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Statistical Taylor series expansion: an approach for epistemic uncertainty propagation in Markov reliability models. (English) Zbl 1472.60124

Summary: In this paper we develop a new Taylor series expansion method for computing model output metrics under epistemic uncertainty in the model input parameters. Specifically, we compute the expected value and the variance of the stationary distribution associated with Markov reliability models. In the multi-parameter case, our approach allows to analyze the impact of correlation between the uncertainty on the individual parameters the model output metric. In addition, we also approximate true risk by using the Chebyshev’ inequality. Numerical results are presented and compared to the corresponding Monte Carlo simulations ones.

MSC:

60J22 Computational methods in Markov chains
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
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