Open Access
Translator Disclaimer
June 1997 Nonparametric estimation for a general repair model
Crisanto Dorado, Myles Hollander, Jayaram Sethuraman
Ann. Statist. 25(3): 1140-1160 (June 1997). DOI: 10.1214/aos/1069362741


The construction and analysis of repair models is an important area in reliability. A commonly used model is the minimal repair model. Under this model, repair restores the state of the system to its level prior to failure. Kijima introduced repair models that could be classified as "better-than-minimal." Under Kijima's models, the system, upon repair, is functionally the same as a working system of lesser age which has never experienced failure. In this paper, we present a new approach to the modeling of better-than-minimal repair models. Using this approach, we construct a general repair model that contains Kijima's models as special cases. We also study the problem of estimating the distribution of the time to first failure of a system maintained by general repair. We make use of counting processes to show strong consistency of the estimator and prove results on weak convergence. Finally, we derive a Hall-Wellner type asymptotic confidence band for the distribution of the time to first failure of the system.


Download Citation

Crisanto Dorado. Myles Hollander. Jayaram Sethuraman. "Nonparametric estimation for a general repair model." Ann. Statist. 25 (3) 1140 - 1160, June 1997.


Published: June 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0937.62103
MathSciNet: MR1447744
Digital Object Identifier: 10.1214/aos/1069362741

Primary: 62N05
Secondary: 60K20 , 62G05

Keywords: Better-than-minimal repair , Confidence band , counting process , Markov renewal process , product integral , supplemented-life-repair , weak convergence

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 3 • June 1997
Back to Top