Hazard rate functions of natural and manufactured systems often show a bathtub shaped failure rate. A high early rate of failures is followed by an extended period of useful working life where failures are rare, and finally the failure rate increases as the system reaches the end of its life. Parametric modelling of such hazard rate functions can lead to unnecessarily restrictive assumptions on the function shape, however the most common non-parametric estimator (the Kaplan-Meier estimator) does not allow specification of the requirement that it be bathtub shaped. In this paper we extend the Lo and Weng (1989) approach and specify four nonparametric bathtub hazard rate functions drawn from Gamma Process Priors. We implement and demonstrate simulation for these four models.

翻译：自然系统与人工系统的危险率函数常呈现浴盆形失效率特征：初始阶段高早期失效率后，跟随一个持续的稳定工作期（该阶段失效率极低），最终随着系统寿命终结，失效率逐渐升高。对这类危险率函数进行参数建模时，可能对函数形状施加不必要限制性假设，而最常用的非参数估计量（Kaplan-Meier估计量）无法满足必须为浴盆形的约束条件。本文对Lo和Weng（1989）的方法进行扩展，提出了四种基于Gamma过程先验的非参数浴盆形危险率函数设定，并对这四种模型进行了仿真实验与结果验证。