The analysis of a two way factorial design with weibull response

Samples of size n, type II censored at the r-th ordered observation are presumed to be drawn randomly from Weibull populations whose scale parameters are affected by the the levels of two external factors. The factor levels form the rows and columns of a two-way data layout. The Weibull shape parameter, though unknown, is presumed not to vary with the factor levels. Five hypotheses are considered for the scale parameter. The most general is that it is multiplicatively composed of row, column and interaction effects. Four further cases correspond to i) no interaction effect, ii) only a row effect, iii) only a column effect, and iv) no effects at all. Maximum likelihood estimates of the shape parameter and the factor effects are derived under each of the five hypotheses. It is established that the ratio of respective shape parameter estimates may be used to test each of the latter four hypotheses against the first. Tables of critical values determined by Monte Carlo simulation are given for analyzing the 2×2, 2×3, and 3×3 layouts for cell sample sizes ranging from 2 to 10.