Guaranteeing acceptable in-control and out-of-control performance of joint X ̅-S control charts with estimated parameters

ABSTRACT Quality control charts are widely used to monitor production processes. To fix the control limits, the distribution of the statistic being controlled must be known. For using and S control charts together, when the parameters are unknown, the mean and standard deviation of the process must be estimated. Errors in these estimates can cause the real performance of the joint charts to be different from that expected by the user, and the in-control and out-of-control ARL may therefore be very different from the theoretical values. To date, only the effect of the estimation errors on the in-control performance of the joint charts has been studied in the literature. In this article, we study jointly this effect on both performance measures, the in-control and out-of-control ARLs for joint charts, and estimate the number of samples needed in Phase I to guarantee a required level in the probability of obtaining joint charts with acceptable in-control and out-of-control performances.