Parallel systems using the Weibull model

A. Polpo; M. A. Coque; C.A. de B. Pereira

doi:10.1063/1.3039002

Parallel systems using the Weibull model

A. Polpo, M. A. Coque, C.A. de B. Pereira

Research output: Chapter in Book/Conference paper › Conference paper › peer-review

Abstract

A series system reliability is based on the minimum life time of its components. Its dual, the parallel system, is based on maximum. Here, we consider the statistical analysis of a parallel system where its components follows the Weibull parametric model. Our perspective is Bayesian. Due to the mathematical complexity, to obtain the posterior distribution we use the Metropolis‐Hasting simulation method. Based on this posterior, we evaluated the evidence of the Full Bayesian Significance Test —FBST— for comparing component reliabilities. The reason for using FBST is the fact that we are testing precise hypotheses. An example illustrates the methodology.

Original language	English
Title of host publication	BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING
Subtitle of host publication	Proceedings of the 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
Editors	M. Lauretto, C. Pereira, J. Stern
Place of Publication	USA
Publisher	American Institute of Physics
Pages	215-223
Volume	1073
ISBN (Print)	9870735406049
DOIs	https://doi.org/10.1063/1.3039002
Publication status	Published - 11 Nov 2008
Externally published	Yes
Event	28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering - Boraceia/SP, Brazil Duration: 6 Jul 2008 → 11 Jul 2008 Conference number: 28

Publication series

Name	AIP Conference Proceedings
Publisher	AIP
Volume	1073
ISSN (Print)	0094-243X

Conference

Conference	28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
Abbreviated title	MaxEnt
Country/Territory	Brazil
City	Boraceia/SP
Period	6/07/08 → 11/07/08

Access to Document

10.1063/1.3039002

http://aip.scitation.org/doi/abs/10.1063/1.3039002

Cite this

Polpo, A., Coque, M. A., & Pereira, C. A. D. B. (2008). Parallel systems using the Weibull model. In M. Lauretto, C. Pereira, & J. Stern (Eds.), BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: Proceedings of the 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (Vol. 1073, pp. 215-223). (AIP Conference Proceedings; Vol. 1073). American Institute of Physics. https://doi.org/10.1063/1.3039002

Polpo, A. ; Coque, M. A. ; Pereira, C.A. de B. / Parallel systems using the Weibull model. BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: Proceedings of the 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. editor / M. Lauretto ; C. Pereira ; J. Stern. Vol. 1073 USA : American Institute of Physics, 2008. pp. 215-223 (AIP Conference Proceedings).

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title = "Parallel systems using the Weibull model",

abstract = "A series system reliability is based on the minimum life time of its components. Its dual, the parallel system, is based on maximum. Here, we consider the statistical analysis of a parallel system where its components follows the Weibull parametric model. Our perspective is Bayesian. Due to the mathematical complexity, to obtain the posterior distribution we use the Metropolis‐Hasting simulation method. Based on this posterior, we evaluated the evidence of the Full Bayesian Significance Test —FBST— for comparing component reliabilities. The reason for using FBST is the fact that we are testing precise hypotheses. An example illustrates the methodology.",

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year = "2008",

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volume = "1073",

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note = "28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt ; Conference date: 06-07-2008 Through 11-07-2008",

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Polpo, A, Coque, MA & Pereira, CADB 2008, Parallel systems using the Weibull model. in M Lauretto, C Pereira & J Stern (eds), BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: Proceedings of the 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. vol. 1073, AIP Conference Proceedings, vol. 1073, American Institute of Physics, USA, pp. 215-223, 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Boraceia/SP, Brazil, 6/07/08. https://doi.org/10.1063/1.3039002

Parallel systems using the Weibull model. / Polpo, A.; Coque, M. A.; Pereira, C.A. de B.
BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: Proceedings of the 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. ed. / M. Lauretto; C. Pereira; J. Stern. Vol. 1073 USA: American Institute of Physics, 2008. p. 215-223 (AIP Conference Proceedings; Vol. 1073).

Research output: Chapter in Book/Conference paper › Conference paper › peer-review

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N2 - A series system reliability is based on the minimum life time of its components. Its dual, the parallel system, is based on maximum. Here, we consider the statistical analysis of a parallel system where its components follows the Weibull parametric model. Our perspective is Bayesian. Due to the mathematical complexity, to obtain the posterior distribution we use the Metropolis‐Hasting simulation method. Based on this posterior, we evaluated the evidence of the Full Bayesian Significance Test —FBST— for comparing component reliabilities. The reason for using FBST is the fact that we are testing precise hypotheses. An example illustrates the methodology.

AB - A series system reliability is based on the minimum life time of its components. Its dual, the parallel system, is based on maximum. Here, we consider the statistical analysis of a parallel system where its components follows the Weibull parametric model. Our perspective is Bayesian. Due to the mathematical complexity, to obtain the posterior distribution we use the Metropolis‐Hasting simulation method. Based on this posterior, we evaluated the evidence of the Full Bayesian Significance Test —FBST— for comparing component reliabilities. The reason for using FBST is the fact that we are testing precise hypotheses. An example illustrates the methodology.

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KW - Evidence

KW - Significance test

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Polpo A, Coque MA, Pereira CADB. Parallel systems using the Weibull model. In Lauretto M, Pereira C, Stern J, editors, BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: Proceedings of the 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. Vol. 1073. USA: American Institute of Physics. 2008. p. 215-223. (AIP Conference Proceedings). doi: 10.1063/1.3039002

Parallel systems using the Weibull model

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