This example illustrates probability plotting and distribution fitting for data grouped by the levels of a special group-variable. The data are from an accelerated life test of an insulating fluid and are the times to electrical breakdown of the fluid under different high voltage levels. Each voltage level defines a subset of data for which a separate analysis and Weibull plot are produced. These data are the 26kV, 30kV, 34kV, and 38kV groups of the data provided by Nelson (1990, p. 129). The following statements create a SAS data set containing the lifetimes and voltages:

data fluid;
    input Time voltage $ @@;
    datalines;                    
5.79    26kv    1579.52 26kv  
2323.7  26kv    7.74    30kv  
17.05   30kv    20.46   30kv  
21.02   30kv    22.66   30kv  
43.4    30kv    47.3    30kv  
139.07  30kv    144.12  30kv  
175.88  30kv    194.90  30kv  
0.19     34kv    .78     34kv  
0.96     34kv    1.31    34kv  
2.78    34kv    3.16    34kv  
4.15    34kv    4.67    34kv  
4.85    34kv    6.50    34kv  
7.35    34kv    8.01    34kv  
8.27    34kv    12.06   34kv  
31.75   34kv    32.52   34kv  
33.91   34kv    36.71   34kv  
72.89   34kv    .09     38kv  
0.39     38kv    .47     38kv  
0.73     38kv    .74     38kv  
1.13    38kv    1.40    38kv  
2.38    38kv                  
;                             

The variable Time provides the time to breakdown in minutes, and the variable Voltage provides the voltage level at which the test was conducted. These data are not censored.

The RELIABILITY procedure plots the data for the different voltage levels on the same Weibull probability plot, fits a separate distribution to the data at each voltage level, and superimposes distribution lines on the plot.

The following statements produce the probability plot shown in Figure 14.5 for the variable Time at each level of the group-variable Voltage:

proc reliability data=fluid;
   distribution weibull;
   pplot time=voltage  / overlay 
                         noconf;
run;

The input data set FLUID is specified by the DATA= option in the PROC RELIABILITY statement. The PROBPLOT statement option OVERLAY specifies that plots for the groups are to be overlaid rather than displayed separately. The option NOCONF specifies that no confidence bands are to be plotted, since these can interfere with one another on overlaid plots; confidence bands are displayed by default.

Figure 14.5 Weibull Probability Plot for the Insulating Fluid Data

A summary table that contains information for all groups is displayed. In addition, information identical to that shown in Figure 14.3 is tabulated for each level of voltage. The summary table for all groups and the tables for the 26kV group are shown in Figure 14.6 and Figure 14.7.