In this paper, confidence bounds on the reliability of a serial system composed of exponential subsystems are considered. Both the classical and the Bayesian analyses are discussed. The main result is that for the case in which there are no previous data, then there are no prior distributions on the subsystem reliabilities that are independent of current data and that yield the uniformly most accurate unbiased confidence bounds available through classical techniques.
"Bayesian Prior Distributions for Systems with Exponential Failure-time Data." Ann. Math. Statist. 43 (5) 1441 - 1448, October, 1972. https://doi.org/10.1214/aoms/1177692376