Correctability of fault-tolerant stochastic discrete-event systems

Failure diagnosis and correction of discrete-event systems (DESs) have received considerable attention in recent years due to the practical and theoretical importance. As a continuation of our prior work on diagnosability of stochastic DESs (i.e., Liu et al., 2008; Liu and Qiu, 2008), this paper aims to investigate the correctability issue, where the considered system is equipped with a probabilistic structure to estimate the likelihood of events occurring. More specifically: (1) We formalize the notion of k-step corrective probability to calculate the correctability of stochastic systems. Roughly speaking, the k-step corrective probability represents the probability that the stochastic system may recover to accepted states from the current state within k steps. (2) By introducing the strategy of adjusting the transition probability of the current state of system, an optimal correction mechanism is presented to achieve the maximal k-step corrective probability. (3) In addition, a novel approach of the computation of supremal corrective probability is developed by constructing the decision tree after introducing the infinitely expandable states. Finally, an example for the evolution process of the voltage in a circuit system modeled by a stochastic automaton is provided to illustrate the proposed results.