Question

5. With the booming world economy, the 2x4 lumber consumed in the construction industry is considerably increasing. To obtain the 2x4's that meet the quality requirements the milling system for 2x4's needs to be effective. The following reliability diagram is established. What is the reliability of the milling system?

Answer 1

0.6 | 10.89] | 0.8 →[092] | 0.92 | —[095 LAL 06] -05] > 0.65 | > 0.67] - 0.69 上

For parallels, the reliability is 1 – (1-reliability)*(1-reliability)*…..

Here:

For

→ 0.65] > 0.67 | 0.69

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

0.6 i - 0.6 |

Reliability = 1 – (1-0.6)*(1-0.6) = 1 – (0.4*0.4) = 1 – 0.16 = 0.84

Now the configuration is

自HIV 0.95 0.95 0.97

For series, reliability = reliability_1*reliability_2*….

Hence for

Reliability = 0.84*0.89*0.92 = 0.687792

For

0.95 0.97

Reliability = 0.95*0.97 = 0.9215

Hence, now the configuration is:

10.687792 10.95 0.9215

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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