Abstract
This article studies the prognosis of failure, i.e., its prediction prior to its occurrence, in stochastic discrete event systems. Prior work has focused on the definition and offline verification of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> -steps stochastic-prognosability, or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S_m$</tex-math></inline-formula> -prognosability, which allows the prediction of a fault at least <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> -steps in advance. This article complements the existing work by proposing an algorithm for the computation of online failure prognoser. The proposed algorithm reduces the condition for issuing an affirmative prognostic decision to verification condition of a safety property of a Markov chain. We discuss how such a verification condition can be computed using a finitely terminating algorithm.
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