Weibull and Reliability/Failure Time Analysis

Fits the two and three-parameter Weibull distribution to survival or failure time data, with or without censoring. Various results graphs and spreadsheets are provided in order to evaluate the quality of the fit (goodness of fit) and to estimate the reliability and hazard functions.

General

Element Name Description
Detail of computed results reported Specifies the level of computed results reported. By default, Statistica will report the parameter estimates for the Weibull distribution, goodness of fit tests, and the histogram of data with the fitted distribution. If All results is requested, Statistica will also report quantile-quantile plots, a hazard function plot, the plot of R-square vs. the Weibull location parameter, the Kaplan-Meier estimator, and other graphical summaries. Plots and estimates of reliability are available as an option.
Input variables Specifies whether the input list of dependent continuous variables describes a list of variables with failure times (multiple analyses will be performed, one for each variable), or a list of variables describing the start/stop times for a single measure. In the latter case (single measure, single analysis) you must specify for input either two (continuous dependent) variables with start and stop times for each observation (the analysis will be performed on the differences between the two values, i.e., on the elapsed times), or you can select six (continuous dependent) variables containing dates. Specifically, these variables should contain the month (1 to 12), day (1 to 31), and year when the particular observation began (e.g., when a patient was admitted to the hospital), and the month, day, and year when the observation was terminated (due to death/failure or censoring, e.g., when a patient was dismissed from the hospital). While processing the data, the program will compute the number of days that elapsed between dates, and perform the analysis on this measure. Note that if the value of the year is less than 100, Statistica will automatically assume that the year refers to the 20th century; for example, the year 88 would be converted into 1988.
Parameter estimates or values By default (Shape and scale), Statistica will compute maximum likelihood parameter estimates for the two-parameter (shape, scale) Weibull distribution, contingent on the user-defined constant offset value (make sure that all data values are greater than 0; see also the Add constant to 0 parameter). Select the Location shape scale option to fit the three-parameter Weibull distribution; however, note that this option may fail because unique maximum likelihood parameters cannot be estimated for all observed distributions (refer to the Electronic Manual for details). If you select User defined, then all final results (graphs, etc.) will be reported for the parameter estimates as specified by you.
Weibull offset This parameter will be used when you selected User-defined parameters for the Weibull distribution, or when you selected the two-parameter (shape and scale) Weibull distribution; in the latter case, this constant is subtracted from the observed data prior to fitting the two-parameter Weibull distribution.
Weibull shape Specifies a user-defined shape parameter for the Weibull distribution; this value will be ignored (estimated from the data) if maximum likelihood parameter estimates are computed (see Parameter estimates or values).
Weibull scale Specifies a user-defined scale parameter for the Weibull distribution; this value will be ignored (estimated from the data) if maximum likelihood parameter estimates are computed (see Parameter estimates or values).
Confidence limits The (percentile) value entered here will be used to construct the confidence intervals for the various results spreadsheets and graphs involving the reliability and distribution functions.

Parameter estimation

Element Name Description
Add Constant Add a constant to all 0 failure times, prior to fitting the Weibull distribution. The Weibull distribution is bounded on the left side; i.e., all values must be greater than the respective location parameter (greater than 0, by default). If the add constant is true, then Statistica replaces zero failure times with the constant before fitting or plotting the Weibull distribution.
Value to add The value (constant) to add to 0 times prior to fitting the Weibull distribution. The Weibull distribution is bounded on the left side; i.e., all values must be greater than the respective location parameter (greater than 0, by default). If the add constant is true, then Statistica replaces zero failure times with the constant before fitting or plotting the Weibull distribution.
Max number of iterations Specifies the maximum number of iterations for the iterative estimation of maximum likelihood parameters.
Convergence criterion Specifies a convergence criterion for the iterative parameter estimation procedure.

Reliability and Distribution function

Element Name Description
Creates reliability Creates various reliability estimates, statistics, and plots.
Confidence interval Choose a method for computing confidence intervals for the reliability estimates.
Failure orders Failure orders for no/single censoring; determines how the cumulative distribution function F(t) will be estimated for probability plots and nonparametric (rank-based) reliability plots. See the Electronic Manual for additional details.