Deck 4: B: Product Design

Question 1

An early warning security fence has three major components which must each perform in order for the system to perform.Their reliabilities are .4,.3,and .2.The system reliability is equal to:

A) .024
B) .076
C) .100
D) .336
E) .900

Answer 1

A

Question 2

The probability that a product will fail within a given amount of time is often described by the:

A) beta distribution.
B) binomial distribution.
C) negative Gaussian distribution.
D) normal distribution.
E) uniform distribution.

Answer 2

D

Question 3

A product comprised of two components whose failure probabilities are .1 each,has a reliability of:

A) 1.80
B) .90
C) .81
D) .80
E) .20

Answer 3

C

Question 4

A component in a product can be considered an "independent" component if it has no relation to whether any other component in the product functions or not.

Question 5

"Independent components" cannot exist in the same product.

Question 6

If a system is composed of two parts which must both operate,and each has a probability of .7 of operating,it is more likely than not that the system will fail.

Question 7

A P/OM student has purchased a four-function calculator for use during exams.This calculator is perfectly reliable except for two parts: its microchip,which has a failure rate of one in every twenty hours of operation; and its battery,which has a failure rate of one in every ten hours of operation.Also,on average the battery will fail in five hours,with a standard deviation of 30 minutes.Assuming that a new battery has just been installed,what is the probability that the calculator will perform reliably during a one-hour exam?

A) 0.800
B) 0.855
C) 0.900
D) 0.950
E) 1.850

Question 8

One operational definition of reliability is the probability that a product or system will function when activated.

Question 9

An important dimension of reliability relates to "prescribed set of conditions".

Question 10

A system is comprised of two separate units which must both function in order for the system to perform as intended.The reliability of one is .4,and the reliability of the other is .5.The overall system reliability is:

A) .90
B) .30
C) .20
D) .10
E) .02

Question 11

Events can be considered "independent events" if they have no relation to the occurrence or non-occurrence of each other.

Question 12

A P/OM student has purchased a four-function calculator for use during exams.This calculator is perfectly reliable except for two parts: its microchip,which has a failure rate of one in every twenty hours of operation; and its battery,which has a failure rate of one in every ten hours of operation.Also,on average the battery will fail in five hours,with a standard deviation of 30 minutes.What service life should the manufacturer specify in order to have a .8413 probability that a battery will not fail within that amount of time?

A) 3.5 hours
B) 4 hours
C) 4.5 hours
D) 5 hours
E) 5.5 hours

Question 13

A system is composed of two parts which must both operate in order for the system to perform as intended.The parts have reliabilities of .6 and .5.There is an identical backup system connected to the main system by a switch which has a reliability of .9.The probability that the overall system will operate is closest to:

A) .30
B) .40
C) .50
D) .60
E) .70

Question 14

The probability that a product will perform its intended function under prescribed conditions is:

A) reliability.
B) failure.
C) functionality.
D) redundancy.
E) manufacturability.

Question 15

Redundancy in product design refers to backup parts or systems.

Question 16

A P/OM student has purchased a four-function calculator for use during exams.This calculator is perfectly reliable except for two parts: its microchip,which has a failure rate of one in every twenty hours of operation; and its battery,which has a failure rate of one in every ten hours of operation.Also,on average the battery will fail in five hours,with a standard deviation of 30 minutes.Assuming that a new battery has just been installed and the student brings one spare battery with him,what is the probability that the calculator will perform reliably during a one-hour exam?

A) 0.89775
B) 0.9405
C) 0.987525
D) 0.99
E) 0.9975

Question 17

A P/OM student has purchased a four-function calculator for use during exams.This calculator is perfectly reliable except for two parts: its microchip,which has a failure rate of one in every twenty hours of operation; and its battery,which has a failure rate of one in every ten hours of operation.Also,on average the battery will fail in five hours,with a standard deviation of 30 minutes.What is the probability that a new battery will fail within six hours?

