Performance Assessment of Industrial Plants Using Laplace Transform and Chapman-Kolmogorov Differential Equations

Abstract

Industrial facilities require rigorous performance evaluation methods to guarantee operating
efficiency, dependability, and safety. Conventional reliability models often depend on statistical
techniques; however, sophisticated mathematical methods like the Laplace transform and
Chapman-Kolmogorov (C-K) differential equations may provide more profound insights into
system dynamics. This study introduces a dependability model for industrial plants based on a
Markov process, using C-K equations to delineate state transitions and employing the Laplace
transform to enable analytical solutions. The suggested approach assesses system availability,
mean time between failures (MTBF), and failure probability. A case study of a thermal power
plant illustrates the model's efficacy, exhibiting enhanced accuracy compared to traditional
dependability methods. The findings underscore the promise of this technology for predictive
maintenance and system improvement i.e. This study introduces a mathematical framework for
evaluating the performance of industrial facilities using Laplace Transform and Chapman-
Kolmogorov differential equations. The research examines the dynamic behavior and
dependability of system components under stochastic settings. The amalgamation of these
mathematical instruments offers a formidable methodology for modeling transitions between
operational states, forecasting system behavior over time, and enhancing maintenance and
operating methods.