Suppose thatf(t; θ) is the density function of the time to failure random variable of a device under an environment defined by a vector of generalized stressesS. It is desired to predict θu, the value of θ at some low values of .the stress, saySu. The elements of θ are re-parameterized as a function ofS, such that θj=fi(S;aj), wherefjare known functions and the ai are unknown. Life tests are conducted atkdifferent accelerated values ofS,Si(i= 1, 2, …k), and estimates of the elements of θ, θji, are obtained from item censored samples. These estimates are then used to obtain point and interval estimates ofai, using either the method of least squares, or the method of maximum likelihood. Having obtained the estimates ofai, an inference about θu, can be made. Some problems in obtaining the least squares estimates ofaiare pointed out in this paper. To illustrate this, an unrealistic but simple case is treated and discussed in this paper. It is assumed thatf(t; θ) = λ exp (—λt), and that λi=BVi, where λiis the hazard rate under an environmentVi, andBis unknown. A weighted least squares estimator forBis obtained, and it is shown that asymptotically this estimator converges in distribution to that of a unit normal. The maximum likelihood estimator forBis shown to have an inverted gamma dist.ribution. Properties of the estimator of λuare discussed.