Optimal economic statistical design of combined double sampling and variable sampling interval multivariate T 2 control charts

Abstract

Recent studies have shown that an adaptive T2 chart with double sampling and variable sampling interval DSVSIT2 chart shows a good performance in detecting small to moderate shifts in the mean vector. This paper develops an economic statistical model for the DSVSIT2 chart. The statistical performance of the proposed establish is evaluated using the average number of false alarms (ANF) and the adjusted average time to signal (AATS) criteria. The Wald's identity approach is used to derive an expression for the AATS. The unified Lorenzen and Vance's cost model is generalized to establish the economic model. Using numerical examples, we illustrate the application of the proposed model and compare its performance with the other T2 and MEWMA schemes. A sensitivity analysis is also carried out to investigate the effects of model parameters on the solution of the economic statistical design. The results indicate that the DSVSI T2 chart economically outperforms the existing standard T2 and other adaptive T2 charts. The economic performance of the DSVSI T2 chart is also favourable compared to the MEWMA chart.Abbreviations: SPC Statistical process control; FRS Fixed ratio sampling; DS Double sampling; VSS Variable sample size; VSI Variable sampling interval; VSSI Variable sample size and sampling interval; VP Variable parameters; FA Full adaptive; DSVSI Double sampling and variable sampling interval; MEWMA Multivariate exponentially weighted moving average; ANF Average number of false alarms; ATS Average time to signal; AATS Adjusted average time to signal; ANS Average number of samples; ARL Average run length; SD Statistical design; ED Economic design; ESD Economic statistical design; GA Genetic algorithm

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