An optimal design algorithm of the SPRT chart for minimizing weighted ATS

The Sequential Probability Ratio Test (SPRT) chart is a very effective control chart. It is much faster to detect out-of-control cases compared with the X̄ and CUSUM charts, even their VSSI (Variable Sample Sizes and Sampling Intervals) versions. The new contribution of this paper is the development of an algorithm for the optimal design of the SPRT chart based on the Average Extra Quadratic Loss (AEQL). More importantly, the results of the systematic comparative studies show that this design algorithm is indeed effective. Using the design algorithm proposed here yields charts that significantly outperform other designs in terms of the proposed AEQL performance criteria for detecting process mean shifts. Moreover, this paper conducts a designed experiment to study the effect of the Average Sample Number (ASN) (i.e., the average sample size) on the chart's performance. It is found that, in order to achieve higher overall detection effectiveness, the ASN of the SPRT chart should be set substantially smaller compared with that recommended by the existing guidelines.