what\'s the answer for B and C thanks One of the industrial robots designed by a

Question

what's the answer for B and C

thanks

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 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).

Explanation / Answer

if p1 and p2 be the reliability of tow components in parallel

reliability of system =

1- (1-p1)(1-p2)

now

B) here p1 = p2 = p

1 - (1 -p)^2

reliability of complete system

= (1 - (1 -p)^2 ) p1 * p2   

here p ,p1 and p2 can be from 0.8,0.85,0.95

we can check by putting 3 different values of p to get that

we always to backup the component with lowest reliability

hence to maximize we have to put

p = 0.8

c) here p2 = 0.99 , p1 = p

1 - (1 -p1)(1-p2) = 1 - 0.01*(1- p)

= 1 + 0.01p -0.01

=0.99 + 0.01 p

so

Z = (0.99 + 0.01 p) *p1 *p2

if p = 0. 8

(0.99 + 0.01 *0.8) *0.85*0.95 = 0.805885

p = 0.85

(0.99 + 0.01 *0.85) *0.8*0.95 = 0.75886

p = 0.95

(0.99 + 0.01 *0.95) *0.85*0.8 = 0.67966

hence p = 0.8 should be back up

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