An efficient adaptive r-MD multivariate single control chart for nonlinear multiple quality characteristics

Abstract

An efficient multivariate single control chart to simultaneously monitor ‘location or mean’ and ‘scale or variabilities’, based on individual observations of multiple quality characteristics (MQC), is a continuous research endeavour. Compared to rational subgroups, time-ordered individual sample observations of MQC are common in manufacturing. However, few researchers proposed parametric and nonparametric multivariate control charts to monitor individual observations in this context. The proposed parametric approach has limited applicability due to the restrictive distribution assumption of MQC. In addition, most of the suggested parametric or nonparametric approaches recommend multiple charts to monitor process ‘location’ and ‘scale’ parameters simultaneously. Multiple charts can increase the control complexities and overall false-alarm-rate . MQC can also have significant nonlinear correlation structures and follow unknown or nonnormal distributions in real-life scenarios. Single parametric or nonparametric multivariate charts for individual observations can exhibit poor performance in such situations. In this study, an adaptive Mahalanobis depth and k-nearest neighbour (k-NN) rule-based r-AMD chart is proposed and verified to address the lacuna mentioned above. Monte-Carlo simulation studies are used to evaluate the performance of the r-AMD chart. Four real-life manufacturing scenarios are also considered to validate the suitability and superiority of r-AMD over the existing ‘r-MD’ and other competing charts.