Weibull and Reliability/Failure Time Analysis - Grouped Data
In some cases, failure time data are presented in grouped form. Specifically, instead of having available the precise failure time for each observation, only aggregate information is available about the number of items that failed or were censored in a particular time interval. Such life-table data input is also described in the context of the Survival Analysis module. Statistica offers two general approaches for fitting the Weibull distribution to grouped data.
First, one can treat the tabulated data as if they were continuous. In other words, one 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 after the observed failures). Lawless (1982) advises that this method is usually satisfactory if the class intervals are relatively narrow.
Alternatively, you may treat the data explicitly as a tabulated life table, and use a weighted least squares methods algorithm (based on Gehan and Siddiqui, 1973; see also Lee, 1992) to fit the Weibull. 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 the program will choose those that produce the best fit (based on a Chi-square test). In practice, both approaches often yield very similar parameter estimates.