affect the run length properties of the developed chart.

Keywords

Covariance matrix

High-dimensionality

Ridge penalized likelihood ratio

Generalized multiple dependent state sampling

Spars disturbances