Variance and Approximate Confidence Limits for Probability and Frequency of System Failure

Abstract

Two different types of approximation account for the effect of uncertain component failure and repair rates on the probability and the frequency of failure of repairable systems: 1. Use the orthodox statistical procedure of characterizing distributions by their low order moments and then use the conservative Chebyshev inequality to bound the probabilities so that the random variables lie within a certain range. 2. Apply Monte Carlo simulation based on common probability models, with which component test data can be translated into approximate system reliability limits at any s-confidence level. The two types are compared by an example. The performance of both types improve with the sample size of component data, but bounds from the Chebyshev inequality are wider than those obtained from Monte Carlo simulation. Both approaches represent the system by minimal cut-sets. The algorithms are intended for digital-computer implementation; computational times are provided.