Imprecise Statistical Inference for Steady-state Availability of Components in Power Systems

Steady-state availabilities of components are important statistical data in power system reliability evaluation. If sample information is severely incomplete, the traditional estimation of steady-state availability is not accurate. The gap between existing sample information and complete probability information causes imprecision. In such case, imprecise probability can substitute for traditional precise probability and be used to build models for both imprecision and randomness. In this paper, gamma-exponential model was used to build probability boxes of time to failure and time to repair, and then interval-valued steady-state availabilities of components were calculated. The effect of parameter s on the convergence speed of interval-valued steady-state availability was also analyzed. The interval-valued steady-state availability converges to the true value of availability. The value of the interval can reflect randomness, and the width of the interval can reflect imprecision. Numerical example illustrated the practical application of the proposed method; the validity of the algorithm was verified by using Markov renewal process to produce the sample data.