Quality assurance is a field in which statistical techniques and problem-solving methods are used in order to achieve and improve quality. In this project, