Survival Signature-Based Structural Importance Analysis of Multistate System With Binary-State Components

Abstract

System reliability analysis aims to identify a system’s weaknesses or critical components and quantify their failures’ impact. Analyzing the influence of system components on system failure is a common problem in reliability engineering, known as the importance analysis of a system. Reliability analysis uses two main models: the binary-state system and the multistate system (MSS). To evaluate the reliability of MSS with binary-state components, computing methods of survival signature are studied. The structural functions of MSS and the survival signature allow for various mathematical approaches, including logical differential calculus (LDC). LDC can be employed to identify situations where a change in the number of functioning components leads to a change in the system's state, known as the structural importance measure. This paper presents a technique for calculating structural importance measures of MSS with binary-state components. The technique uses the survival signature of MSS instead of the structure function. It is based on logical differential calculus, specifically direct partial logical derivatives (DPLD). Numerical and application examples are provided to demonstrate and validate the technique, exhibiting its superiority and potential for real engineering use.