Machine learning (ML) is opening up new opportunities for the development of innovative systems across a wide range of industries. However, assessing and ensuring the quality of systems with ML components introduces unique challenges related to inherent characteristics of such components like data centricity and unpredictable behavior. Traditional software quality assessment and assurance methods may not be sufficient for ML systems: (1) they focus on software code, while ML systems' quality is influenced by the characteristics of the data and the algorithms used to create ML components; (2) they do not cover the emerging quality characteristics specific to ML systems, such as interpretability, explainability, fairness and trustworthiness. This PhD project aims to develop a comprehensive approach for assessing and assuring the quality of ML systems, with a focus on bias detection and prevention. The research will (1) explore the problem of bias in production ML systems; (2) analyze the gaps in existing software quality models and methods related to bias detection and prevention; and (3) propose an improved approach to quality assessment and assurance to address the challenges associated with bias in ML systems. The results of this PhD project are expected to contribute to the development of better models and methods for assessing and assuring the quality of ML systems, as well as have practical implications for industries that rely on ML systems to automate complex tasks, facilitate decision-making processes and gain insights from large amounts of data.