Refined Asymptotic Costs for Renewal Reward Processes

A common criteria function for the selection of decision variables in renewal reward processes is the leading term in the asymptotic expansion of the expected cost per unit time, namely the ratio of expected cost per cycle to expected cycle length. The general implications of refining this criteria function by adopting the first two terms in the asymptotic expansion as an objective function are discussed. An analysis for both an age based and a cumulative damage based renewal reward process is presented.