Optimal Burn-in Time For Repairable Products Sold Under Two-stage Warranty Policy

Burn-in is a technical method used to improve the quality of products,particularly for products with an initial failure rate. Burning-in the product is that theproduct is operated for a trial period before field operation. If the product is directlyoperated without burn-in, so products will easily fail in operation process. Ifmanufacturers of the product provides customers with after-sale warranty service forthe product, so the manufacturers will spend warranty cost. Different warranty policyproduces different warranty cost. In order to reduce warranty cost, the manufacturersoften carry out burn-in test for products, but burn-in is costly. The content that thispaper researches is optimal burn-in time for repairable products sold under two-stagewarranty policy. This paper assumes that the failure rate function of products isbathtub-shaped failure rate function, the warranty period W (W≥0) is divided intotwo sections of [0,W1) and [W1,W]. Products has two types of failure, one is type Ifailure, this is able to be corrected by minimal repair, and failure rate of the repairedproducts remain the same as just prior to failure; another is type II failure, this is ableto solved by replacement with new products. If the product fails during time interval[0,W1), the manufacturers execute free-replacement warranty (FRW), namely themanufacturers repair freely or replace freely failure products; If the product failsduring time interval [W1,W], the manufacturers execute pro-rata warranty (PRW),namely the manufacturers charge for repairing or charge a fraction of sale price forreplacing failure product by new products. In this paper, firstly the expected totalmanufacturing cost is derived by using the supplementary variable method, secondlyoptimal burn-in time to minimize the expected total manufacturing cost is discussed,finally, numerical example is provided to illustrate the feasibility of the researchconclusion.