Economic and economic-statistical designs of the side sensitive group runs chart with auxiliary information

摘要

This article studies the economic and economic-statistical designs of the auxiliary information (AI) based side sensitive group runs (SSGR-AI) chart. The regression estimator that consists of information not only from the primary variable but also from the auxiliary variable is integrated into the control charting statistic. Optimal designs of the SSGR-AI chart, for the minimization of the expected cost function with and without statistical constraints, are developed based on (i) average run length (ARL) and (ii) expected average run length (EARL). Furthermore, sensitivity analyses are conducted, that is, the impact of various input parameters on the optimal parameters and costs for different values of correlation coefficients (rho) between the primary and auxiliary variables are investigated. In addition, the effects of incorrect specification of the size of the shift on the optimal cost of the SSGR-AI chart are studied. The comparative study reveals that the SSGR-AI chart is superior to the exponentially weighted moving average-AI (EWMA-AI) and synthetic-AI (Syn-AI) charts, for both designs, by giving the smallest costs.