The mean diameter of a part is 28 mm with a variance of 16 mm^2. a) If the speci

Question

The mean diameter of a part is 28 mm with a variance of 16 mm^2. a) If the specifications are 30 mm plusminus 4 mm, and the process output is normally distributed, estimate the fraction of nonconforming (percent out of specification). b) Assume you have to throw away all parts out of specification. In a batch of 5,000 parts, how many parts will you throw away. c) If they cost $5 to make, what is the expected value of the throw away. As the engineer, what would be your focus for improvement? e) What diameter represents 75% of the distribution? f) What is the probability of a part would have a diameter of exactly 27.15 mm?

Explanation / Answer

here a)for non conforming is hould be >34 and <26

hene probabilty of non conforming =1- P(26<X<34)=1-P(-0.5<Z<1.5) =1-(0.9332-0.3085)=0.3753

b)expected parts thrown away =np=5000*0.3753 =1876.72

c) cost =1876.72*5 =9383.62

d)focus should be to reduce variance of process and shift mean to 30

e)for 75%, z=0.6745

hence corresponding value =mean +z*std deviation =30.698

f)P(X=27.15)=0; as point probability of continuous distribution is 0

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