Age replacement policies in multiple time scales
Frickenstein, Scott G.
Whitaker, Lyn R.
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We develop and estimate optimal age replacement policies for devices whose age is measured in multiple time scales. For example, the age of a jet engine can be measured in chronological time, the number of flight hours, and the number of landings. Under a single-scale age replacement policy, a device is replaced at age or upon failure, whichever occurs first. We show that a natural generalization to k > 2 scales is to replace non-failed devices when their usage path crosses the boundary of a k-dimensional region M, where M is a lower set with respect to the matrix partial order. For lifetimes measured in two scales, we consider two contexts. In the first, devices age along linear usage paths. For this case, we generalize the single-scale long-run average cost and estimate optimal two-scale policies. We show these policies are strongly consistent estimators of the true optimal policies under mild conditions, and study small- sample behavior using simulation. For the second context, in which device usage paths are unknown, we use two-dimensional renewal theory to derive the long-run average cost of a policy. We give examples in both settings and note that these ideas generalize to more than two scales.
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