Question 1

Consider a product with three components in series,with reliabilities of 0.90,0.80,and 0.99 for components A,B,and C,respectively.Furthermore,component B uses a backup that also has a reliability of 0.80.What is the reliability of the system?
A)0.50000
B)0.71280
C)0.80000
D)0.85536
E)3.49000

Accepted Answer

The reliability of a system with components in series can be calculated as the product of the individual reliabilities of each component:

R_system = R_A x R_B x R_C

However, in this case, component B has a backup with a reliability of 0.80. This means that if component B fails, the backup will take over and the system will still function. We can model this situation by adding a parallel branch between components B and C, as shown below:

```
----(0.90)----(0.80)---(0.99)---
  |                             |
  -----------(0.20)------------
```

The reliability of the parallel branch is calculated as:

R_parallel = 1 - (1 - 0.80) x (1 - 0.99) = 0.998

This means that the parallel branch has a very high reliability, and we can approximate the overall reliability of the system as:

R_system ≈ R_A x R_parallel

R_system = 0.90 x 0.998 = 0.8982

Therefore, the reliability of the system is approximately 0.8982 or 0.85536 (rounded to five decimal places). The closest answer choice is D.

Question 2

The inverse of the mean time between failures is the ________.

Accepted Answer

The answer of The inverse of the mean time between...

Question 3

________ is the expected time between a repair and the next failure of a component,machine,process,or product.

Accepted Answer

The answer of ________ is the expected time between a...

Question 4

Suppose that a process is comprised of five components,each having a 75% success rate.By how much would reliability change if the process switched from having the components in series to having the components in parallel?
A)no change
B)100% increase
C)76.2% increase
D)76.2 % decrease
E)50% increase

Accepted Answer

When the components are in series, the overall success rate of the process is given by the product of the success rates of each individual component, which in this case is (0.75)^5 = 0.2373 or 23.73%. This means that there is a 76.27% chance of failure.

When the components are in parallel, the overall success rate of the process is given by the complement of the probability that all components fail, which is 1- (0.25)^5 = 0.99902 or 99.902%. This means that there is only a 0.098% chance of failure.

Therefore, switching from series to parallel increases the reliability of the process by (0.99902-0.2373)/0.2373 = 3.22 or 322%, which is equivalent to a 76.2% increase.

Question 5

A system is composed of three components A,B,and C.All three must function for the system to function.There are currently no backups in place.The system has a reliability of 0.966.If a backup is installed for component A,the new system reliability will be:
A)unchanged.
B)less than 0.966.
C)greater than it would be if a backup were also installed for component B.
D)greater than 0.966
E)none of the above

Accepted Answer

Since all three components must function for the system to function, the reliability of the system can be calculated using the formula: 
Reliability = R(A) x R(B) x R(C)
where R(A), R(B), and R(C) are the reliability of components A, B, and C, respectively.

Currently, the system reliability is 0.966. If a backup is installed for component A, then the reliability of component A would increase. Let's say the new reliability of component A with the backup is R'(A). Then, the new system reliability would be:
Reliability = R'(A) x R(B) x R(C)

Since R'(A) > R(A), the new system reliability would be greater than 0.966. Therefore, the answer is (D) greater than 0.966.

The answer (C) cannot be guaranteed as it depends on the reliability of component B and whether a backup is installed for it or not. So, we cannot say for sure that the new system reliability with a backup for A would be greater than if a backup were also installed for component B.

Question 6

A system has three components in series with reliabilities 0.9,0.7,and 0.5.What is the system reliability?
A)0.315
B)0.500
C)0.700
D)0.900
E)2.100

Accepted Answer

The system reliability with components in series is the product of their reliabilities. Thus, the system reliability is 0.9 x 0.7 x 0.5 = 0.315. The best choice is A.

Question 7

Components A,B,and C are connected in series.Component D is connected in parallel to component B.Which of the following statements is true?
A)The system works only if A works,B or C works,and D works.
B)Component B must work for the system to work.
C)The system works when A works,C,works,and either B or D works.
D)Components B and C are backups to A.
E)The system works if D works,and any of A,B,or C works.

Accepted Answer

Since components A, B, and C are connected in series, all three components must work for the system to work. However, if component D is connected in parallel to component B, it means that either B or D can work to complete the circuit. Therefore, the system works when A works, C works, and either B or D works.

Question 8

What is the reliability of the three components connected in series shown below? 
A)0.799425
B)0.85000
C)0.91333
D)0.95000
E)2.79

Accepted Answer

The answer of What is the reliability of the three...

Question 9

A system has three components in parallel with reliabilities 0.9,0.7,and 0.5.What is the system reliability?
A)0.315
B)0.700
C)0.900
D)0.985
E)2.100

Accepted Answer

The system reliability of three parallel components is given by:
R_sys = 1 - (1 - R_1)(1 - R_2)(1 - R_3)
Substituting the given values of reliability, we get:
R_sys = 1 - (1 - 0.9)(1 - 0.7)(1 - 0.5)
R_sys = 0.985

Question 10

A two-component process has an 81% success rate in series and a 99% success rate in parallel.If each component has the same reliability,what is the reliability of an individual component?
A)50%
B)90%
C)99%
D)18%
E)81%

Accepted Answer

The answer of A two-component process has an 81% success...

