A Highly Efficient Monte Carlo Method for Assessment of System Reliability Based on a Markov Model

SYNOPTIC ABSTRACT

This paper proposes a Monte Carlo procedure for evaluating the reliability of a system consisting of independent components with two states, failed and working. This procedure replaces the failure distribution of each individual binary component with a two-state continuous time Markov chain. The transition rates for the process are selected such that the steady-state unavailability index equals the component unreliability. The Markov chain for each component is simulated over a chosen time interval and a simulated value of the system uptime is obtained therefrom using the system logic. The system reliability is estimated as the ratio of the system uptime to the length of the simulation time horizon. An example is given on the application of this procedure to the evaluation of a reliability index extensively used in the electric power industry. This example as well as others on several simple systems show that the proposed procedure is more efficient than crude Monte Carlo in that it requires fewer random numbers on the average than the latter to obtain the same level of precision. The relative efficiency of this procedure increases with increasing value of system reliability.

Key Words and Phrases:

• System Reliability
• Monte Carlo
• Variance Reduction
• Markov Model
• Loss-of-Load Probability
• Electric Power Generation System