Weibull & Reliability/Failure Time Analysis - Grouped Data Tab

Select the Grouped data tab of the Weibull & Reliability/Failure Time Analysis dialog to access options to specify the variables for the Weibull analysis & reliability/failure time analysis, when the input data are already tabulated (grouped data; see the Introductory Overview ). Statistica expects as input a table (the same type of input that can be used for life table analyses in the Survival Analysis module) specified in three variables (one variable containing the lower interval boundaries, a second variable containing the number of observations censored in the respective interval, and a third variable containing the number of observations failing in the respective interval. Then specify the Number (of observations) entering the first interval, and click OK to estimate the parameters of the Weibull distribution. Note that two different methods of parameter estimation are available. You can either treat the data as continuous data (with all failures and censoring occurring at the respective interval mid-points), or you can use weighted least squares methods to estimate the parameters directly from the grouped data (i.e., without first "expanding" the table into continuous data). See Method of parameter estimation below for further information.

Variables

Click the Variables button to display the standard variable selection dialog, in which you select the variables for the analysis. Statistica expects as input three variables.

Var. with lower limits for time interval.

Choose a variable with lower interval boundaries.

Var with number withdrawn (censored)

Choose a variable with the number of observations censored in the respective interval.

Var. with number failing (dying).

Choose a variable with the number of observations failing in the respective interval.

Number entering first interval

Use the Number entering first interval box to enter the number of observations at the beginning of the study, i.e., entering the first interval in the tabulated (grouped) data. Make sure that the Number entering first interval is equal to or greater than the sum of all failed and censored observations as specified in the data file. (If the Number entering first interval is greater than the sum of all failed and censored observations, then the difference is added as censored observations to the last interval.)

Method of parameter estimation

The Method of parameter estimation group box contains two options. Use these options to specify which of the two general approaches Statistica should use for fitting the Weibull distribution to grouped data. In practice; both approaches often yield very similar parameter estimates.

Compute parameter estimates from grouped data

Select this option button if you want to treat the data explicitly as a tabulated life table, and use a weighted least squares algorithm (based on Gehan and Siddiqui, 1973; see also Lee, 1992) to fit the Weibull distribution. This is the same algorithm used in the Survival Analysis module (see also Survival Analysis - Notes and Technical Information), and it uses three different sets of weights for estimating the parameters of the two-parameter Weibull distribution, from which Statistica will choose those that produce the best fit (based on a Chi-square test).

Treat table as continuous data, failures at interval mid-points

Select this option button if you want to treat the tabulated data as if they were continuous. In other words, you can "expand" the tabulated values into continuous data by assuming (1) that each observation in a given time interval failed exactly at the interval mid-point (interpolating out "half a step" for the last interval), and (2) that censoring occurred after the failures in each interval (in other words, censored observations are sorted to follow after the observed failures). Lawless (1982) advises that this method is usually satisfactory if the class intervals are relatively narrow.

For related procedures, see also the Survival Analysis module.