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Estimation of Markovian Reliability Systems with Logistics via Cross-Entropy

Abstract : Urban passenger rail systems are large scale systems comprising highly reliable redundant structures and logistics (e.g., spares or repair personnel availability, inspection protocols, etc). To meet the strict contractual obligations, steady state unavailability of such systems needs to be accurately estimated as a measure of a solution’s life cycle costs. We use Markovian Stochastic Petri Nets (SPN) models to conveniently represent the systems. We propose a multi-level Cross-Entropy (CE) optimization scheme, where we exploit the regenerative structure in the underlying continuous time Markov chain (CTMC) and to determine optimal Importance Sampling (IS) rates in the case of rare events [3]. The CE scheme is used in a pre-simulation and applied to failure transitions of the Markovian SPN models only. The proposed method divides a rare problem into a series of less rare problems by considering increasingly rare component failures. In the first stage a standard regenerative simulation is used for non-rare system failures. At each subsequent stage, the rarity is progressively increased (by decreasing the failure rates of components) and the IS rates of transitions obtained from the previous problem are used at the current stage. The final pre-simulation stage provides a vector of IS rates that are optimized and are used in the main simulation. The experimental results showed bounded relative error (BRE) property as the rarity of the original problem increases, and as a consequence a considerable variance reduction and gain (in terms of work normalized variance).
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Contributor : Bruno Tuffin <>
Submitted on : Monday, December 10, 2018 - 1:47:15 PM
Last modification on : Saturday, July 11, 2020 - 3:14:25 AM


  • HAL Id : hal-01949782, version 1


Ajit Rai, Bruno Tuffin, Rene Valenzuela, Gerardo Rubino, Pierre Dersin. Estimation of Markovian Reliability Systems with Logistics via Cross-Entropy. MCQMC'18 - 13th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Jul 2018, Rennes, France. ⟨hal-01949782⟩



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