Using markov models to compute probability of failed dangerous when repair times are not exponentially distributed

Members of standards committees for safety instrumented systems (SIS) are debating the relative merits of different modeling techniques for assessing the appropriateness of safety system design. One argument against the use of Markov models is that they represent repair times by exponential densities but that repair times are not exponentially distributed. In this paper, we use a simple Markov model with typical non-exponential repair times and calculate, by simulation methods, both the transient and steady state probabilities of the failed dangerous detected (FDD) state over a range of values for failure rates. We compare these results to those obtained using two different Markov models that assume exponentially distributed repair times. We show that the steady state probabilities from all three models are identical though the transients show some differences. We conclude that, to the extent that steady state probability of the FDD state is considered an appropriate measure of system safety, simple Markov models with exponential repair-time densities can be used and will give the same results as more complicated non-exponential repair-time densities