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T<sup>2</sup> control charts with variable dimension

Abstract:

This paper proposes a new multivariate T2 control chart, termed the variable dimension T2 (VDT2) chart, in which the number of monitored quality characteristics is variable. When there are p related variables to be monitored, the approach is useful if there is a subset of p1 variables that are easy and/or inexpensive to measure, while the remaining variables are difficult and/or expensive to measure but provide additional useful information on whether the process mean has shifted. The VDT2 chart adaptively determines the number of variables to be monitored (either p1 or p) depending on the last value of the charted statistic. We provide Windows®-based software to optimize the parameters of the control chart using a Markov chain model to compute the performance measures and a genetic algorithm to conduct the optimization. The optimized VDT2 chart is quite powerful, and we demonstrate the somewhat surprising result that it detects mean shifts faster than a standard T2 chart for which all p variables are always measured, while also reducing sampling costs.