A) 0.0228
B) 0.4772
C) 0.5
D) 0.9544
E) 0.9772

Question 18

A P/OM student has purchased a four-function calculator for use during exams.This calculator is perfectly reliable except for two parts: its microchip,which has a failure rate of one in every twenty hours of operation; and its battery,which has a failure rate of one in every ten hours of operation.Also,on average the battery will fail in five hours,with a standard deviation of 30 minutes.Assuming that a new battery has just been installed,what is the probability that the battery will perform reliably during a one-hour exam?

A) 0.05
B) 0.10
C) 0.20
D) 0.90
E) 0.95

Question 19

A garage door opener has three sections,which have reliabilities of .9,.8,and .9.The lowest of these has an identical backup which automatically goes on if the original fails.All three parts must operate to perform its intended function.The system reliability is closest to:

A) .40
B) .50
C) .60
D) .70
E) .80

Question 20

One of the solar instruments on a satellite has three major parts which must all operate.Two have reliabilities of .7,and the other has a reliability of .9.In case the system fails,there is an identical backup system which kicks on automatically.The overall reliability of the system,including the backup,is closest to:

A) .40
B) .50
C) .60
D) .70
E) .80

Question 21

The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery,which has a random failure rate of one in every five hours of operation; and the light bulb,which has a random failure rate of three in every ten hours.If the company includes a backup light bulb with each flashlight,what is the probability that the flashlight will perform reliably for one hour (excluding light bulb replacement time,if any)?

A) 0.6720
B) 0.7280
C) 0.8736
D) 0.9100
E) 0.9600

Question 22

The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems.This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation.If he were to add just a backup generator,what would be the probability that this system would perform reliably for a period of one year?

A) 0.48
B) 0.60
C) 0.72
D) 0.75
E) 0.96

Question 23

The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems.This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation.What is the probability that this system will perform reliably for a period of one year?

A) 0.4
B) 0.5
C) 0.8
D) 0.9
E) 1.3

Question 24

The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle.One (either)lamp is to be lit if steam pressure drops below the desired level,and two (both)are to be lit if temperature drops below a desired level.His supplier estimates that a lamp has a failure rate of .2 per hour of operation,and a mean wear-out time of seven years with a standard deviation of eight months.If the temperature drops below the desired level,what is the probability the system will perform reliably for one hour?

A) .04
B) .40
C) .60
D) .64
E) .96

Question 25

The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle.One (either)lamp is to be lit if steam pressure drops below the desired level,and two (both)are to be lit if temperature drops below a desired level.His supplier estimates that a lamp has a failure rate of .2 per hour of operation,and a mean wear-out time of seven years with a standard deviation of eight months.If the pressure drops below the desired level,what is the probability the system will perform reliably for one hour?

A) .04
B) .4
C) .6
D) .64
E) .96

Question 26

The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems.This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation.If the transformer has a mean time to wear-out of 20 years with a standard deviation of 2 years,what service life should the manufacturer specify in order to have a .9332 probability that it will last at least that long before failing?

A) 17 years
B) 18 years
C) 19 years
D) 20 years
E) 21 years

Question 27

The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery,which has a random failure rate of one in every five hours of operation; and the light bulb,which has a random failure rate of three in every ten hours.Devices,Inc.supplies Readylite with the on-off switch for this flashlight.These switches,on average,fail in fifty hours with a standard deviation of four hours.What service life should Devices specify to have a .8944 probability that a switch will last at least that long before failing?

A) 43 hours
B) 45 hours
C) 46 hours
D) 50 hours
E) 54 hours

Question 28

The chief of the design team for a new missile wants to know the reliability of its guidance system.This system is comprised of three components: a gyroscope,which has a random failure rate of 3 in every 10 launches; a computer,which has a random failure rate of 2 in every 10 launches; and a rocket motor,which has a random failure of 1 in every 10 launches.If they were to connect an identical,backup gyroscope with a .90 reliable switch to the primary gyroscope,what would be the reliability of the gyroscope function during a launch?

