Question

1. A machine produces parts that are either good (85%), slightly defective (7%), or obviously defective (8%). Produced parts get passed through an automatic inspection machine, which is able to detect any part that is obviously defective and discard it. What is the quality of the parts that make it through the inspection machine and get shipped?
2. Let assume that a one-year warranty is given for the parts that are shipped to customers. Suppose that a good part fails within the first year with probability 0.01, while a slightly defective part fails within the first year with probability 0.15. What is the probability that a customer receives a part that fails within the first-year and therefore is entitled to a warranty replacement?
a warranty replacement?

Answer 1

Question 1

Here,

P(Good) = 0.85

P(slightly defective) = 0.07

P(Obviously defective) = 0.08

so now obviously defective is discarded so, for remaining shipped parts

P(Good parts shipped) = 0.85/(0.85 + 0.07) = 0.924 or 92.4%

P(Slightly defective part shipped) = 0.07/(0.85 + 0.07) = 0.076 or 7.6%

Questtion 2

Now here given is

P(Good part fails within first year) = 0.01

P(Slightly defective part fails withing first year) = 0.15

P(A part fails within one year) = 0.01 * 0.924 + 0.15 * 0.076 = 0.0207 or 2.07%