Why is Confidence Level

Why is confidence level so important in engineering test data analysis?

From the name itself it gives us a very good hint; Confidence level is giving the confidence in data analysis. In the next graph, you can find 10 samples and fitted Weibull 2p distribution with 95% of Confidence level:

From the graph if we are traveling on B10 or R90 line, from fitted line we can predict, that the based on the 10 samples, 90% of population will pass 6.2*10^3 hours, this is the R90C50 value. Lower boundaries predict the 4.7*10^3 hours and upper confidence boundary 8.4*10^3 hours.

So in case of question, having the data of 10 samples, what is my R90C95 ?

And the answer, 90% of population with confidence level of 95% will pass 4.7*10^3 hours.

Confidence level come into the game to cover the limited sample size engineers can get they hands for testing, in the next graphs you can see how the confidence level changing with the sample size:

It is very clear shown, that as sample size increase, the confidence boundaries get closer to the fitted plot line.

So it is telling us, more sample size in test will predict better time to failure, and as sample size very small, the confidence boundaries can be very large, that need to be taking in account when interpreted the fitted line from the test.

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