Software engineering is an approach pre-owned by the researchers and innovators to reduce the ratio of crisis in software. Therefore the designer/ innovator can readily design a valuable quality software, by using various approaches like Component-Based Software Engineering (CBSE). The components quality has a high impact on the quality of a whole application. Several quality models for CBSE and Component-Off-The-Shelf (COTS) are available in the literature so this paper presents various quality models with defined parameters for quality prediction. Several models, like, Boehm's, McCall's, FURPS, ISO 9126, Dromey's, have been developed for quality evaluation using hierarchically related characteristics of quality indicators. Over the years, some models have been developed for structuring software quality for software. Nowadays, researchers are showing their passion for innovation in the area of software reliability. The reliability of a software component relies on the following factors like the reliability of services, environment frequency so finally this paper presents the analysis and assessment of software quality models and their quality parameters for CBS by going through various researchers and practitioners' work.