Combining Boolean Functions Technique and Pentagonal Fuzzy Numbers to Assess Sugar Plant Reliability

Abstract

In this research study, we focused on assessing the reliability of the feeding system within a sugar plant, utilizing a combination of the Boolean function method, Weibull distribution, and pentagonal fuzzy numbers. The sugar plant operates as a complex network of interconnected subsystems, and its overall performance is heavily dependent on the seamless functioning of these components. To analyze this, we developed a mathematical model using a logical matrix, which was further interpreted through the Boolean function approach. The primary objective was to address the uncertainties associated with the lifespan of the plant’s components. For this purpose, we opted for the pentagonal fuzzy Weibull lifetime distribution, which is particularly suited to modeling situations with inherent uncertainties in lifespan parameters. Our analysis included deriving equations for fuzzy reliability, which measures the probability that the system performs without failure over a specified period; fuzzy mean time to future, which predicts the expected operational time before failure; and the fuzzy hazard function, which assesses the instantaneous failure rate. Furthermore, we examined these concepts through their α-cut representation, a technique used to handle fuzzy numbers by breaking them down into intervals that represent different levels of certainty. This approach allowed us to provide a more comprehensive and nuanced understanding of the system’s dependability, accounting for the ambiguity and variability inherent in real-world operations.