The Statistics report includes summary information such as the number of observations, the nonparametric estimates, and parametric estimates.
Model Comparisons
The Model Comparisons report provides fit statistics for each fitted distribution. AICc, BIC, and -2Loglikelihood statistics are sorted to show the best fitting distribution first. Initially, the rows are sorted by AICc.
To change the statistic used to sort the report, select Comparison Criterion from the Life Distribution red triangle menu. If the three criteria agree on the best fit, the sorting does not change. See “Life Distribution Platform Options” on page 40 for details about this option.
Summary of Data
The Summary of Data report shows the number of observations, the number of uncensored values, and the censored values of each type.
Nonparametric Estimate
The Nonparametric Estimate report shows nonparametric estimates for each observation. For right-censored data, the report has midpoint-adjusted Kaplan-Meier estimates, standard
Kaplan-Meier estimates, pointwise confidence intervals, and simultaneous confidence intervals.
For interval-censored data, the report has Turnbull estimates, pointwise confidence intervals, and simultaneous confidence intervals
Pointwise estimates are in the Lower 95% and Upper 95% columns. These estimates tell you the probability that each unit will fail at any given point in time.
See “Nonparametric Fit” on page 47 for more information about nonparametric estimates.
Parametric Estimate
The Parametric Estimate reports summarizes information about each fitted distribution.
Above each Covariance Matrix report, the parameter estimates with standard errors and confidence intervals are shown. The information criteria results used in model comparisons are also provided.
Covariance Matrix Reports
For each distribution, the Covariance Matrix report shows the covariance matrix for the estimates.
Profilers
Four types of profilers appear for each distribution:
• The Distribution Profiler shows cumulative failure probability as a function of time.
• The Quantile Profiler shows failure time as a function of cumulative probability.
• The Hazard Profiler shows the hazard rate as a function of time.
• The Density Profiler shows the density for the distribution.
Parametric Estimate Options
The Parametric Estimate red triangle menu has the following options:
Save Probability Estimates Saves the estimated failure probabilities and confidence intervals to the data table.
Save Quantile Estimates Saves the estimated quantiles and confidence intervals to the data table.
Save Hazard Estimates Saves the estimated hazard values and confidence intervals to the data table.
Show Likelihood Contour Shows or hides a contour plot of the likelihood function. If you have selected the Weibull distribution, a second contour plot appears that shows
alpha-beta parameterization. This option is available only for distributions with two parameters.
Show Likelihood Profile Shows or hides a profiler of the likelihood function.
Fix Parameter Specifies the value of parameters. Enter the new location or scale, select the appropriate check box, and then click Update. JMP re-estimates the other parameters, covariances, and profilers based on the new parameters.
Note that for the Weibull distribution, the Fix Parameter option lets you select the Weibayes method.
Bayesian Estimates Performs Bayesian estimation of parameters for certain distributions based on three methods of prior distribution (Location and Scale Priors, Quantile and Parameter Priors, and Failure Probability Priors). This option is not available for all distributions. Select a prior from the Bayesian Estimation red triangle menu to view the associated parameters:
– Location and Scale Priors - Specify parameters for prior distributions. Select the red triangle next to the prior distributions to select a different distribution for each parameter. You can enter new values for the hyperparameters of the priors. You can also enter the number of Monte Carlo simulation points and a random seed (should be a positive integer greater than 1), and select to show a scatter plot.
– Quantile and Parameter Priors - Specify ranges for quantile and scale. Select the red triangle next to the prior distributions to select a different distribution for each parameter. You can enter new values for the probability and limits. You can also enter the number of Monte Carlo simulation points and a random seed (should be a positive integer greater than 1), and select to show a scatter plot (Meeker and Escobar 1998).
– Failure Probability Priors - Specify failure probability by estimates, error percentages, and ranges. You can enter new values for the failure probability, probability estimates, and estimate errors. A prior probability function versus time plot is displayed. You can also enter the number of Monte Carlo simulation points and a random seed (should be a positive integer greater than 1), and select to show a scatter plot (Kaminskiy and Krivtsov, 2005).
After you click Fit Model, a new report called Bayesian Estimates shows summary statistics of the posterior distribution of each parameter and a scatterplot of the simulated posterior observations. In addition, profilers help you visualize the fitted life distribution based on the posterior medians.
If you have zero failure data, it is possible to run a Bayesian estimation. A preference, Weibayes Only for Zero Failure Data, exists that ensures the Weibayes method is used for zero failure data analysis. The preference is on by default (similar to the behavior in previous releases). If you have zero failure data and want to run a full Bayesian estimation, you can uncheck the platform preference to run a full analysis. To access the preference, select File >
Preferences > Platform > Life Distribution.
Custom Estimation Predicts failure probabilities, survival probabilities, and quantiles for specific time and probability values. Each estimate has its own section. Enter a new time and press the Enter key to see the new estimate. To calculate multiple estimates, click the plus sign, enter another time in the box, and then press Enter.
Mean Remaining Life Estimates the mean remaining life of a unit. Enter a hypothetical time and press Enter to see the estimate. As with the custom estimations, you can click the plus sign and enter additional times. This statistic is available for the following distributions:
Lognormal, Weibull, Loglogistic, Fréchet, Normal, SEV, Logistic, LEV, and Exponential.
For more information about the distributions used in parametric estimates, see “Parametric Distributions” on page 47.