Research On Sequential Test Methods Based On Multiple SPRTs

Motivated by some applied problems, several sequential test methods based on multiple Sequential Probability Ratio Tests (SPRTs) are proposed and summarized in this dissertation. The corresponding problems, such as the hypotheses design and the performance measures, are also discussed.In Section 1, to minimize the maximum sample size, the author proposes the Method of Sequential Mesh Test, which is obtained from multiple SPRT designs. The author proves the performance of the method under the Koopman-Darmois distributions.In Section 2, the designs of the alternative hypotheses, as well as the three-hypothesis sequential test scheme under the Koopman-Darmois distributions, are obtained by solving equations to meet requirements on the average sample number and error rates. Through the numerical quardrature, stochastic diffusion and stochastic approximation, the author develops the formulas of the average sample number and error rates.In Section 3, statistical performance measures for control charts on short-run production are summarized. The author proposes the Average Run Length for Signal (ARLS) to evaluate the short-run control charts. Evaluation and computation based on these performance measures are developed for the two-sided CUSUM, Shewhart and EWMA control charts.In the final section, the mixed variables-attributes test plans for sequential acceptance sampling are proposed to protect "good lots" from attributes aspect and to optimize sample sizes from variables aspect. For the exponential-binomial distributions, the author develops the exact formulas of the average sample number and error rates.