Abstract
The computation of a variety of reliability measures for a system that is observed over a random time horizon is examined. This time interval, which can correspond to the system mission, the system lifetime, etc., is assumed to be distributed as a random variable of phase type. Models are developed that aid a decision-maker to choose among the actions of replace, repair, or do nothing, whenever a system component fails, under several assumptions concerning the amount of information available to the decision-maker. In addition, a policy of replacement after a fixed number of repairs is examined. An example computation of several reliability measures and the application of a cost model are included to illustrate the tractability of the results and their usefulness in design decisions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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