On the Efficient Monitoring of Multivariate Processes with Unknown Parameters

Abstract

Control charts are commonly used tools that deal with monitoring of process parameters in an efficient manner. Multivariate control charts are more practical and are of greater importance for timely detection of assignable causes in multiple quality characteristics. This study deals with multivariate memory control charts to address smaller shifts in process mean vector. By adopting a new homogeneous weighting scheme, we have designed an efficient structure for multivariate process monitoring. We have also investigated the effect of an estimated variance covariance matrix on the proposed chart by considering different numbers and sizes of subgroups. We have evaluated the performance of the newly proposed multivariate chart under different numbers of quality characteristics and varying sample sizes. The performance measures used in this study include average run length, standard deviation run length, extra quadratic loss, and relative average run length. The performance analysis revealed that the proposed control chart outperforms the usual scheme under both known and estimated parameters. An application of the study proposal is also presented using a data set related to Olympic archery, for the monitoring of the location of arrows over the concentric rings on the archery board.

Keywords

• control chart
• parameter estimation
• homogeneous weights
• Hotelling’s T²
• statistical process monitoring