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The normal distribution is often used a s a model for reliability, and censored samples naturally arise in software reliability applications. Bayesian estimation methods have an advantage over the frequentist approach as they provide the user a framework for incorporating important factors such as software complexity, operating system, level and quality of verification and validation in the software reliability estimation process. Our goal in this paper is to compute the Bayes estimate of the mean of a normal population when the data set is censored . The proposed method is illustrated via several examples.