PAPERmaking! Vol11 Nr2 2025

Rasool et al.

evaluation and forecasting using fault identification. Fasihi et al. (2021) proposed a bi-objective mathematical model for improvement of a fish closed-loop supply chain by using several multi- objective metaheuristic approacshes. Prajapati (2022) utilized particle swarm optimization algorithm of large-scale many-objective software for architecture recovery. Saini et al. (2023) developed and optimized the performance of a marine power plant using metaheuristics. Kumar et al. (2024) conducted the performance optimization of steam turbine power plant using computational intelligence techniques. By keeping above facts in mind, this study investigates and develop a mathematical model for performance optimization of stock preparation unit of paper plants. Stock preparation in paper manufacturing involves converting raw stock into finished stock for the paper machine. This process involves several subsystems like storage tanks, repulping/Slushing, deflaking, storage and mixing chests, and the paper machine itself in various redundancy strategies. For the system performance analysis, a mathematical model is developed using Markov birth death process along with RAMD investigation of components. The Chapman-Kolmogorov differential-difference equations derived under the exponential behavior of failure and repair rates. The prediction of prominent system effectiveness measure is made using genetic algorithm and particle swarm optimization. Decision matrices are derived for a particular value of parameters. The derived results are helpful for system designers and maintenance personnel for effective decision-making for plant operations. 2. Materials andMethods 2.1 Notations : The mathematical model for stock preparation under is developed using the notations as appended in Table 1.

Table 1 . Notations for stock preparation unit

Subsystem

Operative Mode

Failure Mode

Failure Rate μi

Repair Rate θj

Storage Tank

A

A

μ1

θ1

Repulping

B

B

μ2

θ2

Deflaking Process

C

C

μ3

θ3

Storage and Mixing Chest

D

D

μ4

θ4

E ݁ݒ ݅ݐ ܽݒ ݅ݎ ݁ܦ ݋݂  ݄݁ݐ ܲ ௜ ሺ ݐ ሻ Probability that at time ݐ the system is at ݅ ௧௛ state E μ5 Represents the state in which one parallel unit is failed. System is in working state with full capacity.

௜ ᇱ ሺ ݐ ሻǣ ௜ ሺ ݐ ሻ

Paper Machine

θ5

C1

System is in failed state.

MTBF MTTR

Mean time between failures Mean time between repairs

2.2 System description

Braz. J. Biom. ǡ˜Ǥ 43 ǡ‡ǦͶ͵͹͸ʹǡʹͲʹͷǤ  3

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