Joint structure importance of components based on Logic Differential Calculus

Reliability engineering addresses the challenge of analyzing how components contribute to system failures when designing large and complex systems. This analysis is commonly referred to as importance analysis. One specific type of importance measure is Joint Structural Importance (JSI), which assesses the significance of two or more components based on their positions within the system. This measure helps in effectively allocating redundancy and guiding design decisions to enhance overall reliability. This paper proposes a new method for computing the JSI of independent components within a coherent system. The key idea is to utilize Logical Differential Calculus, specifically through the Direct Partial Logical Derivatives (DPLD). Applying the DPLD for calculating the JSI based on the indicator function is a novel approach. Notably, this method allows for calculating the JSI from the structure function represented by a truth table without the need to transform the function into a Boolean expression. Numerical examples are provided to illustrate the application and advantages of the proposed method. Additionally, case studies on a substation automation system and an auxiliary feedwater system are conducted to demonstrate the technique's effectiveness in engineering applications.