For parallels, the reliability is 1 – (1-reliability)*(1-reliability)*…..
Here:
For
Reliability = 1 – (1-0.65)*(1-0.67)*(1-0.69) = 1 – (0.35*0.33*0.31) = 1 – (0.0358) = 0.9641 = 0.97
For
Reliability = 1 – (1-0.6)*(1-0.6) = 1 – (0.4*0.4) = 1 – 0.16 = 0.84
Now the configuration is
For series, reliability = reliability_1*reliability_2*….
Hence for
Reliability = 0.84*0.89*0.92 = 0.687792
For
Reliability = 0.95*0.97 = 0.9215
Hence, now the configuration is:
Hence Reliability = 0.95* (1 – (1-0.687792)*(1-0.9215))
= 0.95* (1 – (0.312208*0.0785)) = 0.95*(1 – 0.0245) = 0.95*0.9754 = 0.92671
Hence the reliability is = 0.93
b.
Old:
Series reliability of 0.93, 0.94, 0.92, 0.97
Hence Reliability = 0.93*0.94*0.92*0.97 = 0.78
New:
Series reliability of 0.93, 0.94, 0.92, 0.97 with backup of 0.94
Hence Reliability = (0.93+0.94*(1-0.93))*(0.94+0.94*(1-0.94))*(0.92+0.94*(1-0.92))*(0.97+0.94*(1-0.97))
= (0.93+0.0658)*(0.94+0.0564)*(0.92+0.0752)*(0.97+0.0282)
= 0.9856
= 0.99
Third option:
Series reliability of 0.93, 0.94, 0.92, 0.97 with backup of 0.97
Hence Reliability = (0.93+0.97*(1-0.93))*(0.94+0.97*(1-0.94))*(0.92+0.97*(1-0.92))*(0.97+0.97*(1-0.97))
= (0.93+0.0679)*(0.94+0.0582)*(0.92+0.0776)*(0.97+0.0291)
= 0.99281
= 0.99
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5. With the booming world economy, the 2x4 lumber consumed in the construction industry is considerably...
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