如何避免設備衰敗所帶來的負面影響，一直是製造業最重要的課題之一。要確保良好的設備運作狀態，必須以預防性的角度進行設備維護。而唯有確實掌握設備運作狀態，才能最適切地執行維護。由於目前可結合線上檢測儀器與電腦運算中心，對設備進行立即監控，因此實現了動態預防維護策略應用的可能。
本研究針對具備立即監控技術的設備，採用離散時間異質馬可夫式衰退模型來描述設備狀態的變化，以：（一）上三角轉移機率矩陣描述設備狀態的衰退；（二）轉移機率的改變描述設備的老化現象（狀態衰退的「加速」）。並假設（三）有多種不完全維護動作可供選用；（四）維護動作具有失敗的風險；（五）檢測點之間的運作成本隨設備年齡與狀態而變化。結合動態規劃與滾動時間軸概念，以未來數期內最小期望總成本現值為目標，發展出動態維護策略演算法，時間複雜度為■。

老化機制的相關參數模式假設中，採用中斷式幾何分配描述狀態衰退幅度（即狀態轉移前後的狀態值之差），並將分配參數視為設備年齡的遞增函數（可配適二元羅吉斯迴歸模型），使各期狀態轉移機率隨年齡而變化；此方法可確實簡化參數的估計與縮減其所需歷史資料量。實際應用時，完成參數估計後即可成功地建立模型、策略與演算法，解決此動態預防維護問題。

數值範例之結果顯示，本研究之策略在多種類型的參數設定值組合下，皆具有顯著的成本縮減效果。未來可嘗試以其它形狀的機率分配取代中斷式幾何分配，甚至放鬆狀態衰退的假設，將本研究之老化機制推廣至更一般化之情形。

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.

R.E. Barlow, L.C. Hunter, 1960, “Optimum Preventive Maintenance Policies”, Operations Research, 9, 90-100.
R.E. Barlow, F. Proshan, 1965, Mathematical Theory of Reliability, Wiley, New York.
R.E. Barlow, F. Proshan, 1975, Statistical Theory of Reliability and Life Testing, Holt, Rinehart & Winston, New York.
M. Ben-Daya, A.S. Alghamdi, 2000, “On an Imperfect Preventive Maintenance Model”, International Journal of Quality & Reliability Management, 17(6), 661-670.
B. Bergman, 1978, “Optimal Replacement under a General Failure Model”, Advances in Applied Probability, 10(2), 431-451.
C.T. Chen, Y.W. Chen, J. Yuan, 2003, “On a Dynamic Preventive Maintenance Policy for a System under Inspection”, Reliability Engineering and System Safety, 80, 41-47.
M. Chen, R.M. Feldman, 1997, “Optimal Replacement Policies with Minimal Repair and Age-dependent Costs”, European Journal of Operational Research, 98, 75-84.
A. Chen, R.S. Guo, G.S. Wu, 2000, “Real-time Equipment Health Evaluation and Dynamic Preventive Maintenance”, The Ninth International Symposium on Semiconductor Manufacturing, 375-378.
D. Chen, K.S. Trivedi, 2002, “Closed-form Analytical Results for Condition-based Maintenance”, Reliability Engineering and System Safety, 76, 43-51.
J.H. Chiang, J. Yuan, 2001, “Optimal Maintenance Policy for a Markovian System under Periodic Inspection”, Reliability Engineering and System Safety, 71, 165-172.
C. Derman, 1963, “Optimal Replacement and Maintenance under Markovian Deterioration with Probability Bounds on Failure”, Management Science, 19, 478-481.
R.W. Drinkwater, N.V.J. Hastings, 1967, “An Economic Replacement Model”, Operations Research Quarterly, 18, 121-138.
W.J. Hopp, S.C. Wu, 1990, “Machine Maintenance with Multiple Maintenance Actions”, IIE Transactions, 22, 226-233.
C.C. Hsieh, K.C. Chiu, 2002, “Optimal Maintenance Policy in a Multistate Deteriorating Standby System”, European Journal of Operational Research, 141, 689-698.
C.T. Lam, R.H. Yeh, 1994a, “Comparison of Sequential and Continuous Inspection Strategies for Deteriorating Systems”, Advances in Applied Probability, 26, 423-435.
C.T. Lam, R.H. Yeh, 1994b, “Optimal Maintenance Policies for Deteriorating Systems under Various Maintenance Strategies”, IEEE Transactions on Reliability, 43, 423-430.
M.A.K. Malik, 1979, “Reliable Preventive Maintenance Policy”, AIIE Transactions, 11(3), 221-228.
L.Jr. Mann, A. Saxena, G.M. Knapp, 1995, “Statistical-based or Condition-based Preventive Maintenance? ”, Journal of Quality in Maintenance Engineering, 1(1), 46-59.
A.C. Marquez, A.S. Heguedas, 2002, “Models for Maintenance Optimization: a Study for Repairable Systems and Finite Time Periods”, Reliability Engineering and System Safety, 75, 367-377.
T. Nakagawa, S. Osaki, 1974, “The Optimum Repair Limit Replacement Policies”, Operations Research Quarterly, 25, 311-317.
T. Nakagawa, 1981a, “A Summary of Periodic Replacement with Minimal Repair at Failure”, Journal of the Operations Research Society of Japan, 24, 213-228.
T. Nakagawa, 1981b, “Modified Periodic Replacement with Minimal Repair at Failure”, IEEE Transactions on Reliability, R-30, 165-168.
T. Nakagawa, 1984, “Optimal Policy of Continuous and Discrete Replacement with Minimal Repair at Failure”, Naval Research Logistics Quarterly, 31(4), 543-550.
T. Nakagawa, 1986, “Periodic and Sequential Preventive Maintenance Policies”, Journal of Applied Probability, 23(2), 536-542.
T. Nakagawa, 1988, “Sequential Imperfect Preventive Maintenance Policies”, IEEE Transactions on Reliability, 37(3), 295-298.
S. Osaki, T. Nakagawa, 1976, “Bibliography for Reliability and Availability of Stochastic Systems”, IEEE Transactions on Reliability, R-25, 284-287.
H. Pham, H. Wang, 1996, “Imperfect Maintenance”, European Journal of Operational Research, 94, 425-438.
C.T. Su, S.C. Wu, C.C. Chang, 2000, “Multiaction Maintenance Subject to Action-dependent Risk and Stochastic Failure”, European Journal of Operational Research, 125, 133-148.
H. Wang, H. Pham, 1999, “Some Maintenance Models and Availability with Imperfect Maintenance in Production Systems”, Annals of Operations Research, 91, 305-318.
H. Wang, 2002, “A Survey of Maintenance Policies of Deteriorating Systems”, European Journal of Operational Research, 139, 469-489.
R.H. Yeh, 1997a, “Optimal Inspection and Replacement Policies for Multi-state Deteriorating Systems”, European Journal of Operational Research, 96(2), 248-259.
R.H. Yeh, 1997b, “State-age-dependent Maintenance Policies for Deteriorating Systems with Erlang Sojourn Time Distributions”, Reliability Engineering and System Safety, 58, 55-60.