Investigations into the Transient Analysis of System Reliability/Availability via Cumulant Functions

摘要

The specific problem considered in this research is that of using cumulant functions to describe the reliability function of a system operating in a Markovian environment. The environment consists of non-fatal shocks that have the effect of weakening, though not destroying, the system on impact. Each shock has both an immediate repairable effect and a permanent non-repairable effect that increases the failure rate of the system in a non-linear fashion. These shocks may represent several events, most notably the failure of other system components as was originally described in the proposal. The use of cumulant functions is a novel approach to this problem. Our work focused on how this approach may be applied, the accuracy of the approximation under various cumulant truncation levels, and the computational efficiency of this method. The research findings described in the attached paper may be summarized as follows: 1) Cumulant-based methods may be applied to this reliability model in a straightforward fashion; 2) The accuracy of the reliability functions approximations do not deviate greatly under varying cumulant truncation levels; 3) The robustness of the approximations increases with the order of cumulant truncation; and 4) The stability of the single system model provides evidence to the expandability of this procedure to large interacting systems. Empirical results were gathered using several 'test-sized' models that described various types of state-dependencies. In particular, the polynomial intensity functions were varied in rate, order, and mixture of terms. It was observed that the cumulant method performed well in most for most models under the various truncation levels.