# Estimate of failure rate given large sample size run for period of time

#### yelkenli5

##### New Member
Can anyone recommend the correct calculation to estimate the upper limit of a failure rate given zero to x number of failures in a sample of 200 units, run for some period of time, several weeks. For test planning purposes, I am interested in what that time period needs to be. The number of units in the sample is fixed. I looked at some resources discussing multiplying the observed failure rate by the chi square critical value for 2x the sample size, divided by 2x the sample size, but the chi square tables that I find do not go that high and I read some discussion that it is not applicable to large sample sizes (I think here, I might be mixing the applications).

#### katxt

##### Well-Known Member
estimate the upper limit of a failure rate
It's not clear (to me) what you want. After any number of samples and observing the total number of failures, you can make a confidence interval for the failure rate which lets you say something like "I'm 95% confident that the failure rate is between X% and Y%."

#### yelkenli5

##### New Member
That is what I understand, but for 200 samples, what calculation for the confidence value, and can I use that to back out a desired amount of run-time for a desired confidence. I found one discussing using the chi square, but my sample size is large. Thanks!

#### katxt

##### Well-Known Member
For large samples there is a good normal approximation to chi square you can use, N(df, sqrt(2xdf))
Perhaps you are looking for a sample size that will estimate the failure rate to a chosen accuracy. Eg, how many samples needed to estimate the failure rate to within 10% of its true value. This will depend on the failure rate as well as the sample size.