ID : 1041
Studies ; Stochastic models ; Reliability ; Markov analysis ; Management science
The importance of sampling techniques for the simulation of Markovian systems with highly reliable components is investigated.  The need for simulation arises because the state space of such systems is typically huge, making numerical computating inefficient.  Naive simulation is inefficient due to the rarity of the system failure events.  Failure biasing is a useful importance sampling technique for the simulation of such systems.  A mathematical framework for the study of failure biasing is presented.  Using this framework variance reduction results are derived which explain the magnitude of the variance reduction obtained in practice.  It is shown that in many cases the magnitude of the variance reduction is such that the relative errors of the estimates remain bounded as the failure rates of components tend to zero.
Importance sampling for the simulation of highly reliable Markovian systems, Shahabuddin, Perwez, Management Science, 40:3, Mar 1994
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