10.14. You are quality manager for a company receiving large quantities of mater

Question

10.14. You are quality manager for a company receiving large quantities of materials from a supplier in lots of 1000. The cost of inspecting the lots is $0.76/unit. The cost that is incurred if bad material is introduced into your product is $15.20/unit. A sampling plan of 75 with acceptance number equal to two has been submitted to you by one of your engineers. In the past, lots submitted by the supplier have averaged 3.4% defective (a) Is a sampling plan economically justified? (b) Prepare an operating characteristic curve. (c) If you want to accept only lots of 4% defective or better, what do you think of the sampling plan submitted by the engineer? (d) Suppose that rejected lots are 100% inspected. If a supplier submits many defective lots, what will be the average outgoing quality of these lots?

Explanation / Answer

a) (a)Pb= I / A

= 0.76 / 15.20

= 0.05

As p = 0.034 and p < Pb, a sampling plan is justifiable.

c) p = 0.04,Pa = P(x=0) + P(x=1) + P(x=2)

  Use binomial distribution

P(x=0) = 0.96^75 = 0.04681

P(x=1) = 75*0.96^74*0.04 = 0.146283

P(x=2) = 75*74/2*0.96^73*0.04*0.04 = 0.225519

Pa = 0.418612

The plan is poor. Lots which are 4% defective, only have a Pa of 0.42.

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