On first-passage times in increasing Markov processes
type: Item
instance of: scholarly article
title: On first-passage times in increasing Markov processes
zbMATH Open document ID: 0856.60082
DOI: 10.1016/0167-7152(94)00010-7
author: Rafael Pérez-Ocón
author: María Luz Gámiz Pérez
published in: Statistics \& Probability Letters
publication date: 1996-07-31T00:00:00Z
review text: In the reliability theory, there exists in literature studies on increasing Markov processes. So, \textit{M. Brown} and \textit{N. R. Chaganty} [Ann. Probab. 11, 1000-1008 (1983; Zbl 0529.60069)] explained that if the transition is \(\text{TP}_2\), then the process is IFR, and if the transition matrix is stochastically monotone, then the process is IFRA. \textit{Shaked} and \textit{Shanthikumar} (1987) extended the same model for the IFRA case. \textit{I. Karasu} and \textit{S. Özekici} [J. Appl. Probab. 26, No. 4, 827-834 (1989; Zbl 0758.60095)] showed that if the potential matrix is stochastically monotone, then the process has new better than used in expectation (NBUE) first passage times. In this note, the authors use the same model as that of Karasu and Özekici. Also, the authors extend the existing literature to other reliability classes.
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60J35
zbMATH DE Number: 885153
zbMATH Keywords: first passage times
zbMATH Keywords: life distributions
zbMATH Keywords: stochastically monotone
zbMATH Keywords: reliability classes
MaRDI profile type: Publication
full work available at URL: 0167-7152(94)00010-7
OpenAlex ID: W2029871482
cites work: First-passage times with PFr densities
cites work: On the first passage time distribution for a class of Markov chains
cites work: NBUE and NWUE properties of increasing Markov processes
cites work: New better than used in expectation processes
cites work: New better than used processes
cites work: Q3993079
cites work: IFRA Properties of Some Markov Jump Processes with General State Space
description: scientific article; zbMATH DE number 885153