We consider the problem of the evaluation of the maintenance policy of a component by means of degradation modeling. We assume that the stochastic laws governing the degradation process are uncertain, and so are the related parameters. We assume that the information available is in the form of qualitative judgment by an expert. We develop a representation framework based on possibility theory and the concept of fuzzy random variables. An example of application is given with reference to a medium-voltage circuit-breaker test facility.
ZioECompareM. A snapshot on maintenance modeling and applications. In: Proceedings of the 1st international conference of maritime technology and engineering – MARTECH 2011, 10–12 May2011, Lisbon, Portugal, Volume 2, pp.1413–1425. Taylor & Francis Group, London.
2.
ZioE. The Monte Carlo Simulation Method for System Reliability and Risk Analysis. Springer Series in Reliability Engineering, Springer, London. 2012.
3.
NicolaiRPFrenkJBGDekkerR. Modeling and optimizing imperfect maintenance of coatings on steel structures. Struct Saf2009; 31: 234–244.
4.
ApostolakisGE. The concept of probability in safety assessments of technological systems. Science1990; 250: 1359–1364.
5.
DuboisDPradeH. Possibility theory, probability theory and multiple valued-logics: A clarification. Ann Math Artif Intell2001; 32: 35–66.
DuboisD. Possibility theory and statistical reasoning. Computat Stat Data Analysis2006; 51: 47–69.
8.
BaudritCDuboisDGuyonnetD. Joint propagation and exploitation of probabilistic and possibilistic information in risk assessment. IEEE Trans Fuzzy Sys2006; 14(5): 593–608.
9.
DuboisDPradeH. When upper probabilities are possibility measures. Fuzzy Sets Sys1992; 49: 65–74.
10.
ShapiroAF. Fuzzy random variables. Insurance Math Econ2009; 44(2): 307–314.
11.
DempsterAP. Upper and lower probabilities induced by a multi-valued mapping. Ann Math Stat1967; 38: 325–339.
12.
ShaferG. A mathematical theory of evidence. Princeton, NJ: Princeton University Press, 1976.
13.
FersonSGinzburgbLR. Different methods are needed to propagate ignorance and variability. Reliab Engng Sys Saf1996; 54(2–3): 133–144.
14.
FersonSKreinovichVGinzburgLR. Constructing probability boxes and dempster-shafer structures. SAND REPORT SAND2002–4015, 2003.
15.
ZadehLA. Fuzzy sets. Info Control1965; 8: 338–353.
16.
BaraldiPZioE. A comparison between probabilistic and Dempster-Shafer theory approaches to model uncertainty analysis in the performance assessment of radioactive waste repositories. Risk Analysis2010; 30(7): 1139–1156.
17.
BaraldiPBalestreroACompareM. A modeling framework for maintenance optimization of electrical components based on fuzzy logic and effective age. Qual Reliab Engng Int. Epub ahead of print, April2013. DOI: 10.1002/qre.1388.
18.
BaraldiPCompareMDespujolsA. Modeling of the effect of maintenance actions on the degradation of an electric power plant component. Proc IMechE, Part O: J Risk and Reliability. Submitted, 2010, 225(2), pp.169–183.
19.
BaraldiPCompareMRossettiG. A modelling framework to assess maintenance policy performance in electrical production plants. In: AndrewsBerenguerJackson (eds) Maintenance modeling and applications. An ESREDA Project Group Report, pp.263–282.
20.
JonesBJenkinsonIWangJ. The use of fuzzy set modelling for maintenance planning in a manufacturing industry. Proc IMechE, Part E: J Process Mechanical Engineering2010; 224: 35–48.
21.
BaraldiPCompareMZioE. Maintenance policy performance assessment in presence of imprecision based on Dempster-Shafer theory of evidence. Info Sci Accepted, 2012. DOI: 10.1016/j.ins.2012.11.003
22.
BaraldiPCompareMZioE. Dempster-Shafer theory of evidence to handle maintenance models tainted with imprecision. In: Proceedings of the joint PSAM 11 and ESREL 2012 conference, 25–29 June2012, IAPSAM & ESRA, Helsinki, Finland.
23.
BaraldiPCompareMZioE. Representation and propagation of the uncertainty in expert information on the parameters of degradation models for maintenance policy assessment. Applied Soft Computing. Submitted, 2011.
24.
LimbourgPde RacquignyE. Uncertainty analysis using evidence theory- confronting level-1 and level-2 approaches with data availability and computational constraints. Reliab Engng Sys Saf2010; 95: 550–564.
25.
BojadzievGBojadzievM. Fuzzy sets, fuzzy logic, applications, World Scientific, 2000, Singapore.
26.
LimbourgP. Multi-objective optimization of problems with epistemic uncertainty. Lecture Notes in Computer Science LNCS2005; 3410: 413–427.
27.
DebKGuptaSDaumD. Reliability-based optimization using evolutionary algorithms. IEEE Trans Evolu Comput2009; 13(5): 1054–1074.
28.
BaraldiPCompareMZioE. Importance measures for maintenance prioritization in the presence of imprecision. IEEE Trans Reliab. 2013, 62(1), pp.37–48.
