Multivariate generalized variance control chart under sensitizing rules with an application in petroleum process

In this study, a multivariate generalized variance (MGV) control chart with sensitizing rules is introduced for efficiently monitoring of small-to-moderate variations in the variance-covariance matrix. On this subject, control limit is constructed which depends on the probability of single point (PSP) and prefixed in-control average run length (ARL). To find the PSP such that in-control ARL remains almost equal to prefixed level, a single polynomial equation (SPE) is considered. Moreover, performance of the proposed MGV control chart is evaluated using individual and overall performance measures. Results reveal that behavior of the proposed multivariate generalized variance (MGV) control chart is remained consistent for all choices of sensitizing rules when process is in-control. The in-control ARL is resulted equal to the prefixed in-control ARL. Also, behavior of in-control median run length (MRL) and percentile run length (PRL) is observed similar for all choices of sensitizing rules. A comparative analysis revealed that proposed MGV control chart with an additional sensitizing rules outperformed for detection of small-to-moderate variations relative to the existing control charts with classical rule. Besides, the proposed MGV control chart is applied to petrolatum process as an application for monitoring the three physical diesel characteristics simultaneously.