Weibull and Reliability/Failure Time Analysis - Goodness-of-Fit Indices

A number of different tests have been proposed for evaluating the quality of the fit of the Weibull distribution to the observed data. These tests are discussed and compared in detail in Lawless (1982).

Hollander-Proschan
This test compares the theoretical reliability function to the Kaplan-Meier estimate. The actual computations for this test are somewhat complex, and you may refer to Dodson (1994, Chapter 4) for a detailed description of the computational formulas. The Hollander-Proschan test is applicable to complete, single-censored, and multiple-censored data sets; however, Dodson (1994) cautions that the test may sometimes indicate a poor fit when the data are heavily single-censored. The Hollander-Proschan C statistic can be tested against the normal distribution (z), and STATISTICA will report both the test statistic and the respective (two-sided) p level.
Mann-Scheuer-Fertig
This test, proposed by Mann, Scheuer, and Fertig (1973), is described in detail in, for example, Dodson (1994) or Lawless (1982). The null hypothesis for this test is that the population follows the Weibull distribution with the estimated parameters. Nelson (1982) reports this test to have reasonably good power, and this test can be applied to Type II censored data. For computational details refer to Dodson (1994) or Lawless (1982); the critical values for the test statistic have been computed based on Monte Carlo studies, and have been tabulated for n (sample sizes) between 3 and 25; for n greater than 25, this test is not computed.
Anderson-Darling
The Anderson-Darling procedure is a general test to compare the fit of an observed cumulative distribution function to an expected cumulative distribution function. However, this test is only applicable to complete data sets (without censored observations); otherwise the Anderson-Darling test will not be computed. The critical values for the Anderson-Darling statistic have been tabulated (see, for example, Dodson, 1994, Table 4.4) for sample sizes between 10 and 40; this test is not computed for n less than 10 and greater than 40.