A probabilistic analysis of diagnosability in discrete event systems

This paper shows that we can take advantage of information about the probabilities of the occurrences of events, when this information is available, to refine the classical results of diagnosability: instead of giving a binary answer, the approach we propose allows one to quantify, in particular, the degree of non-diagnosability in case of negative answer. The dynamics of the system is modelled by a reducible Markov chain. A state of this chain contains information about whether it is faulty (resp. ambiguous) or not. The useful refinements of the decision about diagnosability are then obtained from the asymptotic analysis of this Markov chain. This analysis may be very useful in practice since it may lead to take the decision of tolerating some non-diagnosable systems, if their non-diagnosability is not critical, and thus allows one saving the cost of additional sensors necessary to make these systems diagnosable. .