1. Engineering
  2. Mechanical Engineering
  3. one of your suppliers has belatedly realised that about 10...

Question: one of your suppliers has belatedly realised that about 10...

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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 O 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 (i) 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.

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