Reliability is the key factor for software system quality. Several models have been introduced to estimate and predict reliability based on results of software testing activities. Software Reliability Growth Models (SRGMs) are considered the most commonly used to achieve this goal. Over the past decades, many researchers have discussed SRGMs’ assumptions, applicability, and predictability. They have concluded that SRGMs have many shortcomings related to their unrealistic assumptions, environment-dependent applicability, and questionable predictability. Several approaches based on non-parametric statistics, Bayesian networks, and machine learning methods have been proposed in the literature. Based on their theoretical nature, however, they cannot completely address the SRGMs’ limitations. Consequently, addressing these shortcomings is still a very crucial task in order to provide reliable software systems. This paper presents a well-established prediction approach based on time series ARIMA (Autoregressive Integrated Moving Average) modeling as an alternative solution to address the SRGMs’ limitations and provide more accurate reliability prediction. Using real-life data sets on software failures, the accuracy of the proposed approach is evaluated and compared to popular existing approaches.