Order reliability discussion questions

Order reliability discussion questions
Define the term reliability.
2. Explain why a product or system might have an overall reliability that is low even though it is comprised of components that have fairly high reliabilities.
3. What is redundancy and how can it improve product design?
DISCUSSION AND
REVIEW QUESTIONS
PROBLEMS
1. Consider the following system:
.90 .90
Determine the probability that the system will operate under each of these conditions:
a. The system as shown.
b. Each system component has a backup with a probability of .90 and a switch that is 100 percent
reliable.
c. Backups with .90 probability and a switch that is 99 percent reliable.
2. A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts have a .96 probability of functioning, and
two have a probability of .99. What is the overall probability that the product will function properly?
3. A system consists of three identical components. In order for the system to perform as intended, all
of the components must perform. Each has the same probability of performance. If the system is
to have a .92 probability of performing, what is the minimum probability of performing needed by
each of the individual components?
4. A product engineer has developed the following equation for the cost of a system component:
C = (10P)
2
, where C is the cost in dollars and P is the probability that the component will operate as expected. The system is composed of two identical components, both of which must operate
for the system to operate. The engineer can spend $173 for the two components. To the nearest
two decimal places, what is the largest component probability that can be achieved?
5. The guidance system of a ship is controlled by a computer that has three major modules. In order
for the computer to function properly, all three modules must function. Two of the modules have
reliabilities of .97, and the other has a reliability of .99.
a. What is the reliability of the computer?
b. A backup computer identical to the one being used will be installed to improve overall reliability. Assuming the new computer automatically functions if the main one fails, determine the
resulting reliability.
c. If the backup computer must be activated by a switch in the event that the first computer fails,
and the switch has a reliability of .98, what is the overall reliability of the system? (Both the
switch and the backup computer must function in order for the backup to take over.)
6. One of the industrial robots designed by a leading producer of servomechanisms has four major
components. Components’ reliabilities are .98, .95, .94, and .90. 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?
c. If one backup with a reliability of .92 can be added to any one of the main components, which
component should get it to obtain the highest overall reliability?
7. A production line has three machines A, B, and C, with reliabilities of .99, .96, and .93, respectively. The machines are arranged so that if one breaks down, the others must shut down. Engineers
are weighing two alternative designs for increasing the line’s reliability. Plan 1 involves adding
an identical backup line, and plan 2 involves providing a backup for each machine. In either case,
three machines (A, B, and C) would be used with reliabilities equal to the original three.
a. Which plan will provide the higher reliability?
b. Explain why the two reliabilities are not the same.
c. What other factors might enter into the decision of which plan to adopt