Abstract
This paper develops an optimal shut-down logic for a protective system which is composed of: 1) a sensing section, 2) a judging section, and 3) a driving section. Each section has two kinds of failures: fail-dangerous and fail-safe. A shut-down logic which minimizes an s-expected loss caused by failures of the protective system is obtained as a simple switching function. A path-set expression of the logic is shown. An example for a glass-lined reactor illustrates that the optimal logic consists of 7 majority rules; 3 of them belong to a stand-alone part and the remaining 4 to a cross-reference part.
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