Here we show how to do a log-normal regression for the insulating fluid accelerated life test data using the Nonlinear Fit platform of JMP. (We have also done this problem using JMP's Survival platform.) We omit the 32 KV voltage level because the sigma parameter for this level is very different from that at all other levels.
We create three new columns in the JMP data table:
Column x is defined by
Column ModelLN is defined as follows:
Column LossLN is defined as follows:
Using JMP's Nonlinear plaform as follows:
Notice that we have the same values for the parameter estimates as those obtained with JMP's Survival platform:
Notice, however, that JMP's Survival platform is able to obtains confidence intervals for the parameters while the Nonlinear Fit platform failed to converge.
The results obtained with JMP's Nonlinear Fit platform are useful because with them one can calculate the variance-covariance matrix of the parameters.
This variancecovariance matrix is necessary if we are to use the Delta Method to calculate the standard errors of quantities of engineering interest such as:
