Nonparametric Bayesian Estimation of Reliabilities in a Class of Coherent Systems

Adriano Polpo, Debajyoti Sinha, Carlos A. de B. Pereira

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Usually, methods evaluating system reliability require engineers to quantify the reliability of each of the system components. For series and parallel systems, there are limited options to handle the estimation of each component's reliability. This study examines the reliability estimation of complex problems of two classes of coherent systems: series-parallel, and parallel-series. In both of the cases, the component reliabilities may be unknown. We developed estimators for reliability functions at all levels of the system (component and system reliabilities). The main assumption required is that, for all the distributions of the components of a particular system, the sets of discontinuity points have to be disjoint. Nonparametric Bayesian estimators of all sub-distribution and distribution functions are derived, and a Dirichlet multivariate process as a prior distribution is considered for the nonparametric Bayesian estimation of all distributions. For illustration, two simulated numerical examples are presented. The estimators are s-consistent, and one may observe from the examples that they have good performance. Our estimator can accommodate continuous failure distributions, as well as distributions with mass points.

Original languageEnglish
Pages (from-to)455-465
Number of pages11
JournalIEEE Transactions on Reliability
Volume62
Issue number2
DOIs
Publication statusPublished - Jun 2013
Externally publishedYes

Cite this

Polpo, Adriano ; Sinha, Debajyoti ; Pereira, Carlos A. de B. / Nonparametric Bayesian Estimation of Reliabilities in a Class of Coherent Systems. In: IEEE Transactions on Reliability. 2013 ; Vol. 62, No. 2. pp. 455-465.
@article{6c4c68ad176540d0b7956c73defdd645,
title = "Nonparametric Bayesian Estimation of Reliabilities in a Class of Coherent Systems",
abstract = "Usually, methods evaluating system reliability require engineers to quantify the reliability of each of the system components. For series and parallel systems, there are limited options to handle the estimation of each component's reliability. This study examines the reliability estimation of complex problems of two classes of coherent systems: series-parallel, and parallel-series. In both of the cases, the component reliabilities may be unknown. We developed estimators for reliability functions at all levels of the system (component and system reliabilities). The main assumption required is that, for all the distributions of the components of a particular system, the sets of discontinuity points have to be disjoint. Nonparametric Bayesian estimators of all sub-distribution and distribution functions are derived, and a Dirichlet multivariate process as a prior distribution is considered for the nonparametric Bayesian estimation of all distributions. For illustration, two simulated numerical examples are presented. The estimators are s-consistent, and one may observe from the examples that they have good performance. Our estimator can accommodate continuous failure distributions, as well as distributions with mass points.",
keywords = "Coherent systems, Dirichlet multivariate processes, reliability theory, series-parallel systems, SERIES-PARALLEL SYSTEMS, COMPETING-RISKS, MULTISTATE SYSTEMS, COMPONENTS, MODELS",
author = "Adriano Polpo and Debajyoti Sinha and Pereira, {Carlos A. de B.}",
year = "2013",
month = "6",
doi = "10.1109/TR.2013.2263033",
language = "English",
volume = "62",
pages = "455--465",
journal = "IEEE Transactions on Reliability",
issn = "0018-9529",
publisher = "IEEE, Institute of Electrical and Electronics Engineers",
number = "2",

}

Nonparametric Bayesian Estimation of Reliabilities in a Class of Coherent Systems. / Polpo, Adriano; Sinha, Debajyoti; Pereira, Carlos A. de B.

In: IEEE Transactions on Reliability, Vol. 62, No. 2, 06.2013, p. 455-465.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Nonparametric Bayesian Estimation of Reliabilities in a Class of Coherent Systems

AU - Polpo, Adriano

AU - Sinha, Debajyoti

AU - Pereira, Carlos A. de B.

PY - 2013/6

Y1 - 2013/6

N2 - Usually, methods evaluating system reliability require engineers to quantify the reliability of each of the system components. For series and parallel systems, there are limited options to handle the estimation of each component's reliability. This study examines the reliability estimation of complex problems of two classes of coherent systems: series-parallel, and parallel-series. In both of the cases, the component reliabilities may be unknown. We developed estimators for reliability functions at all levels of the system (component and system reliabilities). The main assumption required is that, for all the distributions of the components of a particular system, the sets of discontinuity points have to be disjoint. Nonparametric Bayesian estimators of all sub-distribution and distribution functions are derived, and a Dirichlet multivariate process as a prior distribution is considered for the nonparametric Bayesian estimation of all distributions. For illustration, two simulated numerical examples are presented. The estimators are s-consistent, and one may observe from the examples that they have good performance. Our estimator can accommodate continuous failure distributions, as well as distributions with mass points.

AB - Usually, methods evaluating system reliability require engineers to quantify the reliability of each of the system components. For series and parallel systems, there are limited options to handle the estimation of each component's reliability. This study examines the reliability estimation of complex problems of two classes of coherent systems: series-parallel, and parallel-series. In both of the cases, the component reliabilities may be unknown. We developed estimators for reliability functions at all levels of the system (component and system reliabilities). The main assumption required is that, for all the distributions of the components of a particular system, the sets of discontinuity points have to be disjoint. Nonparametric Bayesian estimators of all sub-distribution and distribution functions are derived, and a Dirichlet multivariate process as a prior distribution is considered for the nonparametric Bayesian estimation of all distributions. For illustration, two simulated numerical examples are presented. The estimators are s-consistent, and one may observe from the examples that they have good performance. Our estimator can accommodate continuous failure distributions, as well as distributions with mass points.

KW - Coherent systems

KW - Dirichlet multivariate processes

KW - reliability theory

KW - series-parallel systems

KW - SERIES-PARALLEL SYSTEMS

KW - COMPETING-RISKS

KW - MULTISTATE SYSTEMS

KW - COMPONENTS

KW - MODELS

U2 - 10.1109/TR.2013.2263033

DO - 10.1109/TR.2013.2263033

M3 - Article

VL - 62

SP - 455

EP - 465

JO - IEEE Transactions on Reliability

JF - IEEE Transactions on Reliability

SN - 0018-9529

IS - 2

ER -