A manufacturing process produces thousands of semiconductor chips per day. On th

Question

A manufacturing process produces thousands of semiconductor chips per day. On the average, 20% of these chips do not conform to specifications. Every hour, an inspector selects a random sample of 25 chips and classifies each chip in the sample as conforming or nonconforming (a) what is the probability of finding exactly 4 chips nonconforming (2 points) (b) What is the probability of finding at least 6 chips nonconforming (2 points) (c) What is the average and variation of number of chips that will be defective (2 points) (d) Suppose we were to plot the process on an np chart, what would be the centerline and control limits of the chart (4 points)

Explanation / Answer

a) This is a binomial distirbuiton.

n=25,p=0.2, x=4

Using BINOM.DIST(4,25,0.2,false) in excel, we get 0.1866.

b) P(x>=6)=1-P(x<5)

P(x>=6)=1-P(x<5)=1-0.616689=0.383311

c) average=np=25*0.2=5

V(x)=npq=25*0.2*0.8=4

d) centerline=np=5

UCL=np+3*sqrt(npq)=11

LCL=np-3*sqrt(npq)=-1=0

x p(x) 0 0.003778 1 0.023612 2 0.070835 3 0.135768 4 0.186681 5 0.196015 0.616689

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