The Annals of Statistics

Sequential Nonparametric Age Replacement Policies

Edward W. Frees and David Ruppert

Full-text: Open access


Under an age replacement policy, a stochastically failing unit is replaced at failure or after being in service for $t$ units of time, whichever comes first. An important problem is the estimation of $\phi^\ast,$ the optimal replacement time when the form of the failure distribution is unknown. Here, $\phi^\ast$ is optimal in the sense that it is the replacement time that achieves the smallest long-run expected cost. It is shown that substantial cost savings can be effected by estimating $\phi^\ast$ sequentially. The sequential methodology employed here is stochastic approximation (SA). When suitably standardized, convergence in distribution of the SA estimator to $\phi^\ast$ is established. This gives precise information about the rate of convergence. A sequential methodology introduced by Bather (1977) has roughly the same aims as ours, but it is not of the SA type. Rates of convergence apparently have not been established for Bather's procedure.

Article information

Ann. Statist., Volume 13, Number 2 (1985), 650-662.

First available in Project Euclid: 12 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 90B25: Reliability, availability, maintenance, inspection [See also 60K10, 62N05]
Secondary: 62L20: Stochastic approximation 62L12: Sequential estimation

Age replacement policy stochastic approximation adaptive control kernel estimation


Frees, Edward W.; Ruppert, David. Sequential Nonparametric Age Replacement Policies. Ann. Statist. 13 (1985), no. 2, 650--662. doi:10.1214/aos/1176349545.

Export citation