െ ߠ ଵܲ ଵ ߤ ଵܲ ൌͲ
Rasool et al. _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
(2)
And the initial conditions are: ܲ ሺͲሻ = ൜ͳͲ݂݂݅݅ ്݅݅ ൌ ͲͲ From equations (1-2) using (3), we get ֜ܲ ଵ ൌ ఓ భ ఏ భ ܲ
(3)
(4) Now using normalization condition i.e the sum of all the probabilities is equal to one [ σܲ ଵ ୀ ൌ ͳሿ , we get Availability ( ܣ ௩ ሻൌܲ ൌ ଵା ଵ ഋ ഇభ భ = 0.955165692 Similarly, Reliability (ܴ ሺ ݐ ሻሻൌ݁ି ఓ భ ௧ ൌ݁ି Ǥଶଷ௧ , Maintainability ሺ ܯ ሺ ݐ ሻሻൌͳെ݁ି Ǥସଽ௧ , ܨܤ ܶܯ ൌ ఓ ଵ భ ൌ Ͷ͵ǤͶͺʹͲͻ݄ , ܴܶܶܯ ൌ ʹǤͲͶͲͺͳ͵݄ , ݁ܦ ܾ݈݁݊݀ܽ݅݅ ݕݐ ሺ݀ ሻ ൌ ʹͳǤ͵ͲͶ͵Ͷͺͳ , ܦ = ͳെቀ ௗି ଵ ଵ ቁቀ݁ି ష భ െ݁ି ష భ ቁ ൌ ͲǤͺͶͻ͵Ͷ͵Ͳͷʹ 3.2 RAMD indices for subsystem- Repulping/Slushing: It is a prominent component in stock preparation unit. It comprises a single component and its failure causes complete system to shut down. The failure and repair rates of repulping/slushing unit are exponentially distributed. By using minimic rule, the differential-difference equations are derived (based on Figure 3) as:
Figure 3. State transition diagram of subsystem-Repulping/Slushing. ሺ ݐ ᶭ ݐ ሻൌሺͳെ ߤ ଶ ᶭ ݐ ሻܲ ሺ ݐ ሻ ߠ ଶ ᶭ ܲݐ ଵ ሺ ݐ ሻ ֜ܲ
ܲ
ሺ ݐ ᶭ ݐ ሻൌܲ ሺ ݐ ሻെ ߤ ଶ ᶭ ܲݐ ሺ ݐ ሻ ሺ ݐ ᶭ ݐ ሻെܲ ሺ ݐ ሻൌᶭ ݐ ሺെ ߤ ଶܲ ሺ ݐ ሻ ᶭ௧ ൌെ ߤ ଶܲ ሺ ݐ ሻ + ߠ ଶܲ ଵ ሺ ݐ ሻ
+ ߠ ଶ ᶭ ܲݐ ଵ ሺ ݐ ሻ ֜ܲ + ߠ ଶܲ ଵ ሺ ݐ ሻሻ ֜
బ ሺ௧ାᶭ௧ሻି బ ሺ௧ሻ Taking limit ᶭ ՜ݐ Ͳ , we get ᶭ௧՜ బ ሺ௧ାᶭ௧ሻି బ ሺ௧ሻ ᶭ௧ ൌെ ߤ ଶܲ ሺ ݐ ሻ + ߠ ଶܲ ଵ ሺ ݐ ሻ ܲ ௧՜ஶ ᇱ ൌെ ߤ ଶܲ ሺ ݐ ሻ + ߠ ଶܲ ଵ ሺ ݐ ሻ Ͳൌെ ߤ ଶܲ + ߠ ଶܲ ଵ Similarly, െ ߠ ଶܲ ଵ ߤ ଶܲ ൌͲ
(5)
(6)
_____________________________________________________________________________________________ 6 Braz. J. Biom. ǡǤ 43 ǡǦͶ͵ʹǡʹͲʹͷǤ
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