Example 6.2: Probability Plotting -Right Censoring

The LIFEREG Procedure

Example 6.2: 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, p. 318).

   title 'Engine Fan Lifetime Study';
   data fan;                                     
      input lifetime censor@@;                   
      lifetime = lifetime / 1000;
      label lifetime = Lifetime;                    
      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 
   ;                                          
   run;

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.

   symbol v=dot c=white;
   proc lifereg;                        
      model lifetime*censor( 1 ) = / d = weibull; 
      probplot 
          cencolor = red
          cframe   = ligr
          cfit     = blue
          ppout 
          npintervals=simul  
          ;
      inset / 
          cfill = white
          ctext = blue;
   run; quit;

The resulting graphical output is shown in Output 6.2.1. The estimated CDF, a line representing the maximum-likelihood fit, and pointwise parametric confidence bands are plotted in the body of Output 6.2.1. The values of right-censored observations are plotted along the top of the graph. The "Cumulative Probability Estimates" table is also shown in Output 6.2.2.

Output 6.2.1: Probability Plot for the Fan Data

Output 6.2.2: CDF Estimates

Engine Fan Lifetime Study

The LIFEREG Procedure

Cumulative Probability Estimates
Lifetime	Cumulative Probability	Simultaneous 95% Confidence Limits		Kaplan-Meier Estimate	Kaplan-Meier Standard Error
Lifetime	Cumulative Probability	Lower	Upper	Kaplan-Meier Estimate	Kaplan-Meier Standard Error
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

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