# Using binary logistic regression to find design for very high reliability and confidence

A design has two predictor variables (both continuous). The response is pass/fail. I would like to know how to use Binary Logistic Regression to know what value of each variable will give me a failure rate of 0.000001 with 95% confidence.

With one predictor variable, it's clear - but not with two. I usually use Minitab, but I would be limited to holding one predictor variable constant while varying the other - this could be done, but is tedious (and isn't really what I want to do).

I also don't want to overdesign.

I don't know if this can be done in Excel or R, but that would be good to know.

In many ways, I'm looking for the creation of a surface, where the predictor variables are on the "x" and "y" axes, and the probability is on the "z" axis. I would want the lower 95th% confidence of this surface meeting a failure rate of 0.000001.

Any responses are much appreciated.

-
Unless you have an extraordinary amount of data, it's possible there will be no solution to this problem at all, because estimating a one-per-million rate is quite an extrapolation. Absent millions of data, you would need a region of intermediate values of the predictor variables where varying proportions of passes are observed, separating a region of all passes from another of all fails. You wouldn't be able to check for continued linearity of the response out in these regions, making the 95% confidence rather illusory. –  whuber Dec 16 '11 at 21:16
Even though this requirement is very demanding, I think that with enough margin - as you say - the requirement could be shown. –  Jay Greenstein Dec 16 '11 at 21:46
This perhaps makes my point more clearly, then: stats.stackexchange.com/a/4968. –  whuber Dec 17 '11 at 22:37