Summary: Suppose that the distribution of the life time of the products follows the two-parameter exponential law $ε(λ, μ)$, in which $λ>0$ is the scale parameter (failure rate), and $μ>0$ is the location parameter (life guarantee). Under the stress $S\sb i$, the failure rate accelerated model and the life guarantee accelerated model are $$\ln θ\sb i = β\sb 0 + β\sb 1 φ\sb 1 (S\sb i) + β\sb 2 φ\sb 2 (S\sb i) \quad \text { and } \quad μ\sb i = α\sb 0 - α\sb 1 f(S\sb i), i = 1,2, \dots, k, \text { respectively}.$$ We have given the statistical analysis of type I censoring data from the constant-stress accelerated life testing method. We obtain the approximate BLUEs (best linear unbiased estimators) of the coefficients $β\sb 0, β\sb 1, β\sb 2, α\sb 0$ and $α\sb 1$. Using the two models, we can obtain the estimators of the various reliability characteristics under the usual stress $S\sb 0$. The results of random simulation show that the method given above is of higher precision.