For the system shown in Figure 1, subsystem S_1 has a failure value (F) 2.5% and

Question

For the system shown in Figure 1, subsystem S_1 has a failure value (F) 2.5% and S_3 has a failure value 3%, S_21, S_22, S_23 and S_24 are identical redundant subsystems. 1) Determine the required reliability of the subsystems (S_21, S_22, S_23 and S_24) necessary for the overall system to have reliability of 90%. 2) Determine the required reliability of the subsystems (S_21, S_22, S_23 and S_24) for the overall system to have the perfect reliability R = 1. Is it possible for this system to have perfect reliability (explain your answer)? 3) What is the highest reliability the overall system could have?

Explanation / Answer

Gven,

Failure rate of S1 = 2.5%

Reliability of S1 = (1 - 0.025) = .975

Failure rate of S3 = 3%

Reliability of S3 = (1 - 0.03) = 0.97

1) Overall System Reliability = 90 %

Let the failure rate of all the sub systems S21 =  S22 = S23 = S24 = r %

So , overall reliability of all the four subsystems in parallel = ( 1 - r4)

Overall all System reliability = Reliability of S1 * Overall reliability of all the four subsystems in parallel * Reliabilty of S3

0.9 = 0.97 * ( 1 - r4) * 0.975

( 1 - r4) = 0.9516

r4 = 1-0.9516

r4 = 0.0484

r = .469

r = 46.9 %

Reliability = 1 - failure rate

Reliability os subsystem = 1-r = 1- 0.469

= 0.531

Reliability of subsytems (S21 =  S22 = S23 = S24) = 53.1 %

2)

Overall all System reliability = Reliability of S1 * Overall reliability of all the four subsystems in parallel * Reliabilty of S3

1 = 0.97 * ( 1 - r4) * 0.975

( 1 - r4) = 1.0573

r4 = - 0.0573

Failure rate can't be negative so R=1 not possible

3) Overall all System reliability = Reliability of S1 * Overall reliability of all the four subsystems in parallel * Reliabilty of S3

At maximum we can have reliability of all the subsytems to be 100 %

Maximum overall Reliabilty of System = 0.97 * 1 * 0.975

= 0.94575

= 94.575 %

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.