Bayesian reliability analysis for fuzzy lifetime data

Huang, Hong‐Zhong; Zuo, Ming J.; Sun, Zhixin

doi:10.1016/j.fss.2005.11.009

Cited by 205 publications

(106 citation statements)

References 35 publications

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“…It looks unrealistic to represent continuous real variables in the form of precise numbers or vectors because exact measurements of real continuous variables are not possible, they are more or less fuzzy. Some books and research papers have already been written dealing with fuzzy observations like [Klir and Yuan 1995;Lee 2005;Viertl and Hareter 2006;Huang et al 2006;Wu 2009]. …”

Section: Fuzzy Informationmentioning

confidence: 99%

Generalized Kaplan Meier Estimator for Fuzzy Survival Times

Shafiq

Viertl²

2015

Śląski Przegląd Statystyczny

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Section: Fuzzy Informationmentioning

confidence: 99%

Generalized Kaplan Meier Estimator for Fuzzy Survival Times

Shafiq

Viertl²

2015

Śląski Przegląd Statystyczny

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“…• Lack of information in input data, small sample size, insufficient information or scarce data (Chen et al, 1999;Mourelatos and Zhou, 2004;Nikolaidis and Haftka, 2001;Huang et al, 2004; • Imprecise data or lack of knowledge Youn and Choi, 2004a;Youn et al, 2004;Aughenbaugh and Paredis, 2005;Huang et al, 2005b;2006d;Limbourg, 2005;Mourelatos and Zhou, 2005) • Large-scale, complex or costly systems (Zhuang et al, 2000) …”

Section: Ajeasmentioning

confidence: 99%

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Huang

Liu

et al. 2013

American Journal of Engineering and Applied Sciences

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Engineering design under uncertainty has gained considerable attention in recent years. A great multitude of new design optimization methodologies and reliability analysis approaches are put forth with the aim of accommodating various uncertainties. Uncertainties in practical engineering applications are commonly classified into two categories, i.e., aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty arises because of unpredictable variation in the performance and processes of systems, it is irreducible even adding more data or knowledge. On the other hand, epistemic uncertainty stems from lack of knowledge of the system due to limited data, measurement limitations, or simplified approximations in modeling system behavior and it can be reduced by obtaining more data or knowledge. More specifically, aleatory uncertainty is naturally represented by a statistical distribution and its associated parameters can be characterized by sufficient data. If, however, the data is limited and can be quantified in a statistical sense, epistemic uncertainty can be considered as an alternative tool in such a situation. Of the several optional treatments for epistemic uncertainty, possibility theory and evidence theory have proved to be the most computationally efficient and stable for reliability analysis and engineering design optimization. This study first attempts to provide a better understanding of uncertainty in engineering design by giving a comprehensive overview of its classifications, theories and design considerations. Then a review is conducted of general topics such as the foundations and applications of possibility theory and evidence theory. This overview includes the most recent results from theoretical research, computational developments and performance improvement of possibility theory and evidence theory with an emphasis on revealing the capability and characteristics of quantifying uncertainty from different perspectives. Possibility and evidence theory-based reliability methods have many advantages for practical engineering when compared with traditional probability-based reliability methods. They can work well under limited data while the latter need large amounts of information, more than possible in engineering practice due to aleatory and epistemic uncertainties. The possible directions for future work are summarized.

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“…One-dimensional visualization of an imprecise value of the fragility function F i (y|Θ) related to the observation j y′ The problem of the Bayesian updating with imprecise data is known in the Bayesian statistical theory and related fields. Some authors model imprecise data with fuzzy numbers (Hryniewicz 2003;Huang et al 2006;Viertl 2006). This approach it is not directly applicable to the case where data is represented as a set of epistemic random variables…”

Section: Creating the Sample Of New Datamentioning

confidence: 99%

Assessment of Structures Subjected to Accidental Actions Using Crisp and Uncertain Fragility Functions

Vaidogas

Juocevičius

2009

Journal of Civil Engineering and Management

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An application of fragility functions to the assessment of potential damage due to an accidental action is analysed. The assessment is carried out as an estimation of the probability of a foreseeable damage event (damage probability). This probability is expressed as a mean value of a fragility function developed for the damage event under study. A Bayesian prior (posterior) distribution specified for this mean value is used as an estimate of the damage probability. The prior distribution is derived by transforming prior knowledge through the fragility function and “mapping” this knowledge on the scale of probability values. The technique of Bayesian bootstrap resampling is applied to update the prior distribution. The new information used for the updating consists of a relatively small number of experimental observations of the accidental action. To facilitate the updating, these observations are transformed into a fictitious statistical sample of fragility function values. The updating is first carried out with a fragility function which expresses aleatory uncertainty only. Then it is proposed how to perform the updating with the fragility function which quantifies both aleatory and epistemic uncertainty. This is done by discretising continuous distributions of the epistemic uncertainty related to values (parameters) of the fragility function. The proposed approach allows to utilise different sources of information for the damage assessment. A potential field of application of this approach is risk studies of hazardous industrial facilities. Santrauka Analizuojamas pažeidžiamumo funkcijų taikymas vertinant potencialius statybinių konstrukcijų pažeidimus avariniais poveikiais. Vertinimas atliekamas skaičiuojant galimos konstrukcijos pažaidos tikimybę. Ši tikimybė yra išreiškiama vidutine pažeidžiamumo funkcijos reikšme. Ta funkcija yra formuojama analizuojamam pažaidos įvykiui. Apriorinis ir aposteriorinis Bajeso skirstiniai yra taikomi pažaidos tikimybės reikšmei vertinti. Apriorinis skirstinys yra gaunamas pasinaudojant turima informacija apie avarinį poveikį ir transformuojant šią informaciją per pažeidžiamumo funkciją. Aposteriorinis skirstinys yra gaunamas pasitelkiant naują, eksperimentinę informaciją apie avarinį poveikį. Aposterioriniam skirstiniui gauti taikomas kartotinio statistinio ėmimo (būtstrapo) metodas. Naują informaciją sudaro eksperimentiniai avarinio poveikio charakteristikų matavimai, kurie tiksliai atitinka konstrukcijos ekspozicijos tiriamo poveikio situaciją. Apriorinis ir aposteriorinis skirstiniai išreiškia episteminį neapibrėžtumą vertinamos pažaidos tikimybės reikšmės atžvilgiu. Šie skirstiniai yra gaunami taikant tiek pažeidžiamumo funkciją, kuri išreiškia tik stochastinį neapibrėžtumą, tiek funkciją, kurios reikšmės yra neapibrėžtos epistemine prasme. Potenciali siūlomo metodo taikymo sritis yra pavojingų pramoninių objektų rizikos vertinimas.

show abstract

Bayesian reliability analysis for fuzzy lifetime data

Cited by 205 publications

References 35 publications

Generalized Kaplan Meier Estimator for Fuzzy Survival Times

Generalized Kaplan Meier Estimator for Fuzzy Survival Times

Possibility and Evidence-Based Reliability Analysis and Design Optimization

Assessment of Structures Subjected to Accidental Actions Using Crisp and Uncertain Fragility Functions

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