<p>The prominent objective of present study is to develop an efficient mathematical model for performance analysis of a bleaching system in the paper manufacturing industry. For this purpose, a mathematical model is developed using the Markov birth–death process using ideas of parallel redundancy at component level and exponentially distributed random variables. The bleaching system consists of two subsystems, viz., the filter and opener, which have unique characteristics and failure patterns. Chapman-Kolmogorov differential-difference equations are derived to model the behaviour of the bleaching system. The RAMD parameters, including reliability, availability, mean time between failures (MTBF), mean time to repair (MTTR), and dependability ratio, are estimated for the bleaching system as well as individual subsystems. Nature-inspired algorithms are utilised to predict the availability of the bleaching system at different iterations. In the bleaching system, it is observed that the predicted optimal availability of the bleaching system is 0.9997. The numerical results of other reliability indices and best-fitted parameters are also derived. The derived results are helpful for system designers and maintenance engineers to plan the plant’s maintenance schedules.</p>