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Software failure remains an important cause of reported system outage. Yet, developing reliable software is still not well understood by the programmer, the Software Engineer and the Program manager. Software reliability growth models (SRGMs) provide a framework to analyze software failures by using past failure data to predict the reliability of the software. Most models that have been used have limitations in predicting accurately. There is a need to conduct research aimed at improving the performance of these models. To accurately predict reliability, the model's parameters should be estimated in such a way that the mathematical function of the model fits with the failure data. While the majority of previous software reliability studies have used classical methods to estimate model's parameters, a few other studies have used a Bayesian approach. Bayesian approaches allow the incorporation of prior information into models and they have been claimed to be more successful than classical approaches in certain situations. Our research goal is to investigate if the use of Bayesian methods improves the predictability of SRGMs by conducting a direct comparative analysis of Bayesian and classical approaches for software reliability assessment.