A Ridge Penalized Likelihood Ratio Chart for Phase II Monitoring of High-Dimensional Process Dispersion Under Measurement System Inaccuracy

In some applications, the number of quality characteristics is larger than the number of observations within subgroups. Common multivariate control charts to monitor the variability of such high-dimensional processes are unsuitable because the sample covariance matrix is not positive semi-definite and invertible. Moreover, the impact of gauge imprecision on detection capability of multivariate control charts under high-dimensional setting has been clearly neglected in the literature. To overcome these shortcomings, this paper develops a ridge penalized likelihood ratio chart for Phase II monitoring of high-dimensional process in the presence of measurement system errors. The developed control chart departures from the assumption of sparse variability shifts in which the assignable cause can only affects a few elements of the covariance matrix. Then, to compensate for the adverse impact of gauge impression, the developed chart is extended by employing multiple measurements on each sampled item. Simulation studies are carried out to study the impact of imprecise measurements on detectability of the developed monitoring scheme under different shift patterns. The results show that the gauge inability negatively affects the run-length distribution of the developed control chart. It is also found that the extended chart under multiple measurements strategy can effectively reduce the error impact.