Rasool et al. _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ From equations (8-10) using (3), we get Now using normalization condition i.e the sum of all the probabilities is equal to one ሾσܲ ଶ ୀ ൌ ሾσܲ ଶ ୀ ൌͳሿ , we get ܲ ଵ ൌʹ ఓ య ఏ య ܲ , ܲ ଶୀ ʹ ఓ యమ ఏ యమ ܲ , ܲ ൌ ଵାଶ ଵ ഋ ഇయ య ାଶ ഋ ഇ యమయమ (11) Availability ( ܣ ௩ ሻൌܲ ܲ ଵ ൌ ሾͳʹ ఓ య ఏ య ʹ ఓ యమ ఏ యమ ሿ -1 ሾͳʹ ఓ య ఏ య ሿ ൌ ͲǤͻ͵Ͳͳ͵ͺ Similarly, Reliability (ܴ ሺ ݐ ሻሻൌ݁ି ఓ య ௧ ൌ݁ି Ǥଵ଼ ௧ , Maintainability ሺ ܯ ሺ ݐ ሻሻൌͳെ݁ି Ǥସଽଽଽଽ଼଼ ௧ , ܨܤ ܶܯ ൌ ఓ ଵ య ൌ ͷǤͷͷͷͷͷͷͷ݄ , ܴܶܶܯ ൌ ͲǤͳʹͻͲ͵ʹʹ݄ , ݁ܦ ܾ݈݁݊݀ܽ݅݅ ݕݐ ሺ݀ ሻ ൌ Ͷ͵ǤͲͷͷͷͷͶͻ , ܦ = ͳെቀ ௗି ଵ ଵ ቁቀ݁ି ష భ െ݁ି ష భ ቁ ൌ ͲǤͻͳͲͷ͵ͷʹͳ͵ 3.4 RAMD indices for subsystem-Storage and Mixing Chest: 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 storage tank are exponentially distributed. By using minimic rule, the differential-difference equations are derived (based on Figure 5) as:
Figure 5 . State transition diagram of subsystem- Storage and Mixing Chest. ሺ ݐ ᶭ ݐ ሻൌሺͳെ ߤ ସ ᶭ ݐ ሻܲ ሺ ݐ ሻ ߠ ସ ᶭ ܲݐ ଵ ሺ ݐ ሻ ֜ܲ
ܲ
ሺ ݐ ᶭ ݐ ሻൌܲ ሺ ݐ ሻെ ߤ ସ ᶭ ܲݐ ሺ ݐ ሻ ሺ ݐ ᶭ ݐ ሻെܲ ሺ ݐ ሻൌᶭ ݐ ሺെ ߤ ସܲ ሺ ݐ ሻ ᶭ௧ ൌെ ߤ ସܲ ሺ ݐ ሻ + ߠ ସܲ ଵ ሺ ݐ ሻ
+ ߠ ସ ᶭ ܲݐ ଵ ሺ ݐ ሻ ֜ܲ + ߠ ସܲ ଵ ሺ ݐ ሻሻ ֜
బ ሺ௧ାᶭ௧ሻି బ ሺ௧ሻ Taking limit ᶭ ՜ݐ Ͳ , we get ᶭ௧՜ బ ሺ௧ାᶭ௧ሻି బ ሺ௧ሻ ᶭ௧ ൌെ ߤ ସܲ ሺ ݐ ሻ + ߠ ସܲ ଵ ሺ ݐ ሻ ܲ ௧՜ஶ ᇱ ሺ ݐ ሻൌെ ߤ ସܲ ሺ ݐ ሻ + ߠ ସܲ ଵ ሺ ݐ ሻ െ ߤ ସܲ + ߠ ସܲ ଵ ൌͲ
(12)
Similarly, െ ߠ
ସܲ ଵ ߤ ସܲ ൌͲ
(13)
From equations (12-13) using (3), we get
_____________________________________________________________________________________________ 8 Braz. J. Biom. ǡǤ 43 ǡǦͶ͵ʹǡʹͲʹͷǤ
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