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Mathematical models for reliability of a redundant system with two classes of failure modes are usually formulated as a nonlinear integer programming (NIP) problem. This paper reformulates the NIP problem into a 0-1 linear programming (ZOLP) problem and a one-to-one correspondence is shown between this NIP problem and the ZOLP problem. A NIP example treated by Tillman is formulated into a ZOLP problem and optimal solutions, identical to Tillman's are obtained by an implicit enumeration method. Calculating the new coefficients of the objective function and the constraints in the ZOLP are straight forward. There are not many constraints or variables in the proposed ZOLP. Consequently, the computation (CPU) time is less.