Acceptance-sampling scheme
Consider an acceptance-sampling scheme in which a factory takes delivery of a batch of components if a random sample of 400 components contains fewer than M defectives. Otherwise the batch is returned tot he supplier. Suppose the factory manager wants to set M so that there is no more than a 10% risk of accepting a batch that has 5% or more defectives. Let P be the sample proportion of defectives. (In the following, use the approximate Normal distribution for P).
a) Suppose that the batch has 5% defectives. What is the value of c for which pr(p>c)=0.10? What value should M have?
b) Suppose the supplier makes a batch in which the true proportion of defectives is only 2%. If the cutoff in (a) is adopted, what is the probability that the batch will be sent back?
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Consider an acceptance-sampling scheme in which a factory takes delivery of a batch of components if a random sample of 400 components contains fewer than M defectives. Otherwise the batch is returned to the supplier. Suppose the factory manager wants to set M so that there is no more than a 10% risk of accepting a batch that has 5% or more defectives. Let P be the sample proportion of defectives. (In the following, use the approximate Normal distribution for P).
a) Suppose that the batch has 5% defectives. What is the value of c for which pr(p> c)=0.10? What value should M have?
p= 5%
q=1-p= 95%
n= 400 (sample size)
s=square root of pq/n= 0.0109 (standard error of proportion)
alpha (a) = 10%
Assuming normal distribution,z value for alpha (a) = 10% is = 1.28155
Acceptance limit (c<p+z*s)
c= 6.40% =0.05+1.28155*0.0109
M=c*n= 25.6 =0r rounded down to 25
b) Suppose the supplier makes a batch in which the true proportion of defectives is only 2%. If the cutoff in (a) is adopted, what is the probability that the batch will be sent back?
c= 6.40%
p= 2%
q=1-p= 98%
n= 400 (sample size)
s=square root of pq/n= 0.007
z=(c-p)/s= 6.285714
Probability value corresponding to z = 6.285714 is = 0.00000002%
Almost zero probability that the batch will be sent back
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