Context: The increasing dependence of our society on software driven systems has led Software Reliability to become a key factor as well as making it a highly active research area with hundreds of works being published every year. It would, however, appear that this activity is much more reduced as regards how to apply representative international standards on Product Quality to industrial environments, with just a few works on Standard Based software reliability modeling (SB-SRM). This is surprising given the relevance of such International Standards in industry. Objective: To identify and analyze the existing works on the modeling of Software Reliability based on International Standards as the starting point for a reliability assessment proposal based on ISO/IEC-25000 "Software Product Quality Requirements and Evaluation" (SQuaRE) series. Method: The work methodology is based on the guidelines provided in Evidence Based Software Engineering for Systematic Literature Reviews (SLR). Results: A total of 1820 works were obtained as a result of the SLR search, more than 800 primary studies were selected after data filtering. After scrutiny, over thirty of those were thoroughly analyze, the results obtained show a very limited application of SB-SRM particularly to industrial environment. Conclusion: Our analysis point to the complexity of the proposed models together with the difficulties involved in applying them to the management of engineering activities as a root cause to be considered for such limited application. The various stakeholder needs are also a point of paramount importance that should be better covered if the industrial applicability of the proposed models is to be increased. (C) 2015 Elsevier B.V. All rights reserved.