### Example 51.5 Probability Plotting—Right Censoring

The following statements create a SAS data set containing observed and right-censored lifetimes of 70 diesel engine fans (Nelson, 1982):

```data Fan;
datalines;
450 0    460 1   1150 0   1150 0   1560 1
1600 0   1660 1   1850 1   1850 1   1850 1
1850 1   1850 1   2030 1   2030 1   2030 1
2070 0   2070 0   2080 0   2200 1   3000 1
3000 1   3000 1   3000 1   3100 0   3200 1
3450 0   3750 1   3750 1   4150 1   4150 1
4150 1   4150 1   4300 1   4300 1   4300 1
4300 1   4600 0   4850 1   4850 1   4850 1
4850 1   5000 1   5000 1   5000 1   6100 1
6100 0   6100 1   6100 1   6300 1   6450 1
6450 1   6700 1   7450 1   7800 1   7800 1
8100 1   8100 1   8200 1   8500 1   8500 1
8500 1   8750 1   8750 0   8750 1   9400 1
9900 1  10100 1  10100 1  10100 1  11500 1
;
```

Some of the fans had not failed at the time the data were collected, and the unfailed units have right-censored lifetimes. The variable LIFETIME represents either a failure time or a censoring time, in thousands of hours. The variable CENSOR is equal to 0 if the value of LIFETIME is a failure time, and it is equal to 1 if the value is a censoring time. The following statements use the LIFEREG procedure to produce the probability plot with an inset for the engine lifetimes:

```ods graphics on;
proc lifereg data=Fan;
model Lifetime*Censor( 1 ) = / d = Weibull;
probplot
ppout
npintervals=simul;
inset;
run;
ods graphics off;
```

The resulting graphical output is shown in Output 51.5.1. The estimated CDF, a line representing the maximum likelihood fit, and pointwise parametric confidence bands are plotted in the body of Output 51.5.1. The values of right-censored observations are plotted along the bottom of the graph. The Cumulative Probability Estimates table is also created in Output 51.5.2.

Output 51.5.1: Probability Plot for the Fan Data

Output 51.5.2: CDF Estimates

Cumulative Probability Estimates
Probability
Simultaneous 95%
Confidence Limits
Kaplan-Meier
Estimate
Kaplan-Meier
Standard Error
Lower Upper
0.45 0.0071 0.0007 0.2114 0.0143 0.0142
1.15 0.0215 0.0033 0.2114 0.0288 0.0201
1.15 0.0360 0.0073 0.2168 0.0433 0.0244
1.6 0.0506 0.0125 0.2304 0.0580 0.0282
2.07 0.0666 0.0190 0.2539 0.0751 0.0324
2.07 0.0837 0.0264 0.2760 0.0923 0.0361
2.08 0.1008 0.0344 0.2972 0.1094 0.0392
3.1 0.1189 0.0436 0.3223 0.1283 0.0427
3.45 0.1380 0.0535 0.3471 0.1477 0.0460
4.6 0.1602 0.0653 0.3844 0.1728 0.0510
6.1 0.1887 0.0791 0.4349 0.2046 0.0581
8.75 0.2488 0.0884 0.6391 0.2930 0.0980