THE CONTROL CHART FOR INDIVIDUAL OBSERVATIONS FROM A MULTIVARIATE NON-NORMAL DISTRIBUTION

Abstract

The Hotelling's T2statistic has been used in constructing a multivariate control chart for individual observations. In Phase II operations, the distribution of the T2statistic is related to the F distribution provided the underlying population is multivariate normal. Thus, the upper control limit (UCL) is proportional to a percentile of the F distribution. However, if the process data show sufficient evidence of a marked departure from multivariate normality, the UCL based on the F distribution may be very inaccurate. In such situations, it will usually be helpful to determine the UCL based on the percentile of the estimated distribution for T2. In this paper, we use a kernel smoothing technique to estimate the distribution of the T2statistic as well as of the UCL of the T2chart, when the process data are taken from a multivariate non-normal distribution. Through simulations, we examine the sample size requirement and the in-control average run length of the T2control chart for sample observations taken from a multivariate exponential distribution. The paper focuses on the Phase II situation with individual observations.