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On the sensitivity on NMR unreliability to non-exponential repair distributions.

Kieckhafer, R.M.; Azadmanesh, M.H.; Hui, Y.

In: Proc. 5th Int. IEEE High-Assurance Systems Engineering Symposium, 15-17 November 2000, Albuquerque, NM, pages 293-300. 2000.

Abstract: The failure and repair of modules in an N-modular redundant (NMR) system are governed by a failure time distribution and 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). The proposed approach is to embed Erlang distribution in generalized stochastic Petri net (GSPN) models of NMR systems and evaluate the unreliability. The results show that for a wide range of system parameters, the choice of repair time distribution has minimal impact on the calculated unreliability. Rather, it is the MTTR that is the dominant parameter affecting unreliability.

Keywords: N-modular redundant systems, NMR systems, stochastic Petri nets.

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