Adapted importance sampling schemes for the simulation of dependability models of fault-tolerant systems with deferred repair

This paper targets the simulation of continuous-time Markov chain models of fault-tolerant systems with deferred repair. We start by stating sufficient conditions for a given importance sampling scheme to satisfy the bounded relative error property. Using those sufficient conditions, it is noted that many previously proposed importance sampling techniques such as failure biasing and balanced failure biasing satisfy that property. Then, we adapt the importance sampling schemes failure transition distance biasing and balanced failure transition distance biasing so as to develop new importance sampling schemes which can be implemented with moderate effort and at the same time can be proved to be more efficient for balanced systems than the simpler failure biasing and balanced failure biasing schemes. The increased efficiency for both balanced and unbalanced systems of the new adapted importance sampling schemes is illustrated using examples.