Markov Decision Processes with a Constraint on the Asymptotic Failure Rate

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In this paper, we introduce a Markov decision model with absorbing states and a constraint on the asymptotic failure rate. The objective is to find a stationary policy which minimizes the infinite horizon expected average cost, given that the system never fails. Using Perron-Frobenius theory of non-negative matrices and spectral analysis, we show that the problem can be reduced to a linear programming problem. Finally, we apply this method to a real problem for an aeronautical system.