Reliability Analysis in Series Systems: An Empirical Comparison Between Bayesian and Classical Estimators

Agatha S. Rodrigues; Teresa Cristina M. Dias; Marcelo S. Lauretto; Adriano Polpo

doi:10.1063/1.3703638

Reliability Analysis in Series Systems: An Empirical Comparison Between Bayesian and Classical Estimators

Agatha S. Rodrigues, Teresa Cristina M. Dias, Marcelo S. Lauretto, Adriano Polpo

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

3 Citations (Scopus)

Abstract

In Reliability Analysis, coherent systems represent a most important structure. In many situations systems are arranged in a series configuration, meaning that the system's failure is determined by the first component to fail. A problem of fundamental importance is to estimate the survival function parameters for each component, which allows the specification of adequate maintainance policies. However, reliability data for series systems are usually censored, in the sense that one only has information about the first component to fail. In this work, we focus on two components series systems. We discuss and compare, via numerical experiments on simulated datasets, the performances of three estimation methods: Bayesian, Frequetist maximum likelihood and nonparametric Kaplan-Meier estimators. The results of simulation study suggest that maximum likelihood and Bayesian estimators's are roughly equivalent, while Kaplan-Meier underperforms the other two.

Original language	English
Title of host publication	BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING
Editors	P Goyal, A Giffin, KH Knuth, E Vrscay
Publisher	American Institute of Physics
Pages	214-221
Number of pages	8
DOIs	https://doi.org/10.1063/1.3703638
Publication status	Published - 2012
Externally published	Yes
Event	31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt) - Waterloo, Canada Duration: 9 Jul 2011 → 16 Jul 2011 http://www.maxent2011.org/

Publication series

Name	AIP Conference Proceedings
Publisher	AMER INST PHYSICS
Volume	1443
ISSN (Print)	0094-243X

Conference

Conference	31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt)
Abbreviated title	MaxEnt 2011
Country/Territory	Canada
City	Waterloo
Period	9/07/11 → 16/07/11
Other	For over 30 years, the MaxEnt workshops have explored the use of Bayesian and Maximum Entropy methods in scientific and engineering applications. The workshop invites work on all aspects of probabilistic inference, including novel techniques and applications, and work that sheds new light on the foundations of inference. This meeting will feature a special session on the Principle of Maximum Entropy Production (MEP).
Internet address	http://www.maxent2011.org/

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10.1063/1.3703638

Cite this

Rodrigues, A. S., Dias, T. C. M., Lauretto, M. S., & Polpo, A. (2012). Reliability Analysis in Series Systems: An Empirical Comparison Between Bayesian and Classical Estimators. In P. Goyal, A. Giffin, KH. Knuth, & E. Vrscay (Eds.), BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING (pp. 214-221). (AIP Conference Proceedings; Vol. 1443). American Institute of Physics. https://doi.org/10.1063/1.3703638

Rodrigues, Agatha S. ; Dias, Teresa Cristina M. ; Lauretto, Marcelo S. et al. / Reliability Analysis in Series Systems : An Empirical Comparison Between Bayesian and Classical Estimators. BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING. editor / P Goyal ; A Giffin ; KH Knuth ; E Vrscay. American Institute of Physics, 2012. pp. 214-221 (AIP Conference Proceedings).

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title = "Reliability Analysis in Series Systems: An Empirical Comparison Between Bayesian and Classical Estimators",

abstract = "In Reliability Analysis, coherent systems represent a most important structure. In many situations systems are arranged in a series configuration, meaning that the system's failure is determined by the first component to fail. A problem of fundamental importance is to estimate the survival function parameters for each component, which allows the specification of adequate maintainance policies. However, reliability data for series systems are usually censored, in the sense that one only has information about the first component to fail. In this work, we focus on two components series systems. We discuss and compare, via numerical experiments on simulated datasets, the performances of three estimation methods: Bayesian, Frequetist maximum likelihood and nonparametric Kaplan-Meier estimators. The results of simulation study suggest that maximum likelihood and Bayesian estimators's are roughly equivalent, while Kaplan-Meier underperforms the other two.",

keywords = "Reliability analysis, series systems, competitive risks, censored reliability data",

author = "Rodrigues, \{Agatha S.\} and Dias, \{Teresa Cristina M.\} and Lauretto, \{Marcelo S.\} and Adriano Polpo",

year = "2012",

doi = "10.1063/1.3703638",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics",

pages = "214--221",

editor = "P Goyal and A Giffin and KH Knuth and E Vrscay",

booktitle = "BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING",

address = "United States",

note = "31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt), MaxEnt 2011 ; Conference date: 09-07-2011 Through 16-07-2011",

