Edward W. Frees. on Construction of Sequential Age Replacement Policies via Stochastic Approximation

Stochastic approximation (SA), a stochastic analog of iterative techniques for finding the zeroes of a function (e.g., Newton-Raphson), is applied to a problem in resource allocation, the age replacement policy (ARP) problem. A stochastically failing unit is replaced at failure or at time t, whichever comes first, under an age replacement policy. When the form of the failure distribution is unknown the question of estimating ~, the optimal replacement time (optimal in terms of achieving the smallest long-run expected cost), is important. SA is superior to other existing sequential methodologies introduced by Bather (1977). Further, this application motivates novel ways in which the theory of SA is extended.