4.16 Reliability of a manufacturing network. Refer to the Jour- nal of Systems S

Question

4.16 Reliability of a manufacturing network. Refer to the Jour- nal of Systems Sciences & Systems Engineering (March, 2013) study of the reliability of a manufacturing system that involves multiple production lines, Exercise 4.6 (p. 139). Consider, again, the network for producing inte- grated circuit (IC) cards with two production lines set up in sequence. The probability distribution of the maximum capacity level of each line is reproduced below. a. Find the mean maximum capacity for each line. Inter- pret the results practically. b. Find the standard deviation of the maximum capacity for each line. Interpret the results practically. Line Maximum Capacity, y 0 12 24 36 0 35 70 p(y .01 .02 .02 .95 002 002 .996

Explanation / Answer

for line 1)

for line 2)

from above

a) mean for line 1 =34.92

and mean for line 2 =69.79

above mean being a fraction can not represent maximum capacity but repesent average value for a large number of observations to measure expected value of maximum capacity.

b) std deviation for line 1 =5.1180

std deviation for line 2 =3.4937

std deviation represent expected variation in mean capacity due to intrinsic randomness of process/

x p(x) xP(x) x2P(X) (x-)2 (x-)2P(x) 0 0.0100 0.000 0.000 1219.406 12.194 12 0.0200 0.240 2.880 525.326 10.507 24 0.0200 0.480 11.520 119.246 2.385 36 0.9500 34.200 1231.200 1.166 1.108 total 1 34.92 1245.600 1865.146 2= 26.1936 std deviation=     =    2 = 5.1180

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