A bug in Weibull 6

[Stephane Forster]

I have tested the evaluation version of Weibull6++, and in the exemple given page 48 in the training guide, there is a problem.
The exemple is the following: the data are interval censored time t=[ ] with pdf f and cdf F:

t=[0 6.12] f=5 F=5
t=[6.12 19.92] f=16 F=21
t=[19.92 29.64] f=12 F=33 ...

When I selected the Kaplan Meier estimation method, the probability plot shows for the interval [6.12 19.92] the probability 3% instead of 12.5%.
I think this is a "bug" of the software because when I selected the Median Rank method, the probability plot shows the good value (12.5%).
I have tested the same example with the SAS software, with the KM estimation, and it gives for [6.12 19.92] the probability of 12.5%.

What do you think about these results?

[Discussion Moderator (Moderator)]

The difference between the Kaplan-Meier and median rank methods is somewhat academic in this example; it is not indicative of a "bug" in the software.

When using probability plotting or rank regression to estimate failure distribution parameters, a method is needed to assign unreliability estimates to the failure times. In other words, we have x-axis values in our failure times, but in order to generate a 2-D plot, we need matching y-axis values for our x-axis failure times. Kaplan-Meier and median ranks are the two methods available in Weibull++ for this unreliability estimation.

However, this example uses maximum likelihood estimation (MLE) techniques to determine the failure distribution parameter estimates. Maximum likelihood only uses the failure and suspension times in the calculations; the unreliability estimates are entirely immaterial. This is why you get the same results for MLE, regardless of whether Kaplan-Meier or median ranks is selected.

There will, however, be a difference in the probability plot due to the fact that the two methods estimate the unreliability in two different ways. This difference is only apparent in the probability plot, as there has to be SOME value for the unreliabilities in order to generate the plot. However, all other results will be based on the MLE results (represented by the solid regression line through the points), not the plotting results (unless you are trying to read your reliability results directly off the plot, which is generally not a good idea). Results for this example in the QCP or for a reliability plot will be consistent regardless of whether the user selects Kaplan-Meier or median ranks.