Parametric Model for Recurrent Events Data

The following SAS statements fit a non-homogeneous Poisson process with a power intensity function model to the valve seat data described in the section Analysis of Recurrence Data on Repairs. The FIT=MODEL option in the MCFPLOT statement requests that the fitted model be plotted on the plot with the nonparametric mean cumulative function estimates.

proc reliability data=Valve;                                                                                                                       
   unitid id;                                                                                                                        
   distribution Nhpp(Pow);                                                                                                           
   model   Days*Value(-1);                                                                                                   
   mcfplot Days*Value(-1) / Fit=Model Noconf;                                                                                                                                 

The model parameter estimates are shown in Figure 16.48.

Figure 16.48: Power Model Parameter Estimates for the Valve Seat Data


NHPP-Power Parameter Estimates
Parameter Estimate Standard Error Asymptotic Normal
95% Confidence Limits
Lower Upper
Intercept 553.6430 57.8636 451.0941 679.5048
Shape 1.3996 0.2005 1.0570 1.8533

Figure 16.49 displays a plot of nonparametric estimates of the mean cumulative function and the fitted model mean function. The parametric model matches the data well except at the upper end of the range of repair times, where the parametric model does not capture the rapid increase in the number of replacements of the valve seats. For this reason, the parametric model might not be appropriate for predicting future repairs of the engines.

Figure 16.49: Mean Cumulative Function Plot for the Valve Seat Data

Mean Cumulative Function Plot for the Valve Seat Data

Figure 16.50 shows the parametric model intensity function. The intensity function increases with time, indicating an increasing rate of repairs. This is consistent with the parameter estimates in Figure 16.48, where a shape parameter significantly greater than 1 indicates an increasing failure rate.

Figure 16.50: Intensity Function Plot for the Valve Seat Data

Intensity Function Plot for the Valve Seat Data