Ford's answers to the NHTSA 6.7 Investigation

NewsW wrote:

Weibull wrote:

I didn't assume the normal distribution. I plotted the failure data and matched it to the distribution with the best fit using a regression calculation.

When you do a linear regression, you are assuming a normal distribution.

While this is true for a normal x and y axis, Weibull probability paper does not have a normal x or y axis. Of course, we use software now but back in the day, failure data would be plotted on say three types of paper Normal, Lognormal, and Weibull. All probability papers have scales that transform the cumulative probability distribution into a linear scale. When you plot out the failures on the different paper types, if they produce a straight line on one of them, that supports the supposition that the distribution is appropriate.

Again, I use software to match distributions but I have used the paper before. For using linear regression to match a Weibull distribution the x axis advances in natural logarithms and the y axis advances in the following manner ln(ln(1/(1-F(x)))).

Here is a picture of old school Weibull probability paper. The beta slope and eta shape parameter can be read directly off the paper when the failure mileages with the median ranks are plotted. Also included, what software spits out.