On the sensitivity of NMR unreliability to non-exponential repair distributions

The failure and repair of modules in an N-modular redundant (NMR) system are governed by a failure time distribution and a repair time distribution, respectively. It is generally reasonable to assume that a module´s failure time distribution is a simple exponential distribution. However, it is not reasonable to assume that the repair time distribution is also exponential. Reliability models with non-exponential repair have a higher computational complexity than a model of the same system with an exponential repair time distribution. This paper presents the results of a systematic study to determine whether non-exponential repair distributions produce significant differences in calculated NMR system unreliability, relative to an exponential repair distribution with the same mean time to repair (MTTR). Our approach is to embed Erlang repair distributions in generalized stochastic Petri net (GSPN) models of NMR systems and evaluate the unreliability. Our results show that, for a wide range of system parameters, the choice of a repair time distribution has minimal impact on the calculated unreliability. Rather, it is the MTTR that is the dominant parameter affecting unreliability