Adaptive sampling enhancement for Hotelling’s T2 charts

Abstract

This paper makes a study of an adaptive sampling scheme useful to increase the power of the fixed sampling rate (FSR) T 2 control chart. In our study, the three parameters of T 2 control chart: the sample size, the sampling interval, and the upper percentage factor that is used for determining the action limit, vary between two values for a relaxed or tightened control, depending on the most recent T 2 value. The average time to signal (ATS) and adjusted average time to signal (AATS) a shift in the process mean vector for the new chart are derived and regarded as an objective function respectively to optimize its design parameters. With some minor changes, the new chart can be reduced to the variable sampling interval (VSI) T 2 chart, the sample size (VSS) T 2 chart, the variable sample size and sampling interval (VSSI) T 2 chart, or the FSR T 2 chart. Numerical comparisons among them are made and discussed. Furthermore, the effects of the initial sample number (use for estimating the in-control process parameters) upon the chart’s performance and adaptive design parameters are presented.