Question 1

A system is composed of three components in series having reliabilities of 0.99, 0.95, and 0.90. What is the overall system reliability?
A)0.95
B)0.90
C)0.85
D)0.80
E)0.75

Accepted Answer

The overall reliability of a series system is the product of the reliabilities of its components. Therefore, the overall system reliability is 0.99 * 0.95 * 0.90 = 0.84615, which is approximately 0.85.

Question 2

What is the useful life in hours for a product having a reliability of 0.999 and a failure rate of 0.015 failures per hour?
A)400
B)420
C)440
D)460
E)480

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Question 3

A system is composed of three components in series having reliabilities of 0.85, 0.92, and 0.90. What is the overall system reliability?
A)0.90
B)0.85
C)0.80
D)0.75
E)0.70

Accepted Answer

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Question 4

A system is to be composed of 10 identical components in series. What is the lowest reliability component that can be used in order to have an overall system reliability of 0.90?
A)0.99
B)0.98
C)0.97
D)0.96
E)0.95

Accepted Answer

For a series system, the overall reliability (R_system) is the product of the reliabilities of all individual components (R_component). Given R_system = 0.90 and the system is composed of 10 identical components, we can set up the equation: R_component^10 = 0.90. Solving for R_component gives approximately 0.99.

Question 5

What is the approximate useful life in hours for a product having a reliability of 0.9978 and a failure rate of 0.001 failures per hour?
A)6120
B)5600
C)5000
D)4400
E)3800

Accepted Answer

The useful life in hours can be calculated using the formula for reliability: R(t) = e^(-λt), where R(t) is the reliability at time t, λ is the failure rate, and t is the time in hours. Rearranging the formula to solve for t gives t = -ln(R(t))/λ. Plugging in the given reliability of 0.9978 and a failure rate of 0.001 failures per hour, t = -ln(0.9978)/0.001 ≈ 6120 hours.

Question 6

What is the system availability for something that has a mean time between failures of 50 hours and needs an average of 1 hour to repair when it does fail?
A)0.98
B)0.92
C)0.86
D)0.80
E)0.74

Accepted Answer

System availability is calculated as MTBF / (MTBF + MTTR), where MTBF is Mean Time Between Failures and MTTR is Mean Time To Repair. Plugging in the given values, we get 50 / (50 + 1) = 50 / 51 = 0.98039, which rounds to 0.98.

Question 7

What is the reliability of a product with a failure rate of 0.015 per operating hour and a useful life of 250 hours?
A)0.14
B)0.12
C)0.88
D)0.98
E)0.02

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Question 8

A system is composed of three components in series having reliabilities of 0.99, 0.98, and 0.97. What is the overall system reliability?
A)0.97
B)0.96
C)0.95
D)0.94
E)0.93

Accepted Answer

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Question 9

A system is to be composed of 5 identical components in series. What is the lowest reliability component that can be used in order to have an overall system reliability of 0.90?
A)0.98
B)0.97
C)0.96
D)0.95
E)0.94

Accepted Answer

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Question 10

Two components of reliability 0.95 are in parallel and this subsystem is connected in series to a component with a reliability of 0.90. The overall system reliability is ________.
A)0.82
B)0.84
C)0.86
D)0.88
E)0.90

Accepted Answer

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Question 11

What is the reliability of a product with a failure rate of 0.001 per operating hour and a useful life of 1500 hours?
A)0.14
B)0.22
C)0.50
D)0.78
E)0.86

Accepted Answer

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Question 12

Two components of reliability 0.90 are in parallel and this subsystem is connected in series to a component with a reliability of 0.95. The overall system reliability is ________.
A)0.93
B)0.94
C)0.95
D)0.96
E)0.97

Accepted Answer

The reliability of two components in parallel is calculated by adding the individual reliabilities and subtracting their product from 1. Therefore, the reliability of the parallel subsystem is:

R(parallel) = 1 - (1-0.9)(1-0.9) = 0.99

The overall system reliability is then:

R(overall) = R(parallel) * R(series) = 0.99 * 0.95 = 0.94

Therefore, the correct answer is B) 0.94.