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Rodrigues, AS, Dias, TCM, Lauretto, MS & Polpo, A 2012, Reliability Analysis in Series Systems: An Empirical Comparison Between Bayesian and Classical Estimators. in P Goyal, A Giffin, KH Knuth & E Vrscay (eds), BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING. AIP Conference Proceedings, vol. 1443, American Institute of Physics, pp. 214-221, 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt), Waterloo, Canada, 9/07/11. https://doi.org/10.1063/1.3703638

Reliability Analysis in Series Systems: An Empirical Comparison Between Bayesian and Classical Estimators. / Rodrigues, Agatha S.; Dias, Teresa Cristina M.; Lauretto, Marcelo S. et al.
BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING. ed. / P Goyal; A Giffin; KH Knuth; E Vrscay. American Institute of Physics, 2012. p. 214-221 (AIP Conference Proceedings; Vol. 1443).

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

TY - GEN

T1 - Reliability Analysis in Series Systems

T2 - 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt)

AU - Rodrigues, Agatha S.

AU - Dias, Teresa Cristina M.

AU - Lauretto, Marcelo S.

AU - Polpo, Adriano

PY - 2012

Y1 - 2012

N2 - In Reliability Analysis, coherent systems represent a most important structure. In many situations systems are arranged in a series configuration, meaning that the system's failure is determined by the first component to fail. A problem of fundamental importance is to estimate the survival function parameters for each component, which allows the specification of adequate maintainance policies. However, reliability data for series systems are usually censored, in the sense that one only has information about the first component to fail. In this work, we focus on two components series systems. We discuss and compare, via numerical experiments on simulated datasets, the performances of three estimation methods: Bayesian, Frequetist maximum likelihood and nonparametric Kaplan-Meier estimators. The results of simulation study suggest that maximum likelihood and Bayesian estimators's are roughly equivalent, while Kaplan-Meier underperforms the other two.

AB - In Reliability Analysis, coherent systems represent a most important structure. In many situations systems are arranged in a series configuration, meaning that the system's failure is determined by the first component to fail. A problem of fundamental importance is to estimate the survival function parameters for each component, which allows the specification of adequate maintainance policies. However, reliability data for series systems are usually censored, in the sense that one only has information about the first component to fail. In this work, we focus on two components series systems. We discuss and compare, via numerical experiments on simulated datasets, the performances of three estimation methods: Bayesian, Frequetist maximum likelihood and nonparametric Kaplan-Meier estimators. The results of simulation study suggest that maximum likelihood and Bayesian estimators's are roughly equivalent, while Kaplan-Meier underperforms the other two.

KW - Reliability analysis

KW - series systems

KW - competitive risks

KW - censored reliability data

UR - https://www.scopus.com/pages/publications/84861119186

U2 - 10.1063/1.3703638

DO - 10.1063/1.3703638

M3 - Conference paper

T3 - AIP Conference Proceedings

SP - 214

EP - 221

BT - BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING

A2 - Goyal, P

A2 - Giffin, A

A2 - Knuth, KH

A2 - Vrscay, E

PB - American Institute of Physics

Y2 - 9 July 2011 through 16 July 2011

ER -

Rodrigues AS, Dias TCM, Lauretto MS, Polpo A. Reliability Analysis in Series Systems: An Empirical Comparison Between Bayesian and Classical Estimators. In Goyal P, Giffin A, Knuth KH, Vrscay E, editors, BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING. American Institute of Physics. 2012. p. 214-221. (AIP Conference Proceedings). doi: 10.1063/1.3703638

Reliability Analysis in Series Systems: An Empirical Comparison Between Bayesian and Classical Estimators

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