Abstract
It has always been an important objective for industries to avoid negative effects due to machine deteriorations and failures. Maintenances must be executed in a preventive manner to ensure proper machine operations. However, optimal maintenance actions can only be taken when the exact real-time operating states of the machine are known. Machine can be real-time monitored, in current technology, by equipping on-line inspecting equipments with computer analyzing centers. This realizes the application of dynamic preventive maintenance policies.This research adopts a discrete time non-homogeneous Markovian multi-state deteriorating model to describe the state transitions of a periodically inspected and maintained machine. The model expresses that (1) machine states are deteriorating (via upper triangular transition probability matrices), and (2) machines are aging (via non-homogeneous transition probabilities). By further assuming (3) multiple actions available, (4) each action with its own risk (a maintenance may not achieve its intended result), and (5) that operation costs between successive inspections vary with both machine ages and states, an algorithm of time complexity ■ is developed for this dynamic preventive maintenance problem. By integrating the concepts of dynamic programming and rolling horizon technique, this algorithm is to determine the optimal action according to the present value of minimal expected total cost during a time interval in the near future.To model the aging scheme, interrupted geometric distributions are introduced to describe the degrees of state deterioration (differences between the states before and after transitions), and the distribution parameters are regarded as increasing functions of the machine age (thus can fit dichotomous logistic regression models). This makes the transition probabilities vary with machine age. Data requirements of parameter estimations are thus reduced. In real-world applications, the model, policy, and algorithm can be reconstructed right after parameter estimations, and are used to solve the dynamic preventive maintenance problem.Results of the illustrated numerical example show that the effects of cost reductions of this policy are all significant under various types of parameter combinations. To further generalize the concept of the aging scheme in this research, one may replace interrupted geometric distributions by general distributions or even relaxes the assumption of deterioration, yet it is necessary to rebuild the parameter schemes and estimations.