Development and comparisons of reliability acceptance sampling plans for the weibull distribution under accelerated type-i censoring

Abstract

In this thesis, reliability acceptance sampling plans (RASPs) for the Weibull distribution are developed assuming that the life test is conducted at an accelerated condition at which the acceleration factor (AF) is known and the test is Type-I censored. Two classes of RASPs are considered. In the first class, the shape as well as the scale parameter of the Weibull distribution is assumed to be unknown and the test time at the accelerated condition is set to the mission time at the use condition divided by AF. Two types of RASPs are developed in the first class. One is the ‘exact’ variables RASP in which each item is continuously monitored for failure, and the other is the attributes RASP in which test items are inspected only once at the censoring time. Then, for both types of RASPs, sensitivity analysis is conducted to assess the effect of the uncertainty in the assumed AF on the actual producer and consumer risks, and a method is developed for constructing RASPs that can accommodate the uncertainty in AF. In addition, these two types of plans are compared in terms of the sample size, the sensitivity to the uncertainty in AF, and the power. In the second class of RASPs, the shape parameter is assumed to be known, and attributes RASPs are developed in which the censoring time can be selected regardless of the mission time and AF. Sensitivity analyses are also conducted to assess the effects of the uncertainties in the assumed shape parameter and AF on the actual producer and consumer risks, and a method is developed for constructing RASPs that can accommodate these uncertainties. The Weibull distribution is one of the most frequently used lifetime distributions in reliability engineering. In addition, accelerated, Type-I censored life testing schemes are commonly adopted in practice to reduce the amount of testing time and effort. It is therefore expected that reliability engineers can benefit from the results presented in this thesis for the reliabili...