B0643
Title: Computational tools for the calculus of some performance measures in a degradation system
Authors: Inma Torres Castro - University of Extremadura (Spain) [presenting]
Abstract: Performance measures are used in various stages of the system life cycle to measure the system behaviour. From a mathematical point of view, Markov models with finite state spaces are commonly used tools for the evaluation of these transient performance measures. For Markov models,the holding times are exponentially distributed which eases the calculus of the performance measures. However, the assumption of exponential holding times is often too restrictive. Considering more general holding-times leads to semi-Markov processes, which are less amenable to analyze but provide more flexible models. The functioning of a degradation process subject to a maintenance program is evaluated. The degradation of this system is modelled using a gamma process. A gamma process is a stochastic process with independent, non negative gamma distributed increments. The functioning of the system is described as a semi-regenerative process with continuous state space. To evaluate the performance of this system, some transient performance measures are calculated. These performance measures fulfill Markov renewal equations. To solve these Markov renewal equations, a numerical method that combines numerical integration, interpolation techniques and Monte Carlo simulation is used. The accuracy of this numerical method is analyzed by making comparisons with the results obtained by using strict Monte Carlo simulation.
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