Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
805972 | Reliability Engineering & System Safety | 2009 | 8 Pages |
Abstract
Non-homogeneous semi-Markov processes (NHSMP) are important stochastic tools for modeling reliability metrics over time for systems where the future behavior depends on the current and next states as well as on sojourn and process times. The classical method to solve the interval transition probabilities of NHSMPs consists of directly applying any general quadrature method to some non-convolution integral equations. However, this approach has a considerable computational effort. Namely, N2-coupled integral equations with two variables must be solved, where N is the number of states. Therefore, this article proposes a more efficient mathematical formulation and numerical treatment, which are based on transition frequency densities and general quadrature methods respectively, for NHSMPs. The approach consists of only solving N-coupled integral equations with one variable and N straightforward integrations. Two examples in the context of reliability are also presented. The first one addresses a case where a semi-analytical solution is available. Then an example of application concerning pressure-temperature optical monitoring systems for oil wells is discussed. In both cases, the proposed approach is validated via the comparison against the results obtained from the semi-analytical solution (for the first example) as well as from both the classic and the Monte Carlo methods.
Keywords
Related Topics
Physical Sciences and Engineering
Engineering
Mechanical Engineering
Authors
Márcio das Chagas Moura, Enrique López Droguett,