Age replacement policy based on imperfect repair with random probability

• We propose a new age replacement policy with random probability of perfect repair.
• We develop the expected cost per unit time.
• We discuss the optimal age for replacement minimizing the expected cost rate.

In most of literatures of age replacement policy, failures before planned replacement age can be either minimally repaired or perfectly repaired based on the types of failures, cost for repairs and so on. In this paper, we propose age replacement policy based on imperfect repair with random probability. The proposed policy incorporates the case that such intermittent failure can be either minimally repaired or perfectly repaired with random probabilities. The mathematical formulas of the expected cost rate per unit time are derived for both the infinite-horizon case and the one-replacement-cycle case. For each case, we show that the optimal replacement age exists and is finite.