(90e) Optimal Design and Maintenance Strategy for Multi-Layer Protective Systems

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.

Two examples are provided in this paper to demonstrate the feasibility and effectiveness of the proposed approach.