In order to mitigate the detrimental outcomes of accidents in the modern chemical plants, it is a common practice to install protective systems on processes operated under hazardous conditions. Since any failure should be treated as a random event, the corresponding safety function must function properly at all time. The system structure and its maintenance policy are the two key features that must be considered to ensure the availability of the protective system.
A complete protection system can be divided into two parts, i.e., the alarm subsystem and shutdown subsystem. The former is facilitated by one or more independent sensors. Based on online sensor signals, a hardwired logic is often followed to determine whether or not an alarm should be set off. The latter subsystem usually consists of one or more solenoid valve or power switches. In response to the alarm decision, these shutdown units can be either be energized or de-energized to carry out the required emergency response operation(s).
Any sensor may fail safely (FS) or dangerously (FD). The normal sensor state is usually recoverable after a FS failure, while repairs or replacements must be performed to overcome the FD failures. Obviously, both types of failures must be considered in conjecturing the alarm logic. To achieve a desired availability level, a common practice in process industries is to introduce hardware redundancy. Specifically, several independent sensors are installed to simultaneously monitor the same process condition and a voting device is incorporated to determine whether or not an unsafe state is actually detected. In the present study, the spare-supported corrective maintenance policy is adopted to further enhance sensor availability.
On the other hand, every shutdown unit may also experience FS and FD failures. Since the FD failures in this case are often unobervable under the normal operating conditions, a preventive maintenance strategy must be adopted to ensure availability. Specifically, such units are required to be inspected at designated intervals to identify the unrevealed malfunctions. If confirmed, the broken units should be repaired or replaced immediately. If otherwise, the normal ones should be allowed to stay online before the next inspection. The durations of inspection intervals are regarded as design parameters in this work.
The purpose of this study is to develop a mathematical programming model to minimize the total expected expenditure of any multilayer multichannel protective system. In particular, the failure rate of the system is assumed to increase over time, thus the previous maintenance policies (Liang and Chang, 2008; Liao and Chang, 2010) are modified accordingly. By solving the model, the optimal configurations of sensors and shutdown units, the best corrective and preventive maintenance policies and alarm/shutdown logics could be identified. Two examples are provided in this thesis to demonstrate the feasibility and effectiveness of the proposed approach.

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