A posterior probability based sequential binomial test method for verification of success ratio p

Abstract

Testing the lifetimes of components or products by means of the verification of probability of success ratio p on which to base a statistical probability of the binomial distribution is often a costly and difficult undertaking. Sometimes tests cannot reach at a desirable target, particularly, in the reliability assurance tests. A Bayesian sequential binomial test model (BSBTM) is proposed for obtaining the composite hypothesis of p, which posterior criteria are taken into consideration. In order to get robust decision criteria and closed continuation-sampling regions, a modified Bayesian sequential binomial test model (MBSBTM) is also developed. By using BSBTM and MBSBTM, the upper and lower boundaries of a continuation-sampling region can be determined and the decision criteria can be made. A simulation method of calculating the average sample number (ASN) by using MBSBTM is also presented in this paper. Two case examples are used to demonstrate the proposed BSBTM and MBSBTM methodologies. The results indicate that by using MBSBTM sample numbers can be decided effectively and efficiently in the reliability tests.