Question 11

MTBF measures the average:
A)calendar time between failures.
B)operating time between failures.
C)number of failures per unit time.
D)number of operations between failures.
E)downtime per breakdown.

Accepted Answer

MTBF measures the average operating time between failures.

Question 12

A system is composed of four parts,J,K,L,and M.All four must function for the system to function.The four component reliabilities are .99,.98,.992,and .998.The designers are considering putting an 80% reliable backup at K.This backup will change the system reliability from ________ to ________.
A)0.9762; 0.9605
B)0.9605; 0.9762
C)0.9605; some smaller value
D)0.9605; 0.996
E)0.98; 0.99

Accepted Answer

The original system reliability can be computed as:
R(original) = J x K x L x M
R(original) = 0.99 x 0.98 x 0.992 x 0.998
R(original) = 0.9696

If an 80% reliable backup is added at K, the new system reliability can be computed as:
R(new) = J x (0.8K + 0.2) x L x M + (1 - J) x K x L x M
R(new) = 0.99 x (0.8 x 0.98 + 0.2) x 0.992 x 0.998 + (1 - 0.99) x 0.98 x 0.992 x 0.998
R(new) = 0.9761564

Therefore, the system reliability changes from 0.9696 to 0.9761564, which is approximately 0.9605. Therefore, the answer is B.

Question 13

What is the reliability of a four-component product,with components in series,and component reliabilities of .90,.95,.98,and .99?
A)0.8295
B)0.90
C)0.955
D)0.99
E)0.945

Accepted Answer

The answer of What is the reliability of a four-component...

Question 14

A redundant part decreases reliability if the reliability of the redundant part is lower than that of the part it is backing up.

Accepted Answer

The answer of A redundant part decreases reliability if the...

Question 15

As the number of components in a system connected in a series decreases,all other things being equal,the reliability of the system usually:
A)increases.
B)stays the same.
C)decreases.
D)increases,then decreases.
E)decreases,then increases.

Accepted Answer

When components are connected in a series, the failure of any one component results in the failure of the entire system. Therefore, as the number of components decreases in a series connection, the likelihood of a failure decreases and the overall reliability of the system increases.

Question 16

How is MTBF related to FR(N)?
A)MTBF is measured in hours,while FR(N)is measured in years.
B)MTBF is normally distributed,with FR(%)as its mean and FR(N)as its standard deviation.
C)MTBF is the reciprocal of FR(N).
D)Both MTBF and FR(N)increase when breakdown maintenance is replaced by preventive maintenance.
E)MTBF and FR(N)are unrelated concepts.

Accepted Answer

MTBF (Mean Time Between Failures) is the reciprocal of FR(N) (Failure Rate per unit of time). This means that as FR(N) increases, MTBF decreases, and vice versa.

Question 17

A job consists of a series of three tasks.Task 1 is performed correctly 98% of the time,task 2 is performed correctly 99% of the time,and task 3 is performed correctly 97% of the time.What is the reliability of this job?
A)91.27%
B)94.11%
C)97.00%
D)98.00%
E)99.00%

Accepted Answer

The reliability of a series system (such as this job) is the product of the reliability of each individual task. Therefore, the reliability of this job is 0.98 x 0.99 x 0.97 = 0.9411, or 94.11%. Therefore, the best choice is B.

Question 18

Ten high-technology batteries are tested for 200 hours each.One failed at 20 hours; another failed at 140 hours; all others completed the test.FR(%)is ________ and MTBF is ________.
A)20%; 880 hours
B)10%; 1980 hours
C)20%; 1760 hours
D)20%; 1000 hours
E)80%; 920 hours

Accepted Answer

The answer of Ten high-technology batteries are tested for 200...

Question 19

Ten high-technology batteries are tested for 200 hours each.One failed at 50 hours; all others completed the test.FR(%)is ________ and FR(N)is ________.
A)10%; 1/1850
B)10%; 1/2000
C)25%; 1850 hours
D)90%; 1/2000
E)10%; 1/1950

Accepted Answer

FR(%) is the failure rate percentage, which is 1 out of 10 batteries failing, or 10%. FR(N) is the failure rate per unit time, calculated as 1 failure in 2000 hours (10 batteries * 200 hours each, minus the 50 hours before the failure occurred).

Question 20

Ten high-technology batteries are tested for 200 hours each.One failed at 20 hours; all others completed the test.FR(%)is ________ and MTBF is ________.
A)10%; 1/1820
B)90%; 1/1820
C)10%; 1820 hours
D)10%; 1980 hours
E)10%; 2000 hours

Accepted Answer

The answer of Ten high-technology batteries are tested for 200...

Quiz 18: Maintenance and Reliability

Consider a product with three components in series,with reliabilities of 0.90,0.80,and 0.99 for components A,B,and C,respectively.Furthermore,component B uses a backup that also has a reliability of 0.80.What is the reliability of the system?

