We illustrate how to use JMP with the aircraft component data found in
"Tables for obtaining confidence bounds and tolerance bounds based on best linear invariant estimates of parameters of the extreme value distribution." Mann, N. R. and Fertig, K. W. (1973) Technometrics, 15, 87-101.
Import into JMP the aircraft component data:
(Instructions for importing a text file into JMP)
The JMP data table should look as follows:
Notice that a zero code value means that the time was a failure time and that a 1 code value means that the time was a removal time.
The easiest way to get MLEs is doing an exponential plot and them going to the triangle menu:
Theta is the mean of the exponential so the MLE of the hazard rate lambda is 1/2.305 = 0.434. Also a confidence interval for lambda can be obtained by taking reciprocals from the confidence interval for Theta:
.217 = 1/4.60 < lambda < 1/1.314 = 0.761
We now use JMP's Nonlinear Fit platform to calculate the MLE for lambda:
First, we use JMP's calculator to define the loss column:
We define the parameter lambda:
Note that we use 1 as an initial value for lambda. We program the loss column as follows:
We now go to the Nonlinear Fit platform:
Notice that we checked "Loss is -LogLikelihood." We hit Reset and Go:
We hit Confid Limits:
