In recent years, statistical theory has become widely used in the study of reliability. In this study, we shall consider two types of estimators, namely, the Bayes and minimum variance unbiased estimators for the scale parameter θ in the truncated Weibull life testing model when the shape parameter ρ assumed known. In addition, we shall estimate the corresponding reliability function of the above estimators. The first type of estimator of θ and the reliability function we will consider is the Bayes estimator using the general uniform, exponential, and inverted gamma distributions as prior probability density functions for the parameter θ, We shall also derive the minimum variance unbiased estimator (MVUE). For each prior probability density function, the Bayes estimator is compared with the MVUE by Monte Carlo simulation. Also, the Bayes estimators for a given prior density of θ are compared with the results of Canavos and Tsokos [5]. Their model was the Weibull probability density function with guaranteed time τ. / M.S.