optimal length of warranty and burn-in periods considering different types of repair

Failure rate curve based on the failure rate function of many electrical and mechanical systems shows a bathtub-shape form. in the first phase of this curve, where the failure rate has a decreasing form with a high slope, manufacturers use the burn-in method to eliminate defective products before reaching the market. in this phase most of the failures are minor (since the component is completely new, this type of error generally takes happen because of bad assembling, displacement of a socket, and so on) or major type failures (for example because of wrong design, selecting unsuitable raw materials, and so on). in the second phase, where the failure rate curve shows a constant value, manufacturers offer warranty services to their customers to ensure them about the quality and performance of their products. in this paper, we investigate the total cost incurred during the burn-in and warranty periods from the manufacturer's point of view. we consider different types of repair services and obtain the expected total cost in each phase. we present an optimization example to illustrate the efficacy of the proposed model in finding optimal values for burn-in and warranty periods.