On Sensitivity of Reliability Models to the Shape of Life and Repair Time Distributions

The sensitivity analysis of systems´ characteristics to the shape of distributions is a very important task of reliability engineering of stochastic systems and networks. One of the earliest result concerning insensitivity of systems´ characteristics to the shape of service time distribution was obtained in case of Erlang´s formulas for loss queues with Poisson arrival stream, where steady-state distribution depends only on the mean service times. The paper deals with simple finite-source queueing models which completely fail if a source area becomes empty. The inter-arrival or service times are assumed to be generally distributed. It is shown that the steady-state probabilities of the systems with a buffer or with generally distributed inter-arrival times are sensitive to the shape of distributions but simultaneously the waiting time distributions have a weak sensitivity. It was observed that the sensitivity vanishes if the complete failure becomes a rare event. The results are compared with loss queues.