在連續式生產的化工廠中，除了關鍵元件在長時間的運作下有可能發生故障外，下游的需求也有可能會隨市場景氣變動。在這種狀況下，針對重要單元安裝合適的備援系統，除了可以確保工廠運行不輟之外，也可以盡量滿足市場需求。儘管過去已經有相關的研究，但是針對負載變化下關鍵元件的多層備援機制仍然尚未有較為全面且完整的分析。是故本研究主要目標為提出通用的數學模型，藉由最小化全生命週期期望支出來為各種製程單元訂定最合適的備援機制與維修保養策略。在本研究中，我們撰寫了Matlab程式碼，利用基因演算法來執行最佳化的計算。並且針對實際製程設備進行案例測試，來驗證本研究提出之數學模型的正確性與可行性。從最適化結果中可以得到備援系統最佳設計規格，其中包含 (1) 關鍵元件個數，(2) 各個量測通道的邏輯閘，(3) 各個量測通道需要的線上與備用感測器數量，(4) 備用切換裝置的數量，(5) 線上切換裝置的檢測週期，(6) 暖備件的檢測週期，以及(7) 冷備件的數量。

In a continuously operated chemical plant, not only the critical online unit may fail after a long period of operation, but also the process load may vary significantly and frequently. In these situations, it is necessary to incoporate standby mechanisms so as to maintain uninterrupted production and satisfy the downstream demand throughout the operation horizon. Even though a few related studies have been reported in literature Chan et al. (2020), Chan and Chang (2021), a comprehensive analysis of multilayer standby mechanisms in long-term processes under varying loads has not been carried out. A generalized mathematical programming model has been developed in this research to automatically synthesize the optimal designs and maintenance policies of the standby mechanisms for any given processes by minimizing the total expected lifecycle expenditure. A Matlab code has also been developed to carry out the optimization runs via genetic algorithm. The feasibility and effectiveness of the proposed model and solution procedure are demonstrated with case studies concerning the fan and pump systems in a typical chemical plant and the combined gas and steam(COGAS) power plant. From the optimization results, one can obtain the optimum design of the standby mechanisms, which include: (1) the number of protection layers, (2) the corresponding voting-gate logic in each measurement channel, (3) the numbers of both online and spare sensors in each measurement channel, (4) the number of spares for online switch, (5) the inspection interval of online switch, (6) the inspection intervals for warm standbys, and (7) the number of cold standbys.

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