Software engineering is a discipline of Computer Science in which the new sub-areas are constantly added, especially in the area of quality, data management, and architectural design. Nowadays software development languages and processes are rapidly changing to deliver high-quality software products, i.e., usable systems, hybrid, and fulfill users' needs. This paper aims to identify and classify different process models proposed by the researchers based on characteristics of software quality, data management, and software integration and redesign. From a study of several models through a systematic mapping study, we identify different parameters and presented them in a traceability matrix. The parameters are classified into six areas. This paper provides an in-depth theoretical insight into the models and characteristics. A systematic mapping study was conducted through a literature review. The methodology used in this paper is both qualitative and quantitative. Initially, through a systematic mapping study, we study different models working on different parameters. And then proposed a model that can cover all the aspects of software implementation and management. We select ERP systems for it. Later we perform the GAP analysis and statistical evaluation of the model. It has been observed that all of the models are area specific either focused on quality parameters or management issues or architectural-based. The proposed model covers all aspects. The primary research shows that industrialists also need a better model for quality implementation. Our statistical analysis can serve as a decision-making tool for them to add to their decision-making processes. The other could use it to further enhance the framework for quality management. This model will enhance further in the future for better implementation.