T2 Control Charts With Variable Dimension


Aparisi, Francisco; Epprecht, Eugenio K.; Ruiz, Omar   (ASQ)   Universidad Politécnica de Valencia, Valencia, Spain; Pontificia Universidade Católica de Río de Janeiro, Río de Janeiro, Brazil; Escuela Superior Politécnica del Litoral, Guayaquil, Ecuador

Journal of Quality Technology    Vol. 44    No. 4
QICID: 35215    October 2012    pp. 375-393
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Article 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.


Algorithm; Markov chains; Multivariate control charts; Optimization; Statistical process control (SPC); Variable selection

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