Quality and Reliability Methods - SAS

Chapter 19 Reliability and Survival Analysis 357
Univariate Survival Analysis
Figure 19.9 Summary Statistics for the Univariate Survival Analysis
The Summary report gives estimates for the mean survival time, as well as the standard error of the mean.
The estimated mean survival time is
μˆ
D
m D – 1 A2
= Ŝ( t , with a standard error of ,
i – 1
)( t i
– t i – 1
)
σˆ ( μˆ
) = ------------ i
m – 1 ------------------------
n
i = 1
i
( n i
– d i
)
i = 1
i d j D – 1
D
where Ŝ( t i
) = ∏ 1
– --- , A , and .
n i
= Ŝ( t
j = 1 j
j
)( t j + 1
– t j
) m = d j
j = i
j = 1
Ŝ( t i
) is the survival distribution at time t i , D is the number of distinct event times, n i is the number of
surviving units just prior to t i , d i is the number of units that fail at t i , and t 0 is defined to be 0.
When there are multiple groups, the Tests Between Groups table, shown below, gives statistical tests for
homogeneity among the groups. Kalbfleisch and Prentice (1980, chap. 1), Hosmer and Lemeshow (1999,
chap. 2), and Klein and Moeschberger (1997, chap. 7) discuss statistics and comparisons of survival curves.
Figure 19.10 Tests Between Groups
Test
names two statistical tests of the hypothesis that the survival functions are the same across groups.