Reliability analysis of a two-unit parallel system with dissimilar units and general distributions

We study the reliability characteristics of a parallel system attended by a single repair facility and general failure and repair time probability distribution functions (pdf). The basic mathematical problem is the solution of a pair of simultaneous Wiener-Hopf integral equations.A formal solution procedure of the equations has been discussed in the case of unspecified characteristic functions (cf).Fairly explicit solutions are performed if at least one of the failure time pdf's has a rational cf.We compare some of the results presented in previous literature.