Probability of error bounds for failure diagnosis and classification in hidden Markov models

In this paper we consider a formulation of the failure diagnosis problem in stochastic systems as a maximum likelihood classification problem: a diagnoser observes the system under diagnosis online and determines which candidate model (e.g., a fault-free model or a faulty model) is more likely given the observations. We are interested in measuring a priori the diagnosis/classification capability of the diagnoser by computing offline the probability that the diagnoser makes an incorrect decision (irrespective of the actual observation sequence) as a function of the observation step. We focus on hidden Markov models and compute an upper bound on this probability as a function of the length of the sequence observed. We also find necessary and sufficient conditions for this bound to decay to zero exponentially with the number of observations.