Rank Regression
Rank regression is a method of fitting a line (or curve) to data. To fit a statistical model to a life data set, estimates are made for the parameters of the life distribution that will make the function most closely fit the data. The parameters control the scale, shape and location of the pdf function. For example, in the three-parameter Weibull distribution:
• The slope parameter, β, defines the shape of the distribution.
• The scale parameter, η, defines where the bulk of the distribution lies.
• The location parameter, t0, defines the location of the distribution in time.
In almost all cases, the best estimation method is median rank regression, which estimates the Weibull parameters β and η using the method of least squares to best fit a straight line through the failure times and median ranks graphed on the Weibull probability plot. Once you have gathered good life data for a single, well-defined failure mode, Weibull software generates the Weibull probability plot by:
1. Ranking the times of both failures and suspensions from the earliest occurrence to the last occurrence. (Although suspensions are not weighted as much as failures, they must be included in the data set.)
2. Calculating the adjusted ranks for the failures. (Suspensions are not plotted.)
3. Converting the adjusted ranks to median ranks using Benard’s approximation.
4. Converting median ranks to percentages for graphing on Weibull probability plots.
5. Plotting the failure times on the X-axis and the median ranks on the Y-axis.
6. Displaying confidence bounds if confidence parameters are specified.
7. Estimating the characteristic life by reading the B-63.2 life from the Weibull probability plot.
8. Estimating the slope as the ratio of the rise.
Median rank regression seems to be the most accurate parameter estimation method for samples that contain fewer than 100 failures.