One of the industrial robots designed by a leading producer of servomechanisms h
ID: 3201081 • Letter: O
Question
One of the industrial robots designed by a leading producer of servomechanisms has four major components. Components’ reliabilities are 0.98, 0.95, 0.94, and 0.90. All of the components must function in order for the robot to operate effectively.
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. Compute the reliability of the robot. (Round your answers to 4 decimal places.)
Which component should get the backup in order to achieve the highest reliability?
If one backup with a reliability of 0.92 can be added to any one of the main components, which component should get it to obtain the highest overall reliability?
One of the industrial robots designed by a leading producer of servomechanisms has four major components. Components’ reliabilities are 0.98, 0.95, 0.94, and 0.90. All of the components must function in order for the robot to operate effectively.
Explanation / Answer
a.) Reliability = All of the components must function in order for the robot to operate effectively
= 0.98 and 0.95 and 0.94 and 0.90
= 0.98*0.95*0.94*0.90 = 0.787626
b) When we use backups the reliability of the component changes to
reliability of the component + (reliability of the backup * probability of failure of component)
1.) Component 1: New reliability = (0.98 + (0.98 * (1-0.98))) = 0.9996
Reliability of the robot = 0.9996*0.95*0.94*0.90 = 0.8033
Component 2: New reliability = (0.95 + (0.95 * (1-0.95))) = 0.9975
Reliability of the robot = 0.98*0.9975*0.94*0.90 = 0.8270
Component 3: New reliability = (0.94 + (0.94 * (1-0.94))) = 0.9964
Reliability of the robot = 0.98*0.95*0.9964*0.90 = 0.8348
Component 4: New reliability = (0.90 + (0.90 * (1-0.90))) = 0.99
Reliability of the robot = 0.98*0.95*0.94*0.99 = 0.8663
2.) Component 4 should get backup
c.) Component 1: New reliability = (0.98 + (0.92 * (1-0.98))) = 0.9984
Reliability of the robot = 0.9984*0.95*0.94*0.90 = 0.8024
Component 2: New reliability = (0.95 + (0.92 * (1-0.95))) = 0.996
Reliability of the robot = 0.98*0.996*0.94*0.90 = 0.8257
Component 3: New reliability = (0.94 + (0.92 * (1-0.94))) = 0.9952
Reliability of the robot = 0.98*0.95*0.9952*0.90 = 0.8338
Component 4: New reliability = (0.90 + (0.92 * (1-0.90))) = 0.992
Reliability of the robot = 0.98*0.95*0.94*0.992 = 0.8681
"Component 4"
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