This paper considers and extends the preventive replacement model with a cumulative repair-cost limit policy by introducing the random lead time for replacement delivery. A cumulative repair-cost limit policy uses information about a system's entire repair-cost history to decide whether the system is repaired or replaced. A random lead time models delay in delivery of a replacement once it is ordered. Long-run expected cost per unit time is formulated, and the optimal scheduled time for preventive replacement minimizing that cost is derived. Existence and uniqueness of that optimal time are shown, and the structural properties are presented. Various special cases are included and compared, and a numerical example is demonstrated.
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