Estimation of some stochastic models used in reliability engineering

Tapio Huovinen

Research output: Book/ReportReport

Abstract

The work aims to study the estimation of some stochastic models used in reliability engineering. In reliability engineering continuous probability distributions have been used as models for the lifetime of technical components. We consider here the following distributions: exponential, 2-mixture exponential, conditional exponential, Weibull, lognormal and gamma. Maximum likelihood method is used to estimate distributions from observed data which may be either complete or censored. We consider models based on homogeneous Poisson processes such as gamma-poisson and lognormal-poisson models for analysis of failure intensity. We study also a betabinomial model for analysis of failure probability. The estimators of the parameters for three models are estimated by the matching moments method and in the case of gammapoisson and beta-binomial models also by maximum likelihood method. A great deal of mathematical or statistical problems that arise in reliability engineering can be solved by utilising point processes. Here we consider the statistical analysis of nonhomogeneous Poisson processes to describe the failing phenomena of a set of components with a Weibull intensity function. We use the method of maximum likelihood to estimate the parameters of the Weibull model. A common cause failure can seriously reduce the reliability of a system. We consider a binomial failure rate (BFR) model as an application of the marked point processes for modelling common cause failure in a system. The parameters of the binomial failure rate model are estimated with the maximum likelihood method.
Original languageEnglish
Place of PublicationEspoo
PublisherVTT Technical Research Centre of Finland
Number of pages148
ISBN (Print)951-38-3332-1
Publication statusPublished - 1989
MoE publication typeD4 Published development or research report or study

Publication series

SeriesValtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports
Number598
ISSN0358-5077

Fingerprint

Stochastic Model
Maximum Likelihood Method
Beta-binomial Model
Common Cause Failure
Engineering
Weibull
Failure Rate
Marked Point Process
Weibull Model
Non-homogeneous Poisson Process
Intensity Function
Moment Method
Failure Probability
Poisson Model
Continuous Distributions
Point Process
Exponential distribution
Poisson process
Model
Estimate

Keywords

  • reliability
  • estimation
  • modelling
  • failure analysis

Cite this

Huovinen, T. (1989). Estimation of some stochastic models used in reliability engineering. Espoo: VTT Technical Research Centre of Finland. Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports, No. 598
Huovinen, Tapio. / Estimation of some stochastic models used in reliability engineering. Espoo : VTT Technical Research Centre of Finland, 1989. 148 p. (Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports; No. 598).
@book{247cbd01878847fcbb392c39c4fa5205,
title = "Estimation of some stochastic models used in reliability engineering",
abstract = "The work aims to study the estimation of some stochastic models used in reliability engineering. In reliability engineering continuous probability distributions have been used as models for the lifetime of technical components. We consider here the following distributions: exponential, 2-mixture exponential, conditional exponential, Weibull, lognormal and gamma. Maximum likelihood method is used to estimate distributions from observed data which may be either complete or censored. We consider models based on homogeneous Poisson processes such as gamma-poisson and lognormal-poisson models for analysis of failure intensity. We study also a betabinomial model for analysis of failure probability. The estimators of the parameters for three models are estimated by the matching moments method and in the case of gammapoisson and beta-binomial models also by maximum likelihood method. A great deal of mathematical or statistical problems that arise in reliability engineering can be solved by utilising point processes. Here we consider the statistical analysis of nonhomogeneous Poisson processes to describe the failing phenomena of a set of components with a Weibull intensity function. We use the method of maximum likelihood to estimate the parameters of the Weibull model. A common cause failure can seriously reduce the reliability of a system. We consider a binomial failure rate (BFR) model as an application of the marked point processes for modelling common cause failure in a system. The parameters of the binomial failure rate model are estimated with the maximum likelihood method.",
keywords = "reliability, estimation, modelling, failure analysis",
author = "Tapio Huovinen",
year = "1989",
language = "English",
isbn = "951-38-3332-1",
series = "Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports",
publisher = "VTT Technical Research Centre of Finland",
number = "598",
address = "Finland",

}

Huovinen, T 1989, Estimation of some stochastic models used in reliability engineering. Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports, no. 598, VTT Technical Research Centre of Finland, Espoo.

Estimation of some stochastic models used in reliability engineering. / Huovinen, Tapio.

Espoo : VTT Technical Research Centre of Finland, 1989. 148 p. (Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports; No. 598).

Research output: Book/ReportReport

TY - BOOK

T1 - Estimation of some stochastic models used in reliability engineering

AU - Huovinen, Tapio

PY - 1989

Y1 - 1989

N2 - The work aims to study the estimation of some stochastic models used in reliability engineering. In reliability engineering continuous probability distributions have been used as models for the lifetime of technical components. We consider here the following distributions: exponential, 2-mixture exponential, conditional exponential, Weibull, lognormal and gamma. Maximum likelihood method is used to estimate distributions from observed data which may be either complete or censored. We consider models based on homogeneous Poisson processes such as gamma-poisson and lognormal-poisson models for analysis of failure intensity. We study also a betabinomial model for analysis of failure probability. The estimators of the parameters for three models are estimated by the matching moments method and in the case of gammapoisson and beta-binomial models also by maximum likelihood method. A great deal of mathematical or statistical problems that arise in reliability engineering can be solved by utilising point processes. Here we consider the statistical analysis of nonhomogeneous Poisson processes to describe the failing phenomena of a set of components with a Weibull intensity function. We use the method of maximum likelihood to estimate the parameters of the Weibull model. A common cause failure can seriously reduce the reliability of a system. We consider a binomial failure rate (BFR) model as an application of the marked point processes for modelling common cause failure in a system. The parameters of the binomial failure rate model are estimated with the maximum likelihood method.

AB - The work aims to study the estimation of some stochastic models used in reliability engineering. In reliability engineering continuous probability distributions have been used as models for the lifetime of technical components. We consider here the following distributions: exponential, 2-mixture exponential, conditional exponential, Weibull, lognormal and gamma. Maximum likelihood method is used to estimate distributions from observed data which may be either complete or censored. We consider models based on homogeneous Poisson processes such as gamma-poisson and lognormal-poisson models for analysis of failure intensity. We study also a betabinomial model for analysis of failure probability. The estimators of the parameters for three models are estimated by the matching moments method and in the case of gammapoisson and beta-binomial models also by maximum likelihood method. A great deal of mathematical or statistical problems that arise in reliability engineering can be solved by utilising point processes. Here we consider the statistical analysis of nonhomogeneous Poisson processes to describe the failing phenomena of a set of components with a Weibull intensity function. We use the method of maximum likelihood to estimate the parameters of the Weibull model. A common cause failure can seriously reduce the reliability of a system. We consider a binomial failure rate (BFR) model as an application of the marked point processes for modelling common cause failure in a system. The parameters of the binomial failure rate model are estimated with the maximum likelihood method.

KW - reliability

KW - estimation

KW - modelling

KW - failure analysis

M3 - Report

SN - 951-38-3332-1

T3 - Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports

BT - Estimation of some stochastic models used in reliability engineering

PB - VTT Technical Research Centre of Finland

CY - Espoo

ER -

Huovinen T. Estimation of some stochastic models used in reliability engineering. Espoo: VTT Technical Research Centre of Finland, 1989. 148 p. (Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports; No. 598).