1. ## Probability question

An Mechanical part has an average life expectancy of 10,500 hours of operation. A Six Sigma team has incorporated some design changes to improve the life. Five units survive to 11,000 hours. What is the probability that all five would have survived that long?

2. ## Re: Probability question

Is there more information for this problem, say standard deviation or sample size?

3. ## Re: Probability question

I would guess that the life expectancy can be modeled by the exponential distribution. If this is the case: the sum of independently distributed exponential variables follows a gamma distribution. You should be able to forthgo from here

4. ## Re: Probability question

Although I don't think the sum of five exponentials is what we would want. From the question it isn't perfectly clear to me if they mean that 1) out of the five parts the first one that died did so at 11,000 hours or 2) Out of the five parts at 11,000 hours they were all dead.

My guess is that the first interpretation is correct.

This requires finding the distribution of the min (or max) of independent exponentials which isn't actually that bad to do.

5. ## Re: Probability question

I interpret the question as: Find the probability that all parts function for at least 11000 hours, given that each part has expected lifetime equal to 10500. Or this is at least what I think they mean. In reality the question is impossible to answer because of the following statement "A Six Sigma team has incorporated some design changes to improve the life". We do not know the new life expectancy! Heck, we don't even know the probability distribution function at all which makes the problem even more difficult :/

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