A) 0.3
B) 0.504
C) 0.7
D) 0.889
E) 0.97

Question 29

The chief of the design team for a new missile wants to know the reliability of its guidance system.This system is comprised of three components: a gyroscope,which has a random failure rate of 3 in every 10 launches; a computer,which has a random failure rate of 2 in every 10 launches; and a rocket motor,which has a random failure of 1 in every 10 launches.What is the probability that the guidance system will perform reliably during a launch?

A) 0.300
B) 0.504
C) 0.700
D) 0.889
E) 0.910

Question 30

The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery,which has a random failure rate of one in every five hours of operation; and the light bulb,which has a random failure rate of three in every ten hours.What is the probability that the flashlight will perform reliably for one hour?

A) 0.50
B) 0.56
C) 0.70
D) 0.80
E) 1.50

Question 31

The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle.One (either)lamp is to be lit if steam pressure drops below the desired level,and two (both)are to be lit if temperature drops below a desired level.His supplier estimates that a lamp has a failure rate of .2 per hour of operation,and a mean wear-out time of seven years with a standard deviation of eight months.What is the probability that a lamp will last at least until the expiration of the warranty,which is six years?

A) .9772
B) .9332
C) .8664
D) .8413
E) .4332

Question 32

The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle.One (either)lamp is to be lit if steam pressure drops below the desired level,and two (both)are to be lit if temperature drops below a desired level.His supplier estimates that a lamp has a failure rate of .2 per hour of operation,and a mean wear-out time of seven years with a standard deviation of eight months.What warranty period for a lamp would give a probability of .9987 that it would not require warranty service?

A) 5 years
B) 5.67 years
C) 6.33 years
D) 7 years
E) 9 years

Question 33

The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems.This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation.If the transformer has a mean time to wear-out of 20 years with a standard deviation of 2 years,what is the probability that it will fail within 19 years?

A) 0.1915
B) 0.3085
C) 0.383
D) 0.5
E) 0.6915

Question 34

The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery,which has a random failure rate of one in every five hours of operation; and the light bulb,which has a random failure rate of three in every ten hours.If the company includes both a backup light bulb and a backup battery with each flashlight,what is the probability that the flashlight will perform reliably for one hour (excluding replacement time)?

A) 0.6720
B) 0.7280
C) 0.8736
D) 0.9100
E) 0.9600

Question 35

The chief of the design team for a new missile wants to know the reliability of its guidance system.This system is comprised of three components: a gyroscope,which has a random failure rate of 3 in every 10 launches; a computer,which has a random failure rate of 2 in every 10 launches; and a rocket motor,which has a random failure of 1 in every 10 launches.What is the probability that the gyroscope will perform reliably during a launch?

A) 0.300
B) 0.504
C) 0.700
D) 0.889
E) 0.910

Question 36

The Readylite Company produces a flashlight which is perfectly reliable except for two components: the battery,which has a random failure rate of one in every five hours of operation; and the light bulb,which has a random failure rate of three in every ten hours.What is the probability that the battery will perform reliably for one hour?

A) 0.2
B) 0.3
C) 0.5
D) 0.7
E) 0.8

Question 37

The chief of the design team for a new missile wants to know the reliability of its guidance system.This system is comprised of three components: a gyroscope,which has a random failure rate of 3 in every 10 launches; a computer,which has a random failure rate of 2 in every 10 launches; and a rocket motor,which has a random failure of 1 in every 10 launches.If they were to connect an identical,backup gyroscope with a perfectly reliable switch to the primary gyroscope,what would be the reliability of the gyroscope function during a launch?

A) 0.3
B) 0.504
C) 0.7
D) 0.889
E) 0.91

Question 38

The plant manager for the local electric utility company wants to know the reliability of one of his small hydroelectric power generating systems.This system is comprised of two components: a generator which has a random failure rate of one in every two years of operation; and a transformer which has a random failure rate of one in every five years of operation.If he were to add both a backup generator and a backup transformer,what would be the probability that this system would perform reliably for a period of one year?

