Acceptance Sampling Scheme with Warranty for Life Testing Using Bayesian Inference Methods

Abstract

We propose an empirical Bayesian (EB) procedure with a rebate warranty policy to search for optimal sampling plans for three-parameter Burr-type XII distribution (3pBXIID) under truncated life testing. The proposed method requires fewer assumptions than its competitors to search for optimal sampling plans when the lifetimes of products follow a 3pBXIID. The Newton–Raphson method using the quasi-Newton (QN) algorithm, the evolution algorithm method using the particle swarm optimization (PSO) algorithm and genetic algorithm (GA) are used in the proposed EB procedure to search for reliable estimates of the parameters in the Bayesian model, and the obtained estimates are denoted as QN-EB, PSO-EB, and GA-EB, respectively. The performance of the QN-EB, PSO-EB, and GA-EB estimates were evaluated by performing Monte Carlo simulations. The simulation results show that the PSO-EB method outperforms the GA-EB and QN-EB methods in obtaining reliable estimates of the parameters in terms of bias and mean squared error. A grid-searching algorithm with the plug-in parameters of PSO-EB estimates to search for the optimal EB sampling plans is presented. Two examples pertaining to the lifetime of an oil-well pump in a sucker-rod oil pumping system and the first failure time of a small electric cart are used to illustrate the application of the proposed EB method.