Quality and Reliability Methods - SAS

360 Reliability and Survival Analysis Chapter 19
Univariate Survival Analysis
– Show Simultaneous CI toggles the simultaneous confidence bands for all groups on the plot.
Meeker and Escobar (1998, chap. 3) discuss pointwise and simultaneous confidence intervals and
the motivation for simultaneous confidence intervals in survival analysis.
– Midstep Quantile Points changes the plotting positions to use the modified Kaplan-Meier plotting
positions, which are equivalent to taking mid-step positions of the Kaplan-Meier curve, rather than
the bottom-of-step positions. This option is recommended, so by default it is turned on.
– Connect Quantile Points toggles the lines in the plot on and off. By default, this option is on.
– Fitted Quantile toggles the straight-line fit on the fitted Weibull, lognormal, or Exponential
Quantile plot.
– Fitted Quantile CI Lines toggles the 95% confidence bands for the fitted Weibull, lognormal, or
Exponential Quantile plot.
– Fitted Quantile CI Shaded toggles the display of the 95% confidence bands for a fit as a shaded area
or dashed lines.
– Fitted Survival CI toggles the confidence intervals (on the survival plot) of the fitted distribution.
– Fitted Failure CI toggles the confidence intervals (on the failure plot) of the fitted distribution.
Exponential Plot when checked, plots the cumulative exponential failure probability by time for each
group. Lines that are approximately linear empirically indicate the appropriateness of using an
exponential model for further analysis. In Figure 19.15, the lines for Group 1 and Group 2 in the
Exponential Plot are curved rather than straight. This indicates that the exponential distribution is not
appropriate for this data.
Exponential Fit produces the Exponential Parameters table and the linear fit to the exponential
cumulative distribution function in the Exponential Plot. Results are shown in Figure 19.15. The
parameter Theta corresponds to the mean failure time.
Weibull Plot plots the cumulative Weibull failure probability by log(time) for each group. A Weibull plot
that has approximately parallel and straight lines indicates a Weibull survival distribution model might
be appropriate to use for further analysis.
Weibull Fit produces the linear fit to the Weibull cumulative distribution function in the Weibull plot and
two popular forms of Weibull estimates. These estimates are shown in the Extreme Value Parameter
Estimates table and the Weibull Parameter Estimates tables (Figure 19.15). The Alpha parameter is the
63.2 percentile of the failure-time distribution. The Extreme-value table shows a different
parameterization of the same fit, where Lambda = ln(Alpha) and Delta = 1/Beta.
LogNormal Plot plots the cumulative lognormal failure probability by log(time) for each group. A
lognormal plot that has approximately parallel and straight lines indicates a lognormal distribution is
appropriate to use for further analysis.
LogNormal Fit produces the linear fit to the lognormal cumulative distribution function in the
lognormal plot and the LogNormal Parameter Estimates table shown in Figure 19.15. Mu and Sigma
correspond to the mean and standard deviation of a normally distributed natural logarithm of the time
variable.