ON ESTIMATING SURVIVAL FOR RELIABILITY MODELS BASED ON AGE-RELATED STOCHASTIC COMPARISONS

A new class of nonparametric reliability models is introduced and stud ied. A distribution is said to be better at age s than at age t (sBt) if the residual lifetime at age s is stochastically greater than or eq ual to the residual lifetime at age t. Applications to various forms o f replacement policies, including the cannibalization of failed system s, are noted. For fixed s < t, the problem of estimating a survival cu rve assumed to belong to the sBt class is addressed using recursive me thods. An sBt estimator is derived in closed form, and its uniform str ong consistency at an optimal rate of convergence is demonstrated. A s imulation study strongly supports the claim that the sBt estimator ten ds to outperform the empirical survivor function in small- and moderat e-size samples. (C) 1993 John Wiley & Sons, Inc.