Quality and Reliability Methods - SAS

Chapter 19 Reliability and Survival Analysis 363
Univariate Survival Analysis
The following table shows what to plot that makes a straight line fit for that distribution:
Table 19.1 Straight Line Fits for Distribution
Distribution Plot X Axis Y Axis Interpretation
Exponential time -log(S) slope is 1/theta
Weibull log(time) log(-log(S)) slope is beta
Lognormal log(time) Probit(1-S) slope is 1/sigma
Note: S = product-limit estimate of the survival distribution
The exponential distribution is the simplest, with only one parameter, which we call theta. It is a
constant-hazard distribution, with no memory of how long it has survived to affect how likely an event is.
The parameter theta is the expected lifetime.
The Weibull distribution is the most popular for event-time data. There are many ways in which different
authors parameterize this distribution (as shown in Table 19.2 on page 364). JMP reports two
parameterizations, labeled the lambda-delta extreme value parameterization and the Weibull alpha-beta
parameterization. The alpha-beta parameterization is used in the Reliability literature. See Nelson (1990).
Alpha is interpreted as the quantile at which 63.2% of the units fail. Beta is interpreted as follows: if beta>1,
the hazard rate increases with time; if beta