Statistical Taylor series expansion: An approach for epistemic uncertainty propagation in Markov reliability models

¹ Research Unit LaMOS, Department of Operational Research, Faculty of Exact Sciences, University of Bejaia, Bejaia, Algeria
² Tinbergen Institute and Department Econometrics and Operations Research, VU University Amsterdam, Amsterdam, The Netherlands

^* Corresponding author: bachi.katia13@gmail.com

Received: 5 November 2018
Accepted: 18 September 2019

Abstract

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.