Assuming we want to show that we have 80% confidence (right axis) that we'll succeed 80% of the time (left axis, also called reliability), I connect those values on each side with a straight edge and the chart shows that with zero failures (upper right boundary) we need 7 trials. If we have one failure (upper left boundary) the chart shows that we need 12 trials (11 successes). I was provided a formula that defines the zero failure curve [n=Log (1-confidence)/Log (reliability)]...What I need is a more generic equation or excel function that will generate these curves with failures not equal to zero.

Any statistics experts out there that can help me?

Thanks