How to calculate confidence limits in bernoulli trials with only one outcome.

[azira]

I have this problem that I have been trying to figure out all week and can't seem to get.

I have a process that produces one of two outcomes "OK" (in some unknown porportion: p) or "NOT OK" (in porportion q = 1-p). Let's say I ran the process [x] times (like 20) in a row and it reported "OK" each time. How can I calculated a 1-sided (or 2-sided) 95% confidence interval for the value of p?

I think I should be assigning a value of "1" to "OK" and "0" to "NOT OK" and then applying the conventional confidence interval calculations using the t-distribution. The problem I run into is that all I observe are "OK" then my std deviation goes to 0 and the whole thing falls apart.

Is there another method? What am I missing?

Thanks, much appreciated.

 

[azira]

After more searching on this forum, I found a reference to something called the adjusted/modified wald method and the LaPlace method. It seems like those are good candidates to apply to this problem.