Question

One of your suppliers has belatedly realised that about 10% of the batches of a particular component recently supplied to you have a manufacturing fault that has reduced their reliability. There is no external or visual means of identifying thes substandard components. Battch identity has, however been maintained, so your problem is to sort batches that have this fault('bad batches') from the rest ('good batches'). An accelerated test has been devised such that components from good batches have a faliure probability of 0.02, whereas those from bad batches have a faliure probability of 0.2. A sampling plan has been devised as follows:

1. Take a random sample of 25 items from each unknown batch, and subject them to the test.

2. If there are 0 or 1 failed components ddecide that a batch is a good one

3. If there are 2 or more faliures decide that the batch is a bad one

There are risks in this procedure. In particular, there are (i) the risk of dciding that a good batch is bad; and (ii) the risk od deciding that a bbad batch is good. Use Bayes' theorem and your aanswers to questions 2 and 3 to evaluete these risks.

Answer 1

lets take a sample of 25 and 25 from two unknown batches

sample size=50

lnow 10% of components have manufacturing faults therefore for 50 -> 50*10/100 =5

it is more than 2 therefore this batch of 50 components is bad.

yes, there is risk .on an average there are 10% faulty components

so, if we take total 10 components to test from bayes theorem we can conclude that only 1 component is failed and the batch is a good one but that is not necessarily the case.any no. of 10 components can be faulty.

similarly if we take 30 components according to bayes 3 will be faulty components and its a bad sample but this is not necessarily true. any no. of components may be bad 0,1,2..... baye's theorem can not decide the good and bad samples.