The Annals of Statistics
- Ann. Statist.
- Volume 25, Number 3 (1997), 1140-1160.
Nonparametric estimation for a general repair model
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.
Ann. Statist., Volume 25, Number 3 (1997), 1140-1160.
First available in Project Euclid: 20 November 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62N05: Reliability and life testing [See also 90B25]
Secondary: 62G05: Estimation 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx]
Dorado, Crisanto; Hollander, Myles; Sethuraman, Jayaram. Nonparametric estimation for a general repair model. Ann. Statist. 25 (1997), no. 3, 1140--1160. doi:10.1214/aos/1069362741. https://projecteuclid.org/euclid.aos/1069362741