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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.
a. Compute the reliability of the robot. (Round your answer to 4 decimal places.)
Reliability :
b1. 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.)
Component 1 :
Component 2:
Component 3 :
Component 4 :
b2.
Which component should get the backup in order to achieve the highest reliability?
Component 2:
Component 1:
Component 4:
Component 3:
c. 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? Component 3
Component 4
Component 1
Component 2
Expert Answer
b)Component 1:
Step 1: .98+(1-.98)(.98)=.9996
Step 2: .9996 * .96* .94 * .90 = .8118 (rounded to 4 decimals)
Component 2:
Step 1: .96+(1-.96)(.96)=.9984
Step 2: .9984 * .98* .94 * .90 = .8278 (rounded to 4 decimals)
Component 3:
Step 1: .94+(1-.94)(.94)=.9964
Step 2: .9964 * .98* .96 * .90 = .8437 (rounded to 4 decimals)
Component 4:
Step 1: .90+(1-.90)(.90)=.99
Step 2: .99 * .98* .96 * .94 = .8755 (rounded to 4 decimals)
c) The least reliable is 90%. So, a 90% component will have 10% failure rate. So, combined to two 0.1* 0.1 = 0.01 = 1% failure. Which means, 99% reliable.
0.98*0.95*0.94*0.99 = 0.866 = 86.6% reliable.
d) One backup with reliability of 0.92 gives –
0.90 * (1 – 0.90 ) * 0.92 = 0.9920 = 99.2%
Therefore, with backup in place, component 4 with backup has reliability of 0.9920
The new robot reliability is = 0.98 * 0.95 * 0.94 * 0.9920 = 0.8681
