Optimal Age-replacement Policy for Series Systems Considering Maintenance Time

Age-replacement is one of the most commonly usedmaintenance policies based on preventive action to prevent system failure. Inmany age-replacement settings, it is assumed that the maintenance time can beignored since it is short compared with operation time. However, maintenance,especially corrective maintenance, may take a non-negligible amount of time dueto various factors such as ordering replacement parts, equipping themaintenance team, and transporting the maintenance equipment. Neglectingmaintenance time when optimizing maintenance policies for multi-unit systems maythus lead to sub-optimal or even incorrect solutions to the problem, resultingin higher maintenance costs. We present an optimal age-replacement policy forsystems consisting of multiple independent units connected in series. Thefailure of any one of the units causes the entire system to fail, which isimmediately detected. We formulated a model that integrates both preventive andcorrective maintenance times for determining an optimal preventive replacementinterval, minimizing the expected long run cost per unit time. The sufficientconditions for the existence and uniqueness of the corresponding optimalsolution are derived. The performance of the proposed maintenance policy wasevaluated by comparing it with a conventional one that does not take intoaccount maintenance time. Numerical examples illustrate the effects of downtimecost and maintenance time on the proposed maintenance policy.