The failure rate in reliability: Approximations and bounds
type: Item
instance of: scholarly article
title: The failure rate in reliability: Approximations and bounds
zbMATH Open document ID: 0871.60063
DOI: 10.1155/S1048953396000433
author: Christiane Cocozza-Thivent
author: Vladimir Kalashnikov
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1997-09-24T00:00:00Z
full work available at URL: https://eudml.org/doc/47701
review text: This is a partly expository article dedicated to the memory of R. L. Dobrushin. It is concerned with a random process \((\eta_s: s\geq 0)\) describing the dynamics of a system with a state space partitioned into two subsets \(\mathcal M\) and \(\mathcal P\), the latter denoting failed states. Let \(\sigma=\inf\{s:\eta_s\in{\mathcal P}\}\) be the first failure time. The paper is concerned with comparing different failure rate functions, including the hazard function \(\lambda(t)\) of \(\sigma\) and the Vesely failure rate \(\lambda_V(t)=\lim_{\Delta\to 0}\Delta^{-1}P(\eta_{t+\Delta}\in {\mathcal P}\mid \eta_t\in{\mathcal M})\), \(t\geq 0\), especially for large \(t\). Explicit results are obtained by supposing that the dynamics of \((\eta_s)\), up to its first entrance to \(\mathcal P\), are represented by a regenerative process on \(\mathcal M\), which is killed at a self-modulated rate.
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60K15
Mathematics Subject Classification ID: 60K20
zbMATH DE Number: 988087
zbMATH Keywords: failure rate function
zbMATH Keywords: regenerative process
zbMATH Keywords: Markov process
zbMATH Keywords: Cox process
MaRDI profile type: Publication
OpenAlex ID: W2125939169
description: scientific article; zbMATH DE number 988087