QUESTION S 120 MARKS World Elec tronic produces computerized sewing machines. Th

Question

QUESTION S 120 MARKS World Elec tronic produces computerized sewing machines. The sewing machine is made of 3 namely A, B and CThe sewing machine will operate successfully if all the subsystems subsystems work . Subsystem A works if Transistor X or Y works. . Subsystem B works if Module Q and Module R works. . Subsystem C works if Chip 1 and 2 work or Chip 3 and 4 work The success rate of the Transistor X, Y, and Module Q, R is 0.85. The success rate of the Chip 1, 2, 3 and 4 is 0.8. (a) Sketch a block diagram and calculate the probability a computerized sewing machine operates successfully. 110 marks The management of World electronics has decided to improve the success rate of the computerized sewing machine by 10%. Decision was made to replace Chip 1, 2, 3 and 4 with Chip A which has a higher success rate. Same Transistor X, Y and Module Q, R to be used. As the Design Engineer of the sewing machine, suggest the minimunm (b) 110 marks success rate that Chip A must have to achieve the target.

Explanation / Answer

a) P( subsystem A works ) = 1- (X and Y both dont work) = 1-(0.15)*(0.15) = 0.9775

P(subsystem B works) = P( both Q and R work) = 0.85*0.85=0.7225

P(subsystemC works ) = 1-P(chip 1 and 2 dont work and chip 3 and 4 don't work) = 1-(1-(0.8)^2 )^2 = 0.8704

P( sewing machin works) = 0.9775*0.7225*0.8704=0.6147

For success to be increased by 10% , we have subsystem A and B remaining same

0.8704* 1.1 =1- (1-(x)^2)^2

(1-x)^2)^2 = 1-0.8704*1.1= 0.04256

1-x^2 = sqrt(0.04256) =0.2164

(x^2) = ( 0.7936)

x = 0.89

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