How to calculate reliability within a confidence level from a weibull or normal distribution?

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

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?

• 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? – Silas Nov 16 '16 at 19:50
• I have Weibull with three parameters.But let's say I have it with two parameters. – Silas Nov 16 '16 at 20:19
• 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. – Silas Nov 16 '16 at 20:29
• you need confidence intervals on these estimates in order to obtain confidence intervals on reliability prediction – user137329 Nov 17 '16 at 16:41
• 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? – Silas Nov 17 '16 at 17:16