Question 13

Fifty defibrillators are tested for 48 hours per machine. Of all the machines tested, 2 experience malfunctions during the test. What is the failure rate for the machines?
A)0.004
B)0.042
C)0.01
D)0.008
E)0.0008

Accepted Answer

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Question 14

Two components of reliability 0.95 are in parallel and this subsystem is connected in series to a component with a reliability of 0.95. The overall system reliability is ________.
A)0.93
B)0.94
C)0.95
D)0.96
E)0.97

Accepted Answer

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Question 15

A system is to be composed of 4 identical components in series. What is the lowest reliability component that can be used in order to have an overall system reliability of 0.85?
A)0.93
B)0.94
C)0.95
D)0.96
E)0.97

Accepted Answer

To find the overall system reliability, we need to multiply the reliability of each component. Let x be the reliability of one component. Then the overall system reliability is:
0.85 = x^4
Taking the fourth root of both sides, we get:
x = 0.96
Therefore, the lowest reliability component that can be used is 0.96, which is choice D.

Question 16

What is the system availability for something that has a mean time between failures of 168 hours and needs an average of 48 hours to repair when it does fail?
A)0.98
B)0.93
C)0.88
D)0.83
E)0.78

Accepted Answer

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Question 17

Fifty crash helmets are tested for one hundred hours per helmet. Of all the helmets tested, only one experiences a malfunction during the test. What is the failure rate for the helmets?
A)0.0002
B)0.002
C)0.004
D)0.0008
E)0.016

Accepted Answer

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Question 18

What is the useful life in hours for a product having a reliability of 0.985 and a failure rate of 0.015 failures per hour?
A)120
B)200
C)280
D)360
E)440

Accepted Answer

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Question 19

What is the system availability for something that has a mean time between failures of 100 hours and needs an average of 4 hours to repair when it does fail?
A)0.98
B)0.92
C)0.96
D)0.90
E)0.84

Accepted Answer

The system availability can be calculated using the following formula:

Availability = (MTBF) / (MTBF + MTTR)

Where MTBF is the mean time between failures and MTTR is the mean time to repair.

Plugging in the values given, we get:

Availability = (100) / (100 + 4) = 0.96

Therefore, the system availability is 0.96 or 96%. Option (C) is the correct answer.

Question 20

What is the reliability of a product with a failure rate of 0.002 per operating hour and a useful life of 1000 hours?
A)0.14
B)0.22
C)0.50
D)0.78
E)0.86

Accepted Answer

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Quiz 12: Statistically Based Quality Improvement for Attributes

A system is composed of three components in series having reliabilities of 0.99, 0.95, and 0.90. What is the overall system reliability?

What is the useful life in hours for a product having a reliability of 0.999 and a failure rate of 0.015 failures per hour?

A system is composed of three components in series having reliabilities of 0.85, 0.92, and 0.90. What is the overall system reliability?

A system is to be composed of 10 identical components in series. What is the lowest reliability component that can be used in order to have an overall system reliability of 0.90?

What is the approximate useful life in hours for a product having a reliability of 0.9978 and a failure rate of 0.001 failures per hour?

What is the system availability for something that has a mean time between failures of 50 hours and needs an average of 1 hour to repair when it does fail?

What is the reliability of a product with a failure rate of 0.015 per operating hour and a useful life of 250 hours?

A system is composed of three components in series having reliabilities of 0.99, 0.98, and 0.97. What is the overall system reliability?

A system is to be composed of 5 identical components in series. What is the lowest reliability component that can be used in order to have an overall system reliability of 0.90?

Two components of reliability 0.95 are in parallel and this subsystem is connected in series to a component with a reliability of 0.90. The overall system reliability is ________.

What is the reliability of a product with a failure rate of 0.001 per operating hour and a useful life of 1500 hours?

Two components of reliability 0.90 are in parallel and this subsystem is connected in series to a component with a reliability of 0.95. The overall system reliability is ________.

Fifty defibrillators are tested for 48 hours per machine. Of all the machines tested, 2 experience malfunctions during the test. What is the failure rate for the machines?

Two components of reliability 0.95 are in parallel and this subsystem is connected in series to a component with a reliability of 0.95. The overall system reliability is ________.

A system is to be composed of 4 identical components in series. What is the lowest reliability component that can be used in order to have an overall system reliability of 0.85?

What is the system availability for something that has a mean time between failures of 168 hours and needs an average of 48 hours to repair when it does fail?

Fifty crash helmets are tested for one hundred hours per helmet. Of all the helmets tested, only one experiences a malfunction during the test. What is the failure rate for the helmets?

What is the useful life in hours for a product having a reliability of 0.985 and a failure rate of 0.015 failures per hour?

What is the system availability for something that has a mean time between failures of 100 hours and needs an average of 4 hours to repair when it does fail?

What is the reliability of a product with a failure rate of 0.002 per operating hour and a useful life of 1000 hours?