1. Exploratory Data Analysis
1.4. EDA Case Studies
1.4.2. Case Studies
1.4.2.9. Airplane Polished Window Strength

1.4.2.9.3.

Weibull Analysis

Plots for Weibull Distribution

The following plots were generated for a Weibull distribution.

Conclusions

We can make the following conclusions from these plots.

1. The optimal value, in the sense of having the most linear probability plot, of the shape parameter gamma is 2.13.

2. At the optimal value of the shape parameter, the PPCC value is 0.988.

3. At the optimal value of the shape parameter, the estimate of the location parameter is 15.90 and the estimate of the scale parameter is 16.92.

4. Fine tuning the estimate of gamma (from 2 to 2.13) has minimal impact on the PPCC value.

Alternative Plots

The Weibull plot and the Weibull hazard plot are alternative graphical analysis procedures to the PPCC plots and probability plots.

These two procedures, especially the Weibull plot, are very commonly employed. That not withstanding, the disadvantage of these two procedures is that they both assume that the location parameter (i.e., the lower bound) is zero and that we are fitting a 2-parameter Weibull instead of a 3-parameter Weibull. The advantage is that there is an extensive literature on these methods and they have been designed to work with either censored or uncensored data.

Weibull Plot

This Weibull plot shows the following

1. The Weibull plot is approximately linear indicating that the 2-parameter Weibull provides an adequate fit to the data.

2. The estimate of the shape parameter is 5.28 and the estimate of the scale parameter is 33.32.

Weibull Hazard Plot

The construction and interpretation of the Weibull hazard plot is discussed in the Assessing Product Reliability chapter.