Rasool et al.
2.3 Assumptions: The model is developed under the following set of assumptions: x Failure and repair rates are constant. x The unit acts as new after getting repaired. x There are no simultaneous failures among the systems. x Sufficient repair facility available as and when needed. x Repair and or replacement included in the service. x Failure and repair rates follow exponential distribution.
3. RAMD Analysis In this section, mathematical models for each subsystem are formulated using Markov methodology. The RAMD measures of each subsystem are evaluated using failure and repair rates. The failure and repair rates of each subsystem is appended in table 2. 3.1 RAMD indices for subsystem -Storage Tank: 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 2) as:
Figure 2 . State transition diagram of subsystem-Storage Tank. ሺ ݐ ᶭ ݐ ሻൌሺͳെ ߤ ଵ ᶭ ݐ ሻܲ ሺ ݐ ሻ ߠ ଵ ᶭ ܲݐ ଵ ሺ ݐ ሻ
ܲ
ሺ ݐ ᶭ ݐ ሻൌܲ ሺ ݐ ሻെ ߤ ଵ ᶭ ܲݐ ሺ ݐ ሻ + ߠ ଵ ᶭ ܲݐ ଵ ሺ ݐ ሻ ֜ܲ ሺ ݐ ᶭ ݐ ሻെܲ ሺ ݐ ሻൌᶭ ݐ ሺെ ߤ ଵܲ ሺ ݐ ሻ + ߠ ଵܲ ଵ ሺ ݐ ሻሻ ֜ బ ሺ௧ାᶭ௧ሻି బ ሺ௧ሻ ᶭ௧ ൌെ ߤ ଵܲ ሺ ݐ ሻ + ߠ ଵܲ ଵ ሺ ݐ ሻ Taking limit ᶭ ՜ݐ Ͳ , we get ᶭ௧՜ బ ሺ௧ାᶭ௧ሻି బ ሺ௧ሻ ᶭ௧ ൌെ ߤ ଵܲ ሺ ݐ ሻ + ߠ ଵܲ ଵ ሺ ݐ ሻ ܲ ௧՜ஶ ᇱ ሺ ݐ ሻൌെ ߤ ଵܲ ሺ ݐ ሻ + ߠ ଵܲ ଵ ሺ ݐ ሻ Ͳൌെ ߤ ଵܲ + ߠ ଵܲ ଵ Similarly,
֜ܲ
(1)
Braz. J. Biom. ǡǤ 43 ǡǦͶ͵ʹǡʹͲʹͷǤ 5
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