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.

Several fields within the social and technical sciences have identified the importance of theoretical and practical research into complex systems. The sensitivity of these systems is one of the primary focuses. The capsules high-pressure oxygen supply system (HPOSS) prepares a complex system with complex interconnections. The reliability of HPOSS cannot be reduced to a single equivalent component or block by combining series and parallel reductions. The aim of this paper is to demonstrate the application of mathematical detection tests to HPOSS in order to assess the sensitivity of the reliability of complex systems. Using the matrix-based minimal cut methodology and the linear sensitivity model of system reliability, the critical system illustrates the suggested methodologies and their relevance to investigating the sensitivity of complex interconnected systems.