Quality and Reliability Methods - SAS

Chapter 20 Reliability and Survival Analysis II 395
Nonlinear Parametric Survival Models
A characteristic of the exponential distribution is that the instantaneous failure rate remains constant over
time. This means that the chance of failure for any subject during a given length of time is the same
regardless of how long a subject has been in the study.
Weibull Loss Function
The Weibull density function often provides a good model for the lifetime distributions. You can use the
Univariate Survival platform for an initial investigation of data to determine if the Weibull loss function is
appropriate for your data.
There are examples of one-parameter, two-parameter, and extreme-value functions in the Loss Function
Templates folder.
Lognormal Loss Function
The formula shown below is the lognormal loss function where Normal Distribution(model/sigma)
is the standard normal distribution function. The hazard function has value 0 at t = 0, increases to a
maximum, then decreases and approaches zero as t becomes large.
Loglogistic Loss Function
The loglogistic function has a symmetric density with mean 0 and slightly heavier tails than the normal
density function. If Y is distributed as the logistic distribution, Exp(Y) is distributed as the loglogistic
distribution. Once you have selected a loss function, choose the Nonlinear command and complete the
dialog. If the response is included in the model formula, no Y variable is needed. The model is the
prediction column and a loss function column is the loss column.
Exponential Loss Function
Weibull Loss Function