Reliability Analysis of Logical Loop Structure by using Algebraic Solution of Boolean Equation

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  • ブール代数方程式による論理ループ構造の信頼性解析
  • ブール ダイスウ ホウテイシキ ニ ヨル ロンリ ループ コウゾウ ノ シンライセイ カイセキ

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Abstract

A system which has logical loop(s) was not generally solved in terms of the arithmetic operators of Boolean algebra. It appears infinite circulation of the unknown variables in the process of solving simultaneous Boolean equations. An exact method has been proposed for solving this problem in reliability analysis, but it was effective only in a restricted analysis condition. In the present paper, a generalized procedure is proposed for systems with logical loop(s). The proof of the solution for simultaneous Boolean equations is given in a simplified formulation. Discussions are made for time-dependent behavior of system operation to fundamental loop structures. It is shown the relation between operating condition of a loop structure and indefinite constants appeared in the solution of simultaneous Boolean equations. With this relation, it becomes possible to accurately evaluate the reliability of logical loops by the aid of algebraic solution of Boolean equations. Detailed explanation of this analysis procedure is given for an example system.

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