A double sampling ridge penalized likelihood ratio control charting method with variable sample size for Phase II monitoring of high-dimensional covariance matrix

Abstract

Today, manufacturers face two challenges: the financial limitation of sampling and the large number of study quality characteristics. In such situations, the problem dimension is usually larger than the sample size, which is known in the literature of statistical quality control as a high dimensional process. The use of conventional multivariate charts to monitor the covariance matrix of such processes is not possible for two reasons: (1) the non-reversibility of the sample covariance matrix, (2) the possibility of the occurrence of sparse shifts in which only a few elements of the covariance matrix are affected. This paper focuses on Phase II monitoring of the covariance matrix of high-dimensional processes based on integrating the ridge penalized likelihood ratio (RPLR) statistic and the combined DS-VSS sampling method, in which DS and VSS features are used concurrently. The performance of the proposed DS-VSS RPLR control chart is compared with the RPLR one in terms of three metrics of the average run length, standard deviation of the run length, and expected value of sample size under three types of joint diagonal/off-diagonal, diagonal and off-diagonal shift patterns. The results show that the DS-VSS scheme is more sensitive than the RPLR in detecting both sparse and non- sparse changes.