Over-time and over-level replacement policies with random working cycles

When a unit is running successive works with cycle times, it would be uneconomical or impractical to do maintenances during any working cycle. This paper firstly reviews two replacement models proposed in literatures as follows: (1) replacement is done over a planned time $$T$$T at the completion of the working cycle, which is called over-time replacement, and (2) replacement is done over damage level $$Z$$Z at the completion of the forthcoming working cycle, which is called over-level replacement. From the viewpoint of replacement cost savings, we secondly focus on comparisons of over-time replacement and its standard age-based policy, over-level replacement and its standard condition-based policy. Furthermore, modified over-time and over-level replacement costs are obtained to specify critical points at which these new replacements, rather than their standard polices, would save more replacement costs. Discussions in this paper are given analytically and computed numerically.