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2013 | OriginalPaper | Chapter

Closed-Form Approach for Epistemic Uncertainty Propagation in Analytic Models

Authors : Kesari Mishra, Kishor S. Trivedi

Published in: Stochastic Reliability and Maintenance Modeling

Publisher: Springer London

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Abstract

System dependability or performance is often studied using stochastic models. These models capture the natural uncertainty in the system being studied, known as aleatory uncertainty. Randomness in events of interest like times to failure/recovery of components, ability to detect failures, ability to perform recovery action, inter-arrival time, service time, etc., are taken into account in the models, by means of their distributions. The models are usually solved at fixed parameter values. However, the model input parameter values have uncertainty associated with them as they are derived either from a finite number of observations (from lifetime determining experiments or field data) or are based upon expert guesses. This uncertainty in model input parameter values, known as epistemic uncertainty, is not normally taken into account by the stochastic aleatory model.

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Literature
1.
go back to reference Ajmone-Marsan M, Balbo G, Conte G, Franceschinis SG (1995) Modeling with generalized stochastic petri nets. Wiley, Donatelli Ajmone-Marsan M, Balbo G, Conte G, Franceschinis SG (1995) Modeling with generalized stochastic petri nets. Wiley, Donatelli
2.
go back to reference Bobbio A, Trivedi KS (1986) An aggregation technique for the transient analysis of stiff markov chains. IEEE Trans Comp C-35(9):803–814 Bobbio A, Trivedi KS (1986) An aggregation technique for the transient analysis of stiff markov chains. IEEE Trans Comp C-35(9):803–814
3.
go back to reference Devaraj A, Mishra K, Trivedi K (2010) Uncertainty propagation in analytic availability models. In 29th IEEE international symposium on reliable distributed systems, SRDS, pp 121–130 Devaraj A, Mishra K, Trivedi K (2010) Uncertainty propagation in analytic availability models. In 29th IEEE international symposium on reliable distributed systems, SRDS, pp 121–130
4.
go back to reference Hirel C, Tuffin B, Trivedi KS (2000) Spnp: Stochastic petri nets. version 6.0. In computer performance evaluation. Modelling techniques and tools, vol 1786. Springer Berlin/Heidelberg, pp 354–357 Hirel C, Tuffin B, Trivedi KS (2000) Spnp: Stochastic petri nets. version 6.0. In computer performance evaluation. Modelling techniques and tools, vol 1786. Springer Berlin/Heidelberg, pp 354–357
5.
go back to reference Iman RL, Conover WJ (1982) A distribution-free approach to inducing rank correlation among input variables. Comm Stat Simul Comput 11(3):311–334MATHCrossRef Iman RL, Conover WJ (1982) A distribution-free approach to inducing rank correlation among input variables. Comm Stat Simul Comput 11(3):311–334MATHCrossRef
6.
go back to reference Kass-Robert E, Wasserman L (1996) The selection of prior distributions by formal rules. J Am Stat Assoc 91(435):1343–1370MATHCrossRef Kass-Robert E, Wasserman L (1996) The selection of prior distributions by formal rules. J Am Stat Assoc 91(435):1343–1370MATHCrossRef
7.
go back to reference Muppala J, Fricks R, Trivedi KS (2000) Techniques for system dependability evaluation. In: Grassman W (ed) Computational probability. Kluwer Academic Publishers, New York, pp 445–480CrossRef Muppala J, Fricks R, Trivedi KS (2000) Techniques for system dependability evaluation. In: Grassman W (ed) Computational probability. Kluwer Academic Publishers, New York, pp 445–480CrossRef
8.
go back to reference Ng YW, Avizienis AA (1980) A unified reliability model for fault-tolerant computers. IEEE Trans Comp C–29(211):1002–1011 Ng YW, Avizienis AA (1980) A unified reliability model for fault-tolerant computers. IEEE Trans Comp C–29(211):1002–1011
9.
go back to reference Oppenheim AV, Schafer RW, Buck JR (1999) Discrete-time signal processing. Prentice Hall, New York Oppenheim AV, Schafer RW, Buck JR (1999) Discrete-time signal processing. Prentice Hall, New York
10.
go back to reference Rabinowitz P, Davis PJ (2007) Methods of numerical integration. Dover Publications, New YorkMATH Rabinowitz P, Davis PJ (2007) Methods of numerical integration. Dover Publications, New YorkMATH
11.
go back to reference Singpurwalla ND (2006) Reliability and risk: a Bayesian perspective, 1st edn. Wiley, New YorkMATHCrossRef Singpurwalla ND (2006) Reliability and risk: a Bayesian perspective, 1st edn. Wiley, New YorkMATHCrossRef
12.
go back to reference Smith AE, Ryan PB, Evans JS (1992) The effect of neglection correlations when propagating uncertainty and estimating the population distribution risk. Risk Anal 12(4):467–474CrossRef Smith AE, Ryan PB, Evans JS (1992) The effect of neglection correlations when propagating uncertainty and estimating the population distribution risk. Risk Anal 12(4):467–474CrossRef
13.
go back to reference Smith W, Trivedi K, Tomek L, Ackaret J (2008) Availability analysis of blade server systems. IBM Syst J 47(4):155CrossRef Smith W, Trivedi K, Tomek L, Ackaret J (2008) Availability analysis of blade server systems. IBM Syst J 47(4):155CrossRef
14.
go back to reference Trivedi K (2001) Probability and statistics with reliability, queuing and computer science applications. Wiley, New York Trivedi K (2001) Probability and statistics with reliability, queuing and computer science applications. Wiley, New York
15.
go back to reference Trivedi K, Mishra K (2010) A non-obtrusive method for uncertainty propagation in analytic dependability models. In: 4th Asia-Pacific international symposium on advanced reliability and maintenance modeling (APARM 2010) Trivedi K, Mishra K (2010) A non-obtrusive method for uncertainty propagation in analytic dependability models. In: 4th Asia-Pacific international symposium on advanced reliability and maintenance modeling (APARM 2010)
16.
go back to reference Trivedi KS, Sahner R (2009) Sharpe at the age of twenty two. SIGMETRICS Perf Eval Rev 36(4):52–57CrossRef Trivedi KS, Sahner R (2009) Sharpe at the age of twenty two. SIGMETRICS Perf Eval Rev 36(4):52–57CrossRef
Metadata
Title
Closed-Form Approach for Epistemic Uncertainty Propagation in Analytic Models
Authors
Kesari Mishra
Kishor S. Trivedi
Copyright Year
2013
Publisher
Springer London
DOI
https://doi.org/10.1007/978-1-4471-4971-2_14