The inverse of the mean time between failures is the ________.

________ is the expected time between a repair and the next failure of a component,machine,process,or product.

Suppose that a process is comprised of five components,each having a 75% success rate.By how much would reliability change if the process switched from having the components in series to having the components in parallel?

A system is composed of three components A,B,and C.All three must function for the system to function.There are currently no backups in place.The system has a reliability of 0.966.If a backup is installed for component A,the new system reliability will be:

A system has three components in series with reliabilities 0.9,0.7,and 0.5.What is the system reliability?

Components A,B,and C are connected in series.Component D is connected in parallel to component B.Which of the following statements is true?

What is the reliability of the three components connected in series shown below?

A system has three components in parallel with reliabilities 0.9,0.7,and 0.5.What is the system reliability?

A two-component process has an 81% success rate in series and a 99% success rate in parallel.If each component has the same reliability,what is the reliability of an individual component?

MTBF measures the average:

A system is composed of four parts,J,K,L,and M.All four must function for the system to function.The four component reliabilities are .99,.98,.992,and .998.The designers are considering putting an 80% reliable backup at K.This backup will change the system reliability from to .

What is the reliability of a four-component product,with components in series,and component reliabilities of .90,.95,.98,and .99?

A redundant part decreases reliability if the reliability of the redundant part is lower than that of the part it is backing up.

As the number of components in a system connected in a series decreases,all other things being equal,the reliability of the system usually:

How is MTBF related to FR(N) ?

A job consists of a series of three tasks.Task 1 is performed correctly 98% of the time,task 2 is performed correctly 99% of the time,and task 3 is performed correctly 97% of the time.What is the reliability of this job?

Ten high-technology batteries are tested for 200 hours each.One failed at 20 hours; another failed at 140 hours; all others completed the test.FR(%) is and MTBF is .

Ten high-technology batteries are tested for 200 hours each.One failed at 50 hours; all others completed the test.FR(%) is and FR(N) is .

Ten high-technology batteries are tested for 200 hours each.One failed at 20 hours; all others completed the test.FR(%) is and MTBF is .

Quiz 18: Maintenance and Reliability

Consider a product with three components in series,with reliabilities of 0.90,0.80,and 0.99 for components A,B,and C,respectively.Furthermore,component B uses a backup that also has a reliability of 0.80.What is the reliability of the system?

The inverse of the mean time between failures is the ________.

________ is the expected time between a repair and the next failure of a component,machine,process,or product.

Suppose that a process is comprised of five components,each having a 75% success rate.By how much would reliability change if the process switched from having the components in series to having the components in parallel?

A system is composed of three components A,B,and C.All three must function for the system to function.There are currently no backups in place.The system has a reliability of 0.966.If a backup is installed for component A,the new system reliability will be:

A system has three components in series with reliabilities 0.9,0.7,and 0.5.What is the system reliability?

Components A,B,and C are connected in series.Component D is connected in parallel to component B.Which of the following statements is true?

What is the reliability of the three components connected in series shown below?

A system has three components in parallel with reliabilities 0.9,0.7,and 0.5.What is the system reliability?

A two-component process has an 81% success rate in series and a 99% success rate in parallel.If each component has the same reliability,what is the reliability of an individual component?

MTBF measures the average:

A system is composed of four parts,J,K,L,and M.All four must function for the system to function.The four component reliabilities are .99,.98,.992,and .998.The designers are considering putting an 80% reliable backup at K.This backup will change the system reliability from ________ to ________.

What is the reliability of a four-component product,with components in series,and component reliabilities of .90,.95,.98,and .99?

A redundant part decreases reliability if the reliability of the redundant part is lower than that of the part it is backing up.

As the number of components in a system connected in a series decreases,all other things being equal,the reliability of the system usually:

How is MTBF related to FR(N) ?

A job consists of a series of three tasks.Task 1 is performed correctly 98% of the time,task 2 is performed correctly 99% of the time,and task 3 is performed correctly 97% of the time.What is the reliability of this job?

Ten high-technology batteries are tested for 200 hours each.One failed at 20 hours; another failed at 140 hours; all others completed the test.FR(%) is ________ and MTBF is ________.

Ten high-technology batteries are tested for 200 hours each.One failed at 50 hours; all others completed the test.FR(%) is ________ and FR(N) is ________.

Ten high-technology batteries are tested for 200 hours each.One failed at 20 hours; all others completed the test.FR(%) is ________ and MTBF is ________.

A system is composed of four parts,J,K,L,and M.All four must function for the system to function.The four component reliabilities are .99,.98,.992,and .998.The designers are considering putting an 80% reliable backup at K.This backup will change the system reliability from to .

Ten high-technology batteries are tested for 200 hours each.One failed at 20 hours; another failed at 140 hours; all others completed the test.FR(%) is and MTBF is .

Ten high-technology batteries are tested for 200 hours each.One failed at 50 hours; all others completed the test.FR(%) is and FR(N) is .

Ten high-technology batteries are tested for 200 hours each.One failed at 20 hours; all others completed the test.FR(%) is and MTBF is .