Comparison of Testability Verification Test Sample Size Determination Methods Based on Binomial Distribution

Abstract

The classical sample size determination methods in the testability verification test are introduced, including single, double, multiple sampling methods and sequential probability ratio test (SPRT) method. The sampling characteristics of the methods and the expressions of the average sampling times are analyzed and compared. The results show that the SPRT method has similar sampling characteristics to the single sampling method under the same requirements of bilateral testability indexes and risks, and the SPRT method has the smaller average sampling times. It is recommended to use single sampling method and SPRT method in testability verification test. Considering that these four classical methods do not use prior information, the sample size of the testability verification test is often large. Under consideration of the testability prior information, the Bayesian theory is used to improve the SPRT method to obtain the Sequential Posterior Odds Test (SPOT) method. The sampling characteristics and average sampling times of the single sampling method, SPRT method and SPOT method are compared and analyzed under the same constraint parameters in the test. The results indicate that the average sampling times of SPOT method is less than single sampling method and SPRT method with the premise of approximate sampling characteristics. It is recommended to scientifically use priori information reasonably to reduce the sample size.