Joint Monitoring of the Mean and Variance of Combined Control Charts with Estimated Parameters

摘要

Joint (X,S~2), two-sided (CUSUM, S~2), and (EWMA, S~2) control charts are numerically compared when (i) process parameters are known and (ii) process parameters are estimated from retrospective data. In both cases, equations for the conditional and unconditional run length distributions are developed, and expressions for the average run lengths (ARL), the second moment of the run length (SMRL), and the standard deviation of the run lengths (SDRL) are derived for these charts. In-control and out-of-control ARLs and SDRLs are tabulated and compared for a variety of design parameters for each chart. Numerical results and practical recommendations are given.