Shock and wear models under policy N using phase-type distributions

Delia Montoro-Cazorla, Rafael Pérez-Ocón, M. Carmen Segovia

Research output: Contribution to journal › Article

27 Citations (Scopus)

Abstract

A device submitted to shocks and wear is considered. The shocks occur with inter-arrival times phase-type distributed, and can induce the device failure. The device also can fail due to ageing, and the lifetime follows a phase-type distribution. The inter-arrival times between shocks and the lifetime depend on the number of cumulated shocks. The number of shocks that the device can support is limited. For this model, the survival probability is calculated. Other models are considered under these assumptions, and the survival functions are determined and expressed in a well-structured form. A numerical application illustrates the methods introduced in the paper.
LanguageEnglish
Pages543-554
Number of pages12
JournalApplied Mathematical Modelling
Volume33
Issue number1
Early online date3 Dec 2007
DOIs
Publication statusPublished - 1 Jan 2009

Fingerprint

Phase-type Distribution
Shock
Wear of materials
Arrival Time
Aging of materials
Lifetime
Model
Survival Function
Survival Probability
Policy

Keywords

  • phase-type distribution
  • survival function
  • Markov process
  • shock and wear models

Cite this

Montoro-Cazorla, Delia ; Pérez-Ocón, Rafael ; Segovia, M. Carmen. / Shock and wear models under policy N using phase-type distributions. In: Applied Mathematical Modelling. 2009 ; Vol. 33, No. 1. pp. 543-554.
@article{10558aad09f5494a906bce81b66d9ac5,
title = "Shock and wear models under policy N using phase-type distributions",
abstract = "A device submitted to shocks and wear is considered. The shocks occur with inter-arrival times phase-type distributed, and can induce the device failure. The device also can fail due to ageing, and the lifetime follows a phase-type distribution. The inter-arrival times between shocks and the lifetime depend on the number of cumulated shocks. The number of shocks that the device can support is limited. For this model, the survival probability is calculated. Other models are considered under these assumptions, and the survival functions are determined and expressed in a well-structured form. A numerical application illustrates the methods introduced in the paper.",
keywords = "phase-type distribution, survival function, Markov process, shock and wear models",
author = "Delia Montoro-Cazorla and Rafael P{\'e}rez-Oc{\'o}n and Segovia, {M. Carmen}",
year = "2009",
month = "1",
day = "1",
doi = "10.1016/j.apm.2007.11.017",
language = "English",
volume = "33",
pages = "543--554",
journal = "Applied Mathematical Modelling",
issn = "0307-904X",
number = "1",

}

Montoro-Cazorla, D, Pérez-Ocón, R & Segovia, MC 2009, 'Shock and wear models under policy N using phase-type distributions' Applied Mathematical Modelling, vol. 33, no. 1, pp. 543-554. https://doi.org/10.1016/j.apm.2007.11.017

Shock and wear models under policy N using phase-type distributions. / Montoro-Cazorla, Delia; Pérez-Ocón, Rafael; Segovia, M. Carmen.

In: Applied Mathematical Modelling, Vol. 33, No. 1, 01.01.2009, p. 543-554.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Shock and wear models under policy N using phase-type distributions

AU - Montoro-Cazorla, Delia

AU - Pérez-Ocón, Rafael

AU - Segovia, M. Carmen

PY - 2009/1/1

Y1 - 2009/1/1

N2 - A device submitted to shocks and wear is considered. The shocks occur with inter-arrival times phase-type distributed, and can induce the device failure. The device also can fail due to ageing, and the lifetime follows a phase-type distribution. The inter-arrival times between shocks and the lifetime depend on the number of cumulated shocks. The number of shocks that the device can support is limited. For this model, the survival probability is calculated. Other models are considered under these assumptions, and the survival functions are determined and expressed in a well-structured form. A numerical application illustrates the methods introduced in the paper.

AB - A device submitted to shocks and wear is considered. The shocks occur with inter-arrival times phase-type distributed, and can induce the device failure. The device also can fail due to ageing, and the lifetime follows a phase-type distribution. The inter-arrival times between shocks and the lifetime depend on the number of cumulated shocks. The number of shocks that the device can support is limited. For this model, the survival probability is calculated. Other models are considered under these assumptions, and the survival functions are determined and expressed in a well-structured form. A numerical application illustrates the methods introduced in the paper.

KW - phase-type distribution

KW - survival function

KW - Markov process

KW - shock and wear models

UR - http://www.sciencedirect.com/science/article/pii/S0307904X07003101#articles

U2 - 10.1016/j.apm.2007.11.017

DO - 10.1016/j.apm.2007.11.017

M3 - Article

VL - 33

SP - 543

EP - 554

JO - Applied Mathematical Modelling

T2 - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

SN - 0307-904X

IS - 1

ER -

Montoro-Cazorla D, Pérez-Ocón R, Segovia MC. Shock and wear models under policy N using phase-type distributions. Applied Mathematical Modelling. 2009 Jan 1;33(1):543-554. https://doi.org/10.1016/j.apm.2007.11.017

Access to Document