Bayes Confidence Limits for Reliability of Redundant Systems

A method is presented for computing Bayes confidence limits for the reliability R = 1 – Π i = 1 N (1 – Ri ) of a redundant system of N subsystems each having exponential distribution of life with reliabilities Ri = exp (– λ iti ) for given mission times ti . The failure rates are unknown and must be estimated from test data (life samples). The results provide a useful generalization of a previously published treatment in which test conditions were restricted to a single life sample for each subsystem. The present result places no such restriction on the test data. Exact confidence limits are obtained from the posterior distribution of system reliability which is developed in terms of an expansion in shifted Chebyshev polynomials of the second kind readily evaluated by an electronic computer.