A) 0.48
B) 0.60
C) 0.72
D) 0.75
E) 0.96

Question 39

The chief of the design team for a new missile wants to know the reliability of its guidance system.This system is comprised of three components: a gyroscope,which has a random failure rate of 3 in every 10 launches; a computer,which has a random failure rate of 2 in every 10 launches; and a rocket motor,which has a random failure of 1 in every 10 launches.If the battery used to power the computer has a mean time to fail of 60 minutes with a standard deviation of 20 minutes,what is the probability that it will last for a launch of 30 minutes duration without failing?

A) 0.9332
B) 0.8664
C) 0.5668
D) 0.4332
E) 0.0668

Question 40

The chief design engineer for Colonial Warning Systems wants to know the reliability of a two-lamp device intended to warn the operator of potential problems with a commercial steam kettle.One (either)lamp is to be lit if steam pressure drops below the desired level,and two (both)are to be lit if temperature drops below a desired level.His supplier estimates that a lamp has a failure rate of .2 per hour of operation,and a mean wear-out time of seven years with a standard deviation of eight months.What is the probability that a lamp will perform reliably for one hour?

A) 0
B) .2
C) .8
D) .9
E) 1

Question 41

A certain product is comprised of two components:
X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What is the probability that this product will perform reliably for a year?

Question 42

The estimated service life of a part is normally distributed with a mean of 500 hours and a standard deviation of 40 hours.Determine the probability of failing in these intervals :
(i)before its mean life(ii)after 450 hours of operation(iii)between 540 hours and 600 hours

Question 43

A certain product is comprised of two components:
X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What would be the reliability of this product if both components were redundant?

Question 44

A cathode ray tube has a mean time between failures of 80 weeks.Determine these probabilities:
(i)The unit will not last 64 weeks.
(ii)The unit will last for at least 88 weeks.
(iii)Neither of the choices occurs.

Question 45

The average time between failures for a solenoid is 36 months.Determine the following probabilities:
(i)probability of failure before 36 months(ii)the probability that a system which is composed of two such solenoids will fail within 36 months if both must work for the system to work

Question 46

A certain product is comprised of two components:
X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What is the probability that this product will fail within eight years?
Nine years?
Six years?

Question 47

A certain product is comprised of two components:
X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What is the service life for this product which will provide a .5 probability of not failing within that amount of time?
A .6915 probability?
A .8413 probability?
A .9332 probability?

Question 48

A certain product is comprised of two components:
X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What is the probability that component Y will fail during a year of operation?

Question 49

A computer has three main modules which have individual reliabilities of .80,.90,and .90.Because of recent failures,management is now considering adding redundancy.Determine the reliability of the system with backups under these conditions:
(i)Each module has a backup with reliability equal to its own and a backup switch with a reliability of 1.00.
(ii)The backup consists of an identical computer which operates as a whole rather than backing up individual sections.The single switch for the backup computer has a reliability of .96.

Question 50

A certain product is comprised of two components:
X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What is the probability that component Y will perform reliably for a year?

Question 51

A certain product is comprised of two components:
X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What would be the reliability of this product if component X were backed up with an identical component?

Question 52

A certain product is comprised of two components:
X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What is the probability that component X will perform reliably for a year?

Question 53

A certain product is comprised of two components:
X and Y.Component X has a random failure rate of one in every ten years,while component Y's random failure rate is one in every five years.This product has a mean time to wear-out of eight years with a standard deviation of one year.What would be the reliability of this product if component Y were backed up with an identical component?

Question 54

The useful life of a certain valve at a pumping station is normally distributed with a mean of 48 months and a standard deviation of five months.Determine these probabilities:
(i)The valve will fail within 44 months of its installation.(ii)The valve will last at least 40 months,before failing.

Question 55

A life monitoring system can operate an average of 15 months between failures.Determine these probabilities:
(i)a failure within 12 months of the previous failure
(ii)a failure between 12 and 18 months after the previous failure

Question 56

A component of a research instrument has a probability of .98 of operating.It has a backup component that has a probability of .95 of operating.The instrument will function if either component operates.Determine the overall reliability of this subsystem under these conditions:
(i)The backup and the main component are connected by a switch which is certain to function should the main component fail.
(ii)The switch to the backup has a probability of .99 of operating.