Development and comparisons of reliability acceptance sampling plans for exponential and gamma lifetime distributions

Abstract

The lifetime of a product or a component is one of the most important quality characteristics. A reliability acceptance sampling plan(RASP) consists of a set of life test procedures and rules for either accepting or rejecting a collection of items based upon the sampled lifetime data. In this thesis, the RASP``s for the exponential and gamma lifetime distributions are developed. In addition, relative performances of these plans are compared in terms of power and expected completion time to reach a decision to provide guidelines for selecting an appropriate plan for a given situation. We first develop RASP``s without replacement for the exponential case. The first type of RASP``s developed assumes that the censoring time is given and includes RASP(HT) under Hybrid censoring and RASP(TT) under Type I censoring. The second type assumes that the sample size is given and includes RASP(HN) and RASP(TN). Relative performances of these plans and the RASP under Type II censoring(i.e., RASP(II)) are compared in terms of power and expected completion time to reach a decision. Computational results indicate that : for the first type, RASP(II) and RASP(TT) are generally preferred in terms of power and expected completion time, respectively ; and for the second, either RASP(II) or RASP(HN) is preferred in terms of power and either RASP(TN) or RASP(HN) is preferred in terms of expected completion time, the choice being dependent on some specific characteristics of competing plans. We next develop two classes of RASP``s for the gamma lifetime distribution assuming that the shape parameter is known. The first calss includes RASP``s with replacement, namely, RASP(GFF) based on the concept of failure-free period and RASP(GHR) under Hybrid censoring. Comparisons of the two plans indicate among others that RASP(GFF) has a shorter completion time on the average when the true scale parameter is large. The second class includes two types of RASP``s without replacement under Hybrid c...