| Condition Based Maintenance (CBM) or predictive maintenance is based on observing an indicator of the working state of the equipment, at different intervals of time. The objective of this thesis is to determine the optimal policy for the equipment's replacement while the deterioration of the equipment is not outwardly visible. The Proportional Hazard Model (PHM) is used to model the failure behavior of the equipment. In the literature, many papers presented optimal policies when the relation between the equipment state and the indicators is deterministic. We present an optimal CBM policy when a stochastic relation between the unknown equipment's working state and the measured value of the indicator, exists.; A decision criterion which leads to optimum replacement decision is introduced. This criterion is a function of the age, the probability distribution of working state, and the long run average cost of the replacement system. A recursive method for calculating the average cost is also introduced. Some numerical examples are solved and the perfect and imperfect problems' long run average costs are compared. Also the behavior of the long run average cost while the problem's parameters change are studied.; Dynamic programming (DP), Partially Observed Markov Decision Process (POMDP) and applied probabilities are used in this thesis. |
