為了降低化工廠意外事故所造成的影響，通常都會在程序單元中安裝保護系統。單層保護系統主要包含兩個部分：警報系統和停系統。前者配置了一個或多個獨立的感測器，當程序發生緊急情況，警報系統根據線上偵測的數據及預先決定的警報邏輯來自動決定是否發出停的訊號。後者通常會搭配電磁閥，對應於前述所提的控制命令，電磁閥將會被通電(energized)或斷電(de-energized)來啟動停操作。由於感測器及閥件的故障是隨機事件，保護系統的可靠度(或可用度)與警報系統及停系統的結構特性和維修策略息息相關。此外，多個保護系統可以層級式的方式連接成多層保護系統，把重大危害降低至可接受的程度。
傳統上，保護系統的警報邏輯及停組態經常是依據經驗來合成，維修方式也是依據特定的經驗來建立。本研究的目的即為開發整數規劃模式來將總期望支出最小化，總期望支出包含固定投資、期望維修費用和系統失誤的期望損失。從數學規劃所得的最佳解可知(1)感測器的數目及相對應的警報邏輯，(2)閥件的個數及對應的停組態，及(3)所需要的修復和置換策略。本研究中，分別假設以修正型維修策略及預防維修策略來維護感測器和閥件。最適線下感測器備件數目及每個閥的最適檢測週期可由所提出的模式來決定。最後，本論文中將針對兩個化工程序作深入案例研究來展示此模式的可行性和有效性。

In order to mitigate the undesirable effects caused by accidents in chemical plants, it is a common practice to install protective systems on processing units operated under hazardous conditions. A single-layer protective system consists mainly of two components, i.e., the alarm subsystem and the shutdown subsystem. The former is equipped with one or more independent sensor. A predetermined logic is followed in this subsystem on the basis of the on-line measurement data to automatically issue trip signal(s) under emergency situation. The latter subsystem is usually configured with solenoid valves. In response to the aforementioned control command, these valves are energized (or de-energized) to carry out the shutdown operation. Since the failures of sensors and valves are basically random events, the reliability (or availability) of the protective system is highly dependent upon the structural characteristics and also the maintenance policies of the above two subsystems. Finally, it should be noted that, in certain applications, more than one protective system may be nested in multiple layers to reduce the probabilities of catastrophic consequences to acceptable levels.

Traditionally, the alarm logic and shutdown configuration in a protective system were often synthesized according to experience. The maintenance scheme was also established on an ad hoc basis. The aim of this study is thus to develop an integrated mathematical programming model to minimize the total expected expenditure, which is the sum of the capital investments, the expected maintenance costs and the expected losses due to system failures. From the optimal solution, one should be able to identify (1) the number of sensors and the corresponding alarm logic, (2) the number of valves and the corresponding shutdown configuration, and (3) the needed repair/replacement policies. Notice that, in this work, the sensors and valves are assumed to be maintained respectively with the corrective and preventive strategies. Thus, the optimal number of spare sensors stored off-line and the best inspection interval for each valve can also be determined by solving the proposed model. Extensive case studies have been carried out to demonstrate the feasibility and effectiveness of the proposed approach.

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