Testing the Minimal Repair Assumption in an Imperfect Repair Model
提出两种非参数检验方法，用于判断不完美维修系统是否满足最小维修假设，并基于生存函数估计量的渐近联合分布推导大样本理论，提供模拟结果。
Abstract Models assuming minimal repair specify that on repair, a failed system is returned to the working state, while the effective age of the system is held constant; that is, the distribution of the time until the next failure of the repaired system is the same as for a system of the same age that has not yet failed. These models are common in the literature of operations research and reliability, and many probabilistic results as well as inferential procedures depend on the minimal repair assumption. We propose two nonparametric tests of the assumption that imperfectly repaired systems are minimally repaired in some models. The large sample theory for these tests is derived from the asymptotic joint distribution of a survival function estimator and the ordinary empirical survival function based on the initial failure times of new or perfectly repaired systems. Simulation results are also provided for the null hypothesis case and under other alternatives.