Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 4, Pages 497-530
doi:10.1155/S1048953396000433
The failure rate in reliability: approximations and bounds
1Université de Marne-la-Vallée, Equipe d'Analyse et de Mathématiques Appliquées, 2 rue de la Butte Verte, Noisy-le-Grande Cedex 93166, France
2Institute of Systems Analysis, 9, Prospect 60 let Oktyabrya, Moscow 117312 , Russia
Received 1 April 1996; Revised 1 October 1996
Copyright © 1996 Christiane Cocozza-Thivent and Vladimir Kalashnikov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We consider models typical to the area of reliability, and a failure rate function for processes describing the dynamics of these models. Various approximations of the failure rate function are proposed and their accuracies are investigated. The basic case studied in the paper is a regenerative model. Some interesting particular cases (Markov, semi-Markov, etc.) are considered. All proposed
estimates are stated in a tractable analytic form.
This article is dedicated to the memory of Roland L. Dobrushin.