A simple lower bound for reliability of k-out-of-n:G systems

Application of Boole´s inequality results in a simple lower bound for system reliability in terms of reliabilities of subsystems for a k-out-of-n:G system. No assumptions regarding statistical dependence or independence of the outcomes (success or failure) for the subsystems are used. The no assumption lower bound for pure series or parallel systems has been previously published, but the more general case of the title has been overlooked. On the other hand, using the assumption of association of the outcomes, the lower bound in this paper can be improved upon slightly as shown in Barlow and Proschan (1981)