Question

5. MRC is an engine company that builds the engines for GCF cars. GCF is using a control policy of inspection 10% of incoming lots and rejects lots with a fraction defect greater than 5%.

(a) Use binomial formula to find the probability of accepting the following lots: a lot size of 300 of which 5 are defective. (10 points)

(b) Suppose all discovered defective items are replaced with good ones. Compute the Average Outgoing Quality (AOQ).

Answer 1

5)

(a)

It is given that the sample taken for inspection will be 10% of the entire lot size. The lot size given is 300. So, the sample size is 30.

Acceptance criteria is < = 5%

Thus the accpetance number is 30*0.05 = 1.5

p = probability of having the defect = 5/300 = 0.0167

q = probability of having no defect = 1 - p = 0.983

P(X < = 1.5) = P(X=0)+P(X=1) =0.983³⁰ +³⁰C₁ * 0.0167¹ * 0.983²⁹ = 0.911

So, probability of acceptance = 91.1%

(b)

We apply the following formulation:

AOQ = Pd*Pa*(N - n) / N

Where Pd = % defectives of lot as received = 500/300 = 1.667%

Pa = Probability of acceptance = 91.1%

N = 300

n = 30

So, AOQ = 0.1667*0.911*270 / 300 = 0.1367 = 13.67%