Question

You work in the quality check of a chip factory. Your boss claims, that the chips have to function error free for three years on average. Therefore you are planning, to inform your boss, if the average lifetime of a sample is less than 32 months. Since you do not want to disturb your boss for nothing, the probability for disturbing him, although the expected lifetime of the chips is three years, should be smaller than 1%.(i) Which distribution is a good choice for modelling the lifetime of the chips? Assume for the following questions, that the expected lifetime of the chips is 36 months and the variance is 362 months.What is the minimum sample size, if you use the central limit theorem for estimating the probability for disturbing the boss?Let the chip lifetime have the distribution of (i) with an expected value of three years. Simulate the average lifetime of 10 000 samples each having the size calculated in (ii). In how many of the 10 000 samples would you disturb the boss? Is the percentage less than 1 percent?

Answer 1

(i) Normal distribution is a good choice for modelling the lifetime of the chips

(ii) the minimum sample size is 30.

Here is the simulation results

In 5143 out of 10,000 samples he will disturb the boss. No the percentage is 51.43 not less than 1%.