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## How to calculate confidence interval for predicted failure rate

This is a very basic statistics question, which also leads in to a "how do I do it in JMP" question.

Imagine I have a component with a predicted defect rate of 0.5%. I build 500 systems which each use N of these components. The components are chosen at random and independently of each other. I can test for the defect at system level.

To my simple mind, if N=2 the probability of a system being good is 0.995^2 = 99.0025%, which means I should expect five systems out of 500 to fail test. If N=3, then this would change to 0.995^3*500 = 8 systems out of 500. This is just the binomial distribution.

Is this reasoning correct? If so, can I use JMP to calculate a confidence interval around this number, and is this even a meaningful question? What additional information do I need (e.g an estimate of the variation of the defect rate) for this?

Any suggestions or pointers to useful sections of the documentation would be much appreciated!

Many thanks!

2 REPLIES 2
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## Re: How to calculate confidence interval for predicted failure rate

JMP documentation is primarily about JMP, not statistics. There are many good sources about statistics. Please see this article. Yes, the basis for such a problem with the stated assumptions is the binomial distribution model. The model has two parameters, the probability of success and the number of trials. The confidence interval is the estimate of the probability parameter. If you know the parameter, then there is no interval. If you estimate the parameter, then there is a parameter. You could use the interval instead of the point estimate to calculate the range of the number of successes for a given number of trials.

Learn it once, use it forever!
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