Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 4, Pages 497-530

The failure rate in reliability: approximations and bounds

Christiane Cocozza-Thivent1 and Vladimir Kalashnikov2

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.


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.