Decisions on an Optimal Life Test Sampling Plan With Warranty Considerations

Abstract

The choice of an appropriate life test sampling plan is a crucial decision problem because a good plan not only can help producers save testing time, and reduce testing cost; but it also can positively affect the image of the product, and thus attract more consumers to buy it. This study developed a decision model in determining the optimal life test sampling plan with an aim of cost minimization by identifying the appropriate number of product failures in a sample that should be used as a threshold in judging the rejection of a batch. A Weibull distribution with two parameters (i.e. scale factor, and shape factor) was assumed to be appropriate for modeling the lifetime of a product, and a Bayesian decision model was thus constructed to perform the prior, preposterior, and posterior analyses. The cost structure thoroughly encompassed the considerations of rejection, acceptance, testing, and warranty costs for the adoption of an optimal sampling plan, which is capable of providing guidelines for making better decisions. Finally, a practical numerical application was employed to demonstrate the effectiveness of the proposed approach.