Let's say I have all parameters of my Weibull(or normal) distribution. How can I calculate the reliability for a given point within a certain confidence interval? For example, what is the reliability of a device with 99% confidence if we have its Weibull distribution? I assume reliability is the same as probability. Correct me if I am wrong. Thank you
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by definition reliability R(t) = 1 - F(t).
F(t) = 1 - exp(-(t/tau)^beta) for the Weibull model
the confidence intervals come from not knowing tau and beta exactly, but with estimates which themselves have confidence intervals.
Do you know the confidence intervals on your modeled tau and beta estimates?
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$\begingroup$ Thank you. I have alpha, betta and Gamma parameters from my sample distribution. I have sigma and mu for normal distribution as well. what is tau here?Would you provide a link or reference too? $\endgroup$– SilasCommented Nov 16, 2016 at 19:50
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$\begingroup$ I have Weibull with three parameters.But let's say I have it with two parameters. $\endgroup$– SilasCommented Nov 16, 2016 at 20:19
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$\begingroup$ For the confidence Interval, I am not sure but what I want is for example to be 95% confident that with 99% reliability my device will not fail under a standardized force. $\endgroup$– SilasCommented Nov 16, 2016 at 20:29
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$\begingroup$ you need confidence intervals on these estimates in order to obtain confidence intervals on reliability prediction $\endgroup$– user137329Commented Nov 17, 2016 at 16:41
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$\begingroup$ would you explain more? what I understand from your sentence is that I should have two numbers for confidence intervals one for the estimates and one for the reliability which is calculated from the previous one. Am I right? Let 's say I want to be 95% confident that my reliability is 99.0%. What should I do in that case? $\endgroup$– SilasCommented Nov 17, 2016 at 17:16