### 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 language | English |
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Place of Publication | Espoo |

Publisher | VTT Technical Research Centre of Finland |

Number of pages | 148 |

ISBN (Print) | 951-38-3332-1 |

Publication status | Published - 1989 |

MoE publication type | D4 Published development or research report or study |

### Publication series

Series | Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports |
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Number | 598 |

ISSN | 0358-5077 |

### Keywords

- reliability
- estimation
- modelling
- failure analysis

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## Cite this

Huovinen, T. (1989).

*Estimation of some stochastic models used in reliability engineering*. VTT Technical Research Centre of Finland. Valtion teknillinen tutkimuskeskus. Tutkimuksia - Research Reports, No. 598