The Results section of the report window shows more detailed statistics and prediction profilers than those shown in the Comparisons report. Separate result sections are shown for each selected distribution. Weibull Distribution Nested Model Tests for Devalt.jmp Data shows a portion of the Weibull results, Nested Model Tests, and Diagnostics plots for Devalt.jmp.
Statistical results, diagnostic plots, and Distribution, Quantile, Hazard, Density, and Acceleration Factor Profilers are included for each of your specified distributions. The Custom Estimation tab lets you estimate specific failure probabilities and quantiles, using both Wald and Profile interval methods. When the Box-Cox Relationship is selected on the platform launch window, the Sensitivity tab appears. This tab shows how the Loglikelihood and B10 Life change as a function of Box-Cox lambda.
Weibull Distribution Nested Model Tests for Devalt.jmp Data
For each parametric distribution, there is a Statistics section that shows parameter estimates, a covariance matrix, confidence intervals, summary statistics, and diagnostic plots. You can save probability, quantile, and hazard estimates by selecting any or all of these options from the Statistics red triangle menu for each parametric distribution. The estimates and the corresponding lower and upper confidence limits are saved as columns in your data table. Save Options for Parametric Distribution shows the save options available for any parametric distribution.
Assumes that the location and scale parameters are different for all levels of the explanatory variable. This option is equivalent to fitting the distribution by the levels of the explanatory variable. The Separate Location and Scale model has multiple location parameters and multiple scale parameters. See Separate Location and Scale Model with the Weibull Distribution for Devalt.jmp Data.
Assumes that the location parameters are different, but the scale parameters are the same for all levels of the explanatory variable. The Separate Location model has multiple location parameters and only one scale parameter. See Separate Location Model with the Weibull Distribution for Devalt.jmp Data.
Is the default model shown in the initial Fit Life by X report window. See Regression Model with the Weibull Distribution for Devalt.jmp Data.
Assumes that the explanatory variable does not affect the response. This option is equivalent to fitting all of the data values to the selected distribution. The No Effect Model has one location parameter and one scale parameter. See No Effect Model with the Weibull Distribution for Devalt.jmp Data.
Separate Location and Scale, Separate Location, and Regression analyses results are shown by default. Regression parameter estimates and the location parameter formula are shown under the Estimates section, by default. The Diagnostics plots for the No Effect model can be displayed by selecting the check box to the left of No Effect under the Nested Model Tests title.
To see results for each of the models (independently of the other models), click the underlined model of interest (listed under Nested Model Tests) and then uncheck the check boxes for the other models.
If the Nested Model Tests option was not checked in the launch window, then the Separate Location and Scale, and Separate Location models are not assessed. In this case, estimates are given for the regression model for each distribution that you select, and the Cox-Snell Residual P-P Plot is the only diagnostic plot.
The Multiple Probability Plots shown in Weibull Distribution Nested Model Tests for Devalt.jmp Data are used to validate the distributional assumption for the different levels of the accelerating variable. If the line for each level does not run through the data points for that level, the distributional assumption might not hold. Side-by-side comparisons of the diagnostic plots provide a visual comparison for the validity of the different models. See Meeker and Escobar (1998, sec. 19.2.2) for a discussion of multiple probability plots.
The Cox-Snell Residual P-P Plots are used to validate the distributional assumption for the data. If the data points deviate far from the diagonal, then the distributional assumption might be violated. The Cox-Snell Residual P-P Plot red triangle menu has an option called Save Residuals that enables you to save the residual data to the data table. See Meeker and Escobar (1998, sec. 17.6.1) for a discussion of Cox-Snell residuals.
Separate Location Model with the Weibull Distribution for Devalt.jmp Data
Regression Model with the Weibull Distribution for Devalt.jmp Data
No Effect Model with the Weibull Distribution for Devalt.jmp Data
In addition to a statistical summary and diagnostic plots, the Fit Life by X report window also includes profilers and surface plots for each of your specified distributions. To view the Weibull time-accelerating factor and explanatory variable profilers, click the Distribution tab under Weibull Results. To see the surface plot, click the disclosure icon to the left of the Weibull title (under the profilers). The profilers and surface plot behave similarly to other platforms. See Profiler and Surface Plot in the Profilers book.
The report window also includes a tab labeled Acceleration Factor. Clicking the Acceleration Factor tab shows the Acceleration Factor Profiler. This profiler is an enlargement of the Weibull plot shown under the Acceleration Factor tab in the Comparisons section of the report window. Weibull Acceleration Factor Profiler for Devalt.jmp shows the Acceleration Factor Profiler for the Weibull distribution of Devalt.jmp. The baseline level for the explanatory variable can be modified by selecting the Set Time Acceleration Baseline option in the Fit Life by X red triangle menu.
Weibull Acceleration Factor Profiler for Devalt.jmp
