Neil J. Calkin, Jonathan D. Edds, Douglas R. Shier

Department of Mathematical Sciences

Clemson University

Clemson, SC 29634-0975

Abstract: We consider the structure and number of non-zero terms in the reliability polynomials for cyclic consecutive systems. We explain the large amount of cancellation and the fact that all but one of the reduced coefficients are 0, 1, -1. Also, we derive an asymptotic expression for the number of non-zero coefficients.

Key Words: generating function, inclusion-exclusion, k-out-of-n system, reliability