Estimation and inference in sets of Weibull samples

Abstract

Menon’s method of estimation of the Weibull parameters is extended to the analysis of multiple samples of a common size. A methodology is developed for testing the equality of shape parameters among the populations from which the samples are drawn. When the shape parameters are judged to be equal, point and interval estimates of the common shape parameter are constructed. An analysis of variance approach is shown to be valid for testing the equality of scale parameters when a common shape parameter is hypothesized. A post hoc multiple comparison test is developed for assessing which scale parameters differ. Confidence intervals on a percentile may be set for any of the sample populations using the estimated common shape parameter. Tables of the percentage points of the distributions needed for testing hypotheses and constructing interval estimates were obtained by Monte Carlo sampling and are given for a useful range of sample sizes and number of samples. The result is a comprehensive, easily computed, method of analyzing uncensored sets of Weibull data such as occurs when the flexural strength of brittle materials is observed under different conditions of formulation, finishing or test environment. An example analysis of data of this type is included.