Bayesian Confidence Limits for Reliability of Redundant Systems when Tests are Terminated at First Failure

Exact Bayesian confidence limits are derived for the reliability of a redundant system of exponential subsystems, when subsystem tests are terminated at first failure. The application is conceived for the treatment of a redundant system having extremely high reliability, and allows a monomial family of prior density functions which is conjugate when tests are terminated at first failure. The posterior probability density function of system reliability is derived using the Mellin integral transform. The inversion is accomplished by the method of residues. From the density function the distribution function is obtained which yields confidence limits on reliability by numerical inversion.