Burn‐in Time and Estimation of Change‐Point with Weibull‐Exponential Mixture Distribution*
研究如何通过老化程序减少产品早期故障，建立成本模型以确定最优老化时间，并用威布尔-指数混合分布描述产品寿命，当变点未知时用最大似然法估计，分析样本量及参数对模型的影响。
ABSTRACT Many industrial products have three phases in their product lives: infant‐mortality, normal, and wear‐out phases. In the infant‐mortality phase, the failure rate is high, but decreasing; in the normal phase, the failure rate remains constant; and in the wear‐out phase, the failure rate is increasing. A burn‐in procedure may be used to reduce early failures before shipping a product to consumers. A cost model is formulated to find the optimal burn‐in time, which minimizes the expected sum of manufacturing cost, burn‐in cost, and warranty cost incurred by failed items found during the warranty period. A mixture of Weibull hyperexponential distribution with shape parameter less than one and exponential distribution is used to describe the infant‐mortality and the normal phases of the product life. The product under consideration can be either repairable or non‐repairable. When the change‐point of the product life distribution is unknown, it is estimated by using the maximum‐likelihood estimation method. The effects of sample size on estimation error and the performance of the model are studied, and a sensitivity analysis is performed to study the effects of several parameters of the W‐E distribution and costs on the optimal burn‐in time.