Computing consecutive-type reliabilities nonrecursively

The reliability of consecutive-type systems has been approached from various angles. A new method is presented for deriving exact expressions for the generating functions and the reliabilities of various consecutive-type systems. This method, based on Feller's run theory, is easy to implement, and leads to both recursive and nonrecursive formulas for the reliability. The nonrecursive expression is especially advantageous for systems with numerous components. In comparison to the n (number of components) computations that the recursive formulas require, the nonrecursive formula only requires the computation of the roots of a polynomial of order k. The method is extended for computing generating functions and reliabilities of systems with multi-state components as well as systems with s-dependent components.