Bayes credibility intervals for reliability of series systems with very reliable components

Abstract

An asymptotic expansion for the posterior Cdf of the reliability of series systems with very reliable components is obtained. This result allows us not only to calculate the Cdf easily but to estimate the magnitude of error when the infinite series expansion is truncated. Numerical results show that the asymptotic expansion converges very rapidly. Consequently, the computation of Bayes credibility intervals based on the truncated expansion is efficient and accurate.