Rasool et al.
Now using normalization condition i.e the sum of all the probabilities is equal to one ሾσܲ ଵ ୀ ൌͳሿ , we get From equations (5-6) using (3), we get ܲ ఓ మ ఏ మ ܲ ൌͳ֜ܲ ൌ ଵା ଵ ഋ ഇమ మ (7) Availability ( ܣ ௩ ሻൌ ଵା ଵ ഋ ഇమ మ ൌ ͲǤͻͶͲʹͷͻͶ Similarly, Reliability (ܴ ሺ ݐ ሻሻൌ݁ି ఓ మ ௧ ൌ݁ି Ǥଶ௧ , Maintainability ሺ ܯ ሺ ݐ ሻሻൌͳെ݁ି Ǥସଽଽଽଽଽଵଶ௧ , ܨܤ ܶܯ ൌ ఓ ଵ మ ൌͷͲ݄ , ܴܶܶܯ ൌ ͳǤ͵͵͵͵͵͵Ͷͻ݄ , ݁ܦ ܾ݈݁݊݀ܽ݅݅ ݕݐ ሺ݀ ሻ ൌ ͵ǤͶͻͻͻͻͷ , ܦ = ͳെቀ ௗି ଵ ଵ ቁቀ݁ି ష భ െ݁ି ష భ ቁ ൌ ͲǤͻͲͲͲʹͻͻ 3.3 RAMD indices for subsystem-Deflaking: It is a prominent component in stock preparation unit. It comprises two components in parallel and failure of both components resulted complete system to shut down. The failure and repair rates of deflaking unit are exponentially distributed. By using minimic rule, the differential- difference equations are derived (based on Figure 4) as:
Figure 4 . State transition diagram of subsystem- Deflaking. ሺ ݐ ᶭ ݐ ሻൌሺͳെʹ ߤ ଷ ᶭ ݐ ሻܲ ሺ ݐ ሻ ߠ ଷ ᶭ ܲݐ ଵ ሺ ݐ ሻ ֜ܲ
ܲ
ሺ ݐ ᶭ ݐ ሻൌܲ ሺ ݐ ሻെʹ ߤ ଷ ᶭ ܲݐ ሺ ݐ ሻ ሺ ݐ ᶭ ݐ ሻെܲ ሺ ݐ ሻൌᶭ ݐ ሺെʹ ߤ ଷܲ ሺ ݐ ሻ ᶭ௧ ൌെʹ ߤ ଷܲ ሺ ݐ ሻ + ߠ ଷܲ ଵ ሺ ݐ ሻ
+ ߠ ଷ ᶭ ܲݐ ଵ ሺ ݐ ሻ ֜ܲ + ߠ ଷܲ ଵ ሺ ݐ ሻሻ ֜
బ ሺ௧ାᶭ௧ሻି బ ሺ௧ሻ Taking limit ᶭ ՜ݐ Ͳ , we get ᶭ௧՜ బ ሺ௧ାᶭ௧ሻି బ ሺ௧ሻ ᶭ௧ ൌെʹ ߤ ଷܲ ሺ ݐ ሻ + ߠ ଷܲ ଵ ሺ ݐ ሻ ܲ ௧՜ஶ ᇱ ൌെʹ ߤ ଷܲ ሺ ݐ ሻ + ߠ ଷܲ ଵ ሺ ݐ ሻ െʹ ߤ ଷܲ + ߠ ଷܲ ଵ ൌͲ
(8)
Similarly, െሺ ߤ െ ߠ ଷܲ ଶ ߤ ଷܲ ଵ ൌͲ
ଷ ߠ ଷ ሻܲ ଵ ߠ ଷܲ ଶ ʹ ߤ ଷܲ ൌͲ
(9)
(10)
Braz. J. Biom. ǡǤ 43 ǡǦͶ͵ʹǡʹͲʹͷǤ 7
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