Abstract
Generally, a (manufacturing) system either deteriorates continuously due to aging or fails suddenly due to fatal shocks, and so it can’t remain in good operating states without taking maintenance. Maintenance (such as repair, replacement taken preventively) may keep manufacturing systems within good operating states to reduce the scrapping cost, but on the expense of maintenance cost. Therefore, proper maintenance policy should be able to reduce the expected total cost per unit time. For a continuous-time multi-state Markovian deteriorating (manufacturing) system subject to aging and fatal shocks, two control limit maintenance policies under continuous inspection and periodic inspection respectively are proposed. Under continuous inspection, the system is inspected continuously to identify the state upon which an action from {do-nothing, repair, replacement} is to be taken. Under periodic inspection, the system is inspected periodically to identify the state upon which an action from {do-nothing, repair, replacement} is to be taken. Such two policies are generalization of many maintenance policies in the literature. The first policy considers repair threshold, replacement threshold and time limit as decision variables and the second policy considers repair threshold, replacement threshold and inspection interval as decision variables. Both are evaluated in terms of expected long-run cost per unit time. For each policy, an iterated algorithm is developed to obtain the optimal policy(or optimal decision variables) and an illustration of it in terms of a numerical example is also presented.