非齊次連續時間馬可夫模型於可靠度分析上之應用－以電廠泵浦維修為例

Reliability Analysis based on Non-Homogeneous Continuous-Time Markov Modeling with Application to Repairable Pumps of a Power Plant

黃泰瑋(Tai-Wei Huang)

指導教授 ： 吳文方

共同指導教授 ： 徐堯(Yao Hsu)

國立臺灣大學/工學院/工業工程學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201610311

摘要

電廠供電穩定對於用戶影響非常大，為了避免電廠組件失效所帶來停電風險，適時對電廠組件進行維護是有必要的。但有維修行為就會伴隨著成本支出與營運績效等問題，如何在降低停電風險與增加營運績效間找到平衡點就成為一重要研究議題。而為了降低停電風險、提高組件可用度並降低維修成本，本研究針對可維修組件透過非齊次連續時間馬可夫鏈建構可維修模型。過往建構連續時間馬可夫模型往往假設失效率與維修率不隨著時間變動，然而實際情況的失效率與維修率應會隨時間變動，所以隨時間變動的失效率與維修率是本論文特色之一。除了時間的影響外，為了考量更符合實際情況的維修行為，環境因子亦會影響失效率與維修率，所以本研究也加入環境因子影響的考量，以描述失效與維修的不確定性。而在決策變數的設計方面，過往大多僅著重於預防維護週期的制定，本研究除了制定預防維護週期外，更加入組件備品數量的考量，藉由此可維修模型探討提高組件可用度與降低維修成本之預防維護週期和組件備品數量。因為非齊次連續時間馬可夫模型求取轉移機率之解析解有其困難性，本研究透過模擬提供一種求取轉移機率之數值方法。本研究最後將國內某電廠泵浦失效與維修的實際數據，導入本研究之可維修模型，在考量不同泵浦備品數量與預防維護週期下，模擬泵浦之失效與維修行為，並依模擬結果進行可靠度及生命週期成本分析，決定最佳泵浦備品數量與預防維護週期。

關鍵字

可維修模型 ； 非齊次連續時間馬可夫鏈 ； 比例風險模型 ； 可用度 ； 模擬

並列摘要

To avoid equipment breakdown that may result in power outage, equipment maintenance is very important. However, maintenance always accompanies with cost and operating performance. Finding a balance between reducing risk of power outage and increasing cost through maintenance becomes an important issue for power plant owners. To reduce the risk of power outage, increase the availability of equipment and decrease the cost of maintenance, a repair related analytical model by non-homogeneous continuous-time Markov chain is constructed in this thesis. In the past, people always assumed that failure rate and repair rate do not change with time when they constructed continuous-time Markov chain models. However, the failure rate and repair rate may change with time in actual situation. To consider a maintenance process which accords with the actual situation, we add not only the effect of time but also environmental factors including failure rate and repair rate into consideration to describe uncertainties of the process. Moreover, in traditional analyses, people usually emphasized the cycle of preventive maintenance as a decision variable. In this research, we consider not only the cycle of preventive maintenance but also the number of spare parts. By this way, the cycle of preventive maintenance and number of spare parts that increases the availability of equipment and decreases the cost of maintenance can be found. Since it is difficult to obtain a closed-form analytical solution of transition probability in a non-homogeneous continuous-time Markov chain, we propose a method to find the numerical solution. In the end, the failure and repair data of pumps of a domestic power plant are applied into the proposed model. An optimal solution in consideration of the life cycle cost under a certain availability constraint is found through the model.

並列關鍵字

repairable model ； non-homogeneous continuous-time Markov chain ； proportional hazards model ； availability ； simulation

參考文獻

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