1.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?

0.889

0.91

0.504

0.3

0.7

2.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?

5.67 years

9 years

6.33 years

7 years

5 years

3.The Ready Light 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 Ready Light with the on-off switch for this flashlight. These switches, on average, wear out 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 wearing out?

46 hours

50 hours

54 hours

45 hours

43 hours

4.An undergraduate business student has purchased a laptop computer for use during exams. This laptop 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 wear out 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, fully charged battery with him, what is the probability that the laptop will perform reliably during a one-hour exam?

0.9975

0.987525

0.99

0.9450

0.89775

5.Question 6: (2 points)

The Ready Light 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)?

0.7280

0.8736

0.9100

0.9600

0.6720

6.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?

0.75

0.48

0.72

0.60

0.96

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?

0.889

0.91

0.504

0.3

0.7

2.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?

5.67 years

9 years

6.33 years

7 years

5 years

3.The Ready Light 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 Ready Light with the on-off switch for this flashlight. These switches, on average, wear out 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 wearing out?

46 hours

50 hours

54 hours

45 hours

43 hours

4.An undergraduate business student has purchased a laptop computer for use during exams. This laptop 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 wear out 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, fully charged battery with him, what is the probability that the laptop will perform reliably during a one-hour exam?

0.9975

0.987525

0.99

0.9450

0.89775

5.Question 6: (2 points)

The Ready Light 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)?

0.7280

0.8736

0.9100

0.9600

0.6720

6.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?

0.75

0.48

0.72

0.60

0.96

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