Abstract
Allowing several imperfect repairs before a perfect repair can lead to a highly reliable and efficient system by reducing repair time and repair cost. Assuming exponential lifetime and exponential repair time, we determine the optimal probability $p$ of choosing a perfect repair over an imperfect repair after each failure. Based on either the limiting availability or the limiting average repair cost per unit time, we determine the optimal number of imperfect repairs before conducting a perfect repair.
Highlights
An imperfect repair has earned its popularity as an important maintenance strategy since the 1980s
We focus on the (p, q) model for a one-unit system having an exponential lifetime and an exponential repair time, the goal is to determine p based on two criteria—the limiting availability and the limiting average cost per unit time
Interpretation of Condition (3): From Figure 1, we note that if we choose a perfect repair after the first failure, between successive renewal times, the mean system up time (MSUT) is λ1, the mean system down time (MSDT) is μ1, and the limiting availability is given by the left-hand side of (3)
Summary
An imperfect repair has earned its popularity as an important maintenance strategy since the 1980s. Wang and Pham [26] considered imperfect repairs after the first few (a predetermined number of) failures, and they permitted a perfect repair done in a negligible amount of time (or they replaced the system with a brand new one). On the other hand, determine the optimal probability p of choosing a perfect repair over an imperfect repair after each system failure.
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