AbstractIt is sometimes reasonable to assume that the lifetime distribution of an item belongs to a certain parametric family, and that actual parameter values depend upon the testing environment of the item. In the two‐parameter Weibull family setting, suppose both the shape and scale parameters are expressible as functions of the testing environment. For various models of functional dependency on environment, maximum likelihood methods are used to estimate characteristics of interest at specified environmental levels. The methodology presented handles exact, censored, and grouped data. A detailed accelerated life testing analysis of stress‐rupture data for Kevlar/epoxy composites is given.