A Renewal Decision Problem

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Abstract
A system (e.g., a motor vehicle) must operate for t units of time. A certain component (e.g., a battery) is essential for its operation and must be replaced each time it fails. There are n types of replacement components. A type i replacement costs Ci and has a random life with distribution depending on i. There is no salvage value associated with the particular component in use when the system terminates. The problem is to assign the initial component and subsequent replacements from among the n types so as to minimize the total expected cost of providing an operative component for the t units of time. This paper treats this problem when the life distributions are exponential for each type and when t is fixed or has a truncated exponential distribution. Related problems are also considered.

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