Time dependent mechanical breakdown of materials has been a long-standing concern for structural components, and it is especially exacerbated by randomness in material properties, loading conditions, and other sources of uncertainty. A generalized phenomenological cumulative distribution function for lifetime, which is consistent with fundamentals of reliability theory, is presented. The form of the cdf includes a kernel that incorporates functions for time dependent loading, mechanical breakdown, and statistical behavior. The formalism is applicable for a variety of loading conditions including creep rupture, rate dependent tensile loading, and fatigue. Analysis of failure under stress histories such as variable stress amplitude or step-stress loadings is manageable as well. The model is a generalization of the classical accelerated life model in which covariates are included to account for physical attributes that directly influence component lifetime. Specific examples will be provided for fatigue failure. The procedure is well suited to explicitly relate statistical characteristics to classical stress-life analyses.