Rasool et al. ଵ ൌ ఓ ర ఏ ర ܲ Now using normalization condition i.e the sum of all the probabilities is equal to one ሾσܲ ଵ ୀ ൌͳሿ , we get By solving the equation (12) and (13) and substituting the value of ܲ ଵ in equation (3), we get ܲ ൌ ଵା ଵ ഋ ഇర ర (14) Availability ( ܣ ௩ ሻൌܲ ൌ ଵା ଵ ഀరഁ ర ൌͲǤͻ Similarly, Reliability (ܴ ሺ ݐ ሻሻൌ݁ି ఓ ర ௧ ൌ݁ି Ǥଵଵ௧ , Maintainability ሺ ܯ ሺ ݐ ሻሻൌͳെ݁ି Ǥଽଽ௧ , ܨܤ ܶܯ ൌ ఓ ଵ ర ൌ ͻͲǤͻͲͻͲͻͲͻ݄ , ܴܶܶܯ ൌ ͳͲǤͳͲͳͲͳͲͳ݄ , ݁ܦ ܾ݈݁݊݀ܽ݅݅ ݕݐ ሺ݀ ሻൌͻ , ܦ = ͳെቀ ௗି ଵ ଵ ቁቀ݁ି ష భ െ݁ି ష భ ቁ ൌ ͲǤͶͲͲͻͺͲ 3.5 RAMD indices for subsystem-Paper Machine: 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 6) as:
Figure 6 . State transition diagram of subsystem-Paper Machine. ሺ ݐ ᶭ ݐ ሻൌሺͳെ ߤ ହ ᶭ ݐ ሻܲ ሺ ݐ ሻ ߠ ହ ᶭ ܲݐ ଵ ሺ ݐ ሻ ֜ܲ
ܲ
ሺ ݐ ᶭ ݐ ሻൌܲ ሺ ݐ ሻെ ߤ ହ ᶭ ܲݐ ሺ ݐ ሻ ሺ ݐ ᶭ ݐ ሻെܲ ሺ ݐ ሻൌᶭ ݐ ሺെ ߤ ହܲ ሺ ݐ ሻ ᶭ௧ ൌെ ߤ ହܲ ሺ ݐ ሻ + ߠ ହܲ ଵ ሺ ݐ ሻ
+ ߠ ହ ᶭ ܲݐ ଵ ሺ ݐ ሻ ֜ܲ + ߠ ହܲ ଵ ሺ ݐ ሻሻ ֜
బ ሺ௧ାᶭ௧ሻି బ ሺ௧ሻ Taking limit ᶭ ՜ݐ Ͳ , we get ᶭ௧՜ బ ሺ௧ାᶭ௧ሻି బ ሺ௧ሻ ᶭ௧ ൌെ ߤ ହܲ ሺ ݐ ሻ + ߠ ହܲ ଵ ሺ ݐ ሻ ܲ ௧՜ஶ ᇱ ሺ ݐ ሻൌെ ߤ ହܲ ሺ ݐ ሻ + ߠ ହܲ ଵ ሺ ݐ ሻ െ ߤ ହܲ + ߠ ହܲ ଵ ൌͲ
(15)
Similarly, െ ߠ
ହܲ ଵ ߤ ହܲ ൌͲ
(16)
Braz. J. Biom. ǡǤ 43 ǡǦͶ͵ʹǡʹͲʹͷǤ 9 ܲ
Made with FlippingBook. PDF to flipbook with ease