Reference no: EM13743450
1. One of the industrial robots designed by a leading producer of servomechanisms has three major components. Components' reliabilities are 80, 85, and 95%. All of the components must function in order for the robot to operate effectively.
a. Compute the reliability of the robot.
b. Designers want to improve the reliability by adding a backup component. Due to space limitations, only one backup can be added. The backup for any component will have the same reliability as the unit for which it is the backup. Which component should get the backup in order to achieve the highest reliability? Show proof of your answer by computing the overall reliabilities of the three options (assume 100% reliable backup switch)
c. If one backup with a reliability of 99% can be added to any of the main components, which component should get it to obtain the highest overall reliability? Show proof of your choice by computing the overall reliabilities of the three options (assume a backup switch with 100% reliability).
2. Lucky Lumen light bulbs have an expected life that is exponentially distributed with a mean of 20,000 hours. Determine the probability that one of these light bulbs will last:
a. At least 24,000 hours
b. No longer than 4,000 hous
c. Between 4,000 and 24,000 hours
3. An office manager has received a report from a consultant that includes a section on equipment replacement. The report indicates that scanners have a service life that is normally distributed with a mean of 41 months and a standard deviation of 4 months.
On the basis of this information, determine the percentage of scanners that can be expected to fail in the following time periods.
a. Before 38 months of service.
b. Between 40 and 45 months of service.
c. Within +/- 2 months of service.
d. If the manufacturer of the scanner offers a service contracts of 3 years on these scanners, what percentage of scanners can be expected to fail from wear-out during the service period?
e. If the cost of replacement each scanner is $250, and if 1,000 units of this scanner are sold, what is the expected warranty replacement cost to the manufacturer.
4. How high must reliability be? Prime business customers expect public carrier-class communications data links to be available 99.999 percent of the time. The so-called five nines rule implies only 5 minutes of downtime per year. Such high reliability is needed not only in telecommunications but also for mission-critical systems such as airline reservation systems or banking fund transfers.
Suppose a certain network web server is up only 90 percent of the time (i.e. its probability of being down is 0.10). How many independent servers are needed to ensure that the system is up at least 99.999 percent of the time?
Show your work and explain your answer.
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