Reliability analysis of repairable systems using Petri nets and vague Lambda-Tau methodology.

Area of Science:

• Reliability Engineering
• System Analysis
• Operations Research

Background:

• Traditional reliability analysis methods often struggle with uncertainty and imprecision in system parameters.
• Vague set theory offers a more nuanced approach to representing uncertain data compared to classical or fuzzy set theories.
• Petri nets provide a powerful graphical tool for modeling complex, concurrent system processes.

Purpose of the Study:

• To develop and present the novel vague Lambda-Tau methodology for the reliability analysis of repairable systems.
• To address the limitations of existing probabilistic reliability approaches by incorporating vague set theory.
• To provide a more accurate and comprehensive understanding of system behavior and performance.

Main Methods:

• Qualitative system modeling using Petri nets (PN) to capture asynchronous and concurrent operations.
• Quantitative reliability analysis employing the vague Lambda-Tau method.
• Representation of failure rates and repair times using vague set theory, specifically intuitionistic fuzzy numbers with triangular membership functions.
• Sensitivity analysis to evaluate the impact of parameters on system Mean Time Between Failures (MTBF).

Main Results:

• The vague Lambda-Tau methodology successfully models and analyzes the reliability of a repairable system.
• The application of vague set theory enhances the representation of uncertainty in failure and repair data.
• Sensitivity analysis provides insights into critical parameters affecting system MTBF.
• The graphical representation from Petri nets aids in understanding system dynamics.

Conclusions:

• The proposed vague Lambda-Tau methodology offers an improved approach to reliability analysis for repairable systems.
• The methodology enhances the understanding of system behavior by effectively handling uncertainty.
• The findings can guide plant personnel in optimizing maintenance strategies for improved system performance, as demonstrated by the paper mill case study.