Simple bounds for terminating Poisson and renewal shock processes
type: Item
instance of: scholarly article
title: Simple bounds for terminating Poisson and renewal shock processes
zbMATH Open document ID: 1032.62099
DOI: 10.1016/S0378-3758(02)00111-8
author: M. S. Finkelstein
published in: Journal of Statistical Planning and Inference
publication date: 2003-05-19T00:00:00Z
review text: A reliabilility system driven by a point process of shocks is considered. The shocks occur in accordance with a renewal or non-homogeneous Poisson process. Each shock independently of the previous history leads to a system failure with probability \(\theta\) and survives with the complimentary probability \(1-\theta\). It is well known that the exact form of the probability of survival is given by an infinite series. In this paper, new simple bounds for the probability of survival are given. In the proofs, stochastic hazard rate processes are used. Thus, the case is treated where the probability of a system failure under the effect of a current shock depends on the time since the previous one.
reviewed by: Evgeny Spodarev
Mathematics Subject Classification ID: 62N05
Mathematics Subject Classification ID: 60K10
zbMATH DE Number: 1912373
zbMATH Keywords: survival
zbMATH Keywords: reliability
zbMATH Keywords: Poisson process
zbMATH Keywords: renewal process
zbMATH Keywords: shock process
zbMATH Keywords: hazard rate process
Wikidata QID: Q58293347
MaRDI profile type: Publication
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full work available at URL: s0378-3758(02)00111-8
OpenAlex ID: W2027122785
description: scientific article; zbMATH DE number 1912373