Bayesian analysis of system reliability using the Burr distribution

A two-component parallel or series system is studied where the failure time of each component follows the Burr distribution. The testing environment of the system is assumed different from the operating one, causing the parameters pi (i=1,2) to increase or decrease by a positive, random amount η. Two priors are considered for the behaviour of η, a gamma and a uniform. The Bayesian reliability is derived in closed form. Three hypothetical examples show how this approach could be used by reliability engineers.