在連續製造程序中的每個關鍵設備必須維持正常運行，通常會配置備援系統以維持不間斷運行。在本研究中考慮兩類備援機制：在類型I系統中，穩態程序的需求往往改變不大，但在長時間的操作中關鍵設備有可能故障，因此需配置暖備件來確保前述需求能持續得到滿足；在類型II系統中，程序需求會在短時間隨機改變，雖然在此時間範圍中關鍵設備的故障機率不大，但仍需配置暖備件以便及時反應需求的改變。
雖然過去已經開發出了數學規劃模型來配置和維護專門用於緊急關斷操作的連鎖系統，但它對於上述備援機制卻不適用。因此，本研究的主要工作是建造多層備援系統的事件樹，以便以推導相應數學規劃模式，並從最適解中得到保護層的適當數量以及每層的最佳規格，其中包括：（1）測量管道的數量，（2）每個管道中的線上感測器的數量，（3）每個通道的感測器備件，（4）切換裝置的檢測週期，（5）切換裝置的備件數，（6）暖備件的檢測週期，以及（7）離線冷備件的數量。本論文中會提供兩個應用實例的計算結果來展示所提的方法之可行性。

Generally speaking, every online unit in a continuous chemical process must always function normally, and a standby mechanism should be put in place to maintain uninterrupted operation. Two types of mechanisms are studied in this research. A type-I standby is needed in cases when the process demand is not expected to vary considerably, while the online unit could fail in a long period of operation time. The type-II counterpart is applicable if the process demand fluctuates over a relatively short horizon. Although the risk of equipment failure in a short time period is negligible, it is still necessary to install warm standbys so as to cope with the random changes in a timely manner.
Although a mathematical programming model has already been developed in the past to configure and maintain an interlock dedicated to emergency shutdown operation (Liang and Chang, 2008), it is not directly applicable to the aforementioned two standby mechanisms. Therefore, the main tasks of this study are to build event trees to enumerate and analyze all possible scenarios in these mechanisms, to derive explicit formulas accordingly for computing the expected life-cycle losses of the multi-layer protection systems, and to construct the corresponding mathematical programming models. By solving such a model for a given application, it is possible to determine the appropriate number of protective layers and the corresponding specifications of each layer, i.e., (1) the number of measurement channels, (2) the number of online sensors in each channel, (3) the number of spares for each measurement channel, (4) the inspection interval of switch, (5) the number of spares for switch, (6) the inspection interval of warm standby, (7) the number of offline cold standbys. The optimization results of the two application examples are presented in this thesis to demonstrate the feasibility of the proposed method.

Badia, F. G., Berrade, M. D., & Campos, C. A. (2001). Optimization of inspection intervals based on cost. Journal of Applied Probability, 38(4), 872-881.
Clavareau, J., & Labeau, P. E. (2009). Maintenance and replacement policies under technological obsolescence. Reliability engineering & system safety,94(2), 370-381.
Gregory et al. (2018) Reliability analysis of phased mission system with non-exponential and partially repairable components.
Reliability engineering & system safety,175(2), 119-127.
Haupt, R. L. and Haupt, S. E. (2004). "Practical Genetic Algorithms", John Wiley & Sons.
Hellmich, M., & Berg, H. P. (2015). Markov analysis of redundant standby safety systems under periodic surveillance testing. Reliability Engineering & System Safety, 133, 48-58.
Høyland, A., & Rausand, M. (1994). System reliability theory: models and statistical methods. John Wiley & Sons.
Kletz, T. A. (1986). HAZOP & HAZAN, 2nd edition (Institution of Chemical Engineers, Rugby, UK).
Lai, C. A., Chang, C. T., Ko, C. L., & Chen, C. L. (2003). Optimal sensor placement and maintenance strategies for mass-flow networks. Industrial & engineering chemistry research, 42(19), 4366-4375.
Levitin, G., Xing, L., & Dai, Y. (2014a). Optimal component loading in 1-out-of-N cold standby systems. Reliability Engineering & System Safety, 127, 58-64.
Levitin, G., Xing, L., & Dai, Y. (2014b). Cold vs. hot standby mission operation cost minimization for 1-out-of-N systems. European Journal of Operational Research, 234(1), 155-162.
Lepar, Y. Y., Y. C. Wang, & C. T. Chang, (2017). Automatic generation of interlock designs using genetic algorithms. Computers & Chemical Engineering, 101, 167 – 192.
Lipták, B. G. (1987). Optimization of Unit Operations. CRC Press.
Liang, K. H., & Chang, C. T. (2008). A simultaneous optimization approach to generate design specifications and maintenance policies for the multilayer protective systems in chemical processes. Industrial & Engineering Chemistry Research, 47(15), 5543-5555.
Liao, Y. C., & Chang, C. T. (2010). Design and Maintenance of Multichannel Protective Systems. Industrial & Engineering Chemistry Research, 49(22), 11421-11433.
Nakagawa, T. (1977). A 2-unit repairable redundant system with switching failure. IEEE Transactions on Reliability, 2, 128-130.
Nakagawa, T., & Osaki, S. (1974). Stochastic Behaviour Of A Two-Unit Standby Redundant System*. INFOR: Information Systems and Operational Research, 12(1), 66-70.
Pan, J. N. (1997). Reliability prediction of imperfect switching systems subject to multiple stresses. Microelectronics Reliability, 37(3), 439-445.
Raje, D. V., Olaniya, R. S., Wakhare, P. D., & Deshpande, A. W. (2000). Availability assessment of a two-unit stand-by pumping system. Reliability Engineering & System Safety, 68(3), 269-274.
Tsai, C. S., & Chang, C. T. (1996). A statistics based approach to enhancing safety and reliability of the batch-reactor charging operation. Computers & chemical engineering, 20, S647-S652.
Tsai, C. S., Chang, C. T., Yu, S. W., & Kao, C. S. (2000). Robust alarm generation strategy. Computers & Chemical Engineering, 24(2), 743-748.
Vaurio, J. K. (1999). Availability and cost functions for periodically inspected preventively maintained units. Reliability Engineering & System Safety, 63(2), 133-140.
Wang, Y. C., & Chang, C. T. (2016). On Optimal Assignment of Cold Standby Components for Multi-Channel Safety Interlocks. (master’s thesis). National Cheng Kung University, Tainan, Taiwan.
Wibisono, E., Adi, V. S. K., & Chang, C. T. (2014). Model Based Approach To Identify Optimal System Structures and Maintenance Policies for Safety Interlocks with Time-Varying Failure Rates. Industrial & Engineering Chemistry Research, 53(11), 4398-4412.
Wu, Q., & Wu, S. (2011). Reliability analysis of two-unit cold standby repairable systems under Poisson shocks. Applied Mathematics and computation,218(1), 171-182.
Yun, W. Y., & Cha, J. H. (2010). Optimal design of a general warm standby system. Reliability Engineering & System Safety, 95(8), 880-886.
Zhang, T., Xie, M., & Horigome, M. (2006). Availability and reliability of k-out-of-(m+n): g warm standby systems. Reliability Engineering & System Safety,91(4), 381-387.
Zhong, C., & Jin, H. (2014). A novel optimal preventive maintenance policy for a cold standby system based on semi-Markov theory. European Journal of Operational Research, 232(2), 405-411.
羅易凱 (2016). Optimal Structural Designs and
Maintenance Policies for Standby System. (master’s thesis). National Cheng Kung University, Tainan, Taiwan.
台灣電力公司
https://www.taipower.com.tw/tc/index.aspx