Quality and Reliability Methods - SAS

Chapter 20 Reliability and Survival Analysis II 403
Nonlinear Parametric Survival Models
The lognormal loss function can be very sensitive to starting values for its parameters. Because the
lognormal is similar to the normal distribution, you can create a new variable that is the log 10 of Time and
use Distribution to find the mean and standard deviation of this column. Then, use those values as starting
values for the Nonlinear platform. In this example the mean of log 10 of Time is 2.05 and the standard
deviation is 0.15.
Run this example as described in the previous examples. Assign lognormal as the Loss function. In the
Nonlinear Fit Control Panel give Mu and Sigma the starting values 2.05 and 0.15 and click Go. After the
Solution is found, you can click Confidence Limits on the Control Panel and see the table shown here.
Figure 20.26 Solution Report
Note: Remember to Save Estimates before requesting confidence limits.
The maximum likelihood estimates of the lognormal parameters are 2.2223 for Mu and 0.3064 for Sigma
(in base 10 logs). The corresponding estimate of the median of the lognormal distribution is the antilog of
2.2223 (10 2.2223 ), which is approximately 167. This represents the typical life for a locomotive engine.