Performance of Multivariate Homogeneously Weighted Moving Average Chart for Monitoring the Process Mean in the Presence of Measurement Errors

Abstract

Multivariate control charts are useful tools for monitoring the product quality in which the process outcome is expressed by several correlated variables. The multivariate homogeneously weighted moving average (MHWMA) control chart is one of the most efficient extensions of the multivariate exponentially weighted moving average (MEWMA) procedure. However, this control chart has been proposed under the assumption of precise measurements. This paper explores the impact of the measurement system inability on sensitivity of MHWMA control chart in Phase II monitoring of the mean vector of multivariate normally distributed quality characteristics. Through simulation studies, the run length (RL) properties of MHWMA chart in the presence of measurement errors are investigated and compared to without-error scenario. The results indicate that the imprecise measurements degrade the detection ability of MHWMA control chart in detecting different process disturbances. The undesired impact of gauge measurement errors increases as the error variance increases. Moreover, multiple measurements on each sampled item are utilized to compensate for the undesired effect of the measurement errors on run length characteristics of the MHWMA control chart. It is also concluded that, as the number of measurements on each sampled point increases, the detection capability of MHWMA chart reduces and approaches the without-error case. Finally, a realistic illustrative example from a healthcare system is utilized to elaborate on the impact of imprecise measurements on chart performance.