Optimal SPRT and CUSUM procedures with compressed-limit gauges

Methodology is presented for the design of single and double compressed-limit sequential probability ratio tests (SPRT) and cumulative sum (CUSUM) control charts to detect one-sided mean shifts in a symmetric probability distribution. We also show how to evaluate the average run length properties with the fast initial response (FIR) feature. The resulting CUSUM plans have a simple scoring procedure, and are extremely simple to derive and implement. The use of two compressed-limit gauges is more efficient than a single compressed-limit gauge. In the case of SPRTs, the use of two compressed limit gauges minimizes the average sampling number required for specified operating characteristics. In the case of CUSUM, the gain in efficiency reduces the out-of-control average run length for a given in-control average run length.