Question

The ABC Transistor Corporation ships out transistors in lots of 12. 10% of all transistors produced are defective. ABC promises to repair any defectives which are shipped out. It also gives a money-back guarantee to customers is a lot has more than 2 defectives. The cost of ABC to repair a transistor is $10.00. The money-back guarantee costs ABC $30.00 in addition to repair costs.

1. Computer the probability that a lot of transistors will have more than 2 defectives.

2. For every lot which is shipped out, what is the expected cost to ABC resulting from defective production of transistors?

3. By major rehaul of the production process, the defective rate can be reduced to 5%. The cost of carrying this out, based on debt amortization, is $200,000 per annum. ABC cells approximately 100,000 lots (dozens) of transistors per year. Should ABC reduce the defective rate?

4. What other considerations aside from the monetary cost of defective production of transistors, should be taken into account in ABC's decision of whether or not to reduce the defective rate?

Answer 1

The the number of defective transistors in lot of size follows Binomial distribution with
The PMF of is  ,

1)  The probability that a lot of transistors will have more than 2 defectives is

2)The cost of ABC to repair a transistor is $10.00. The money-back guarantee costs ABC $30.00 in addition to repair costs.

The expected cost is sum of expected repair cost + $30 if defectives are more than 2.

Expected repair cost is

The expected cost to ABC resulting from defective production of transistors is

3) As in part (2) The expected cost to ABC resulting from defective production of transistors with is

The savings in annual  cost is .

Saving for 100,000 lots (dozens) of transistors per year is

Which is more than $200,000 per annum so ABC reduce the defective rate.

4) The ABC should make sure that the rate of defectives across the lots remain constant so we can apply binomial model.