Performance analysis of hotelling T² under multivariate inspection errors

Abstract

In this paper, we analysed the effect of multivariate normal inspection errors on the performance of the Hotelling T² for individual observations during Phase II. The computed and charted statistic based on contaminated measurements may lead to inferior performance in the false alarm rate, power of detection and average run length (ARL). In this paper, we derive explicitly how the multivariate inspection errors are related to the Hotelling T² statistic. Performance of the multivariate statistical process control approach in terms of in-control and out-of-control ARL is reported with respect to different cases/structures of the inspection errors. Given fixed sizes of measurement error covariances, both the false alarm rate and detection time are dramatically affected by just 10% measurement error. High correlations of the measurement errors induce larger variances and covariances of the observed process characteristics, leading to inferior performance of the T² chart. This research finding has advantages that one can predict how the Hotelling T² chart will be inferior with respect to the measurement structure, i.e. %GRR. The lemmas provided in this research yield an explicit expression for numerical analysis of the inferior performance of the T² chart.

Keywords:

• Measurement error
• MSA
• multivariate SPC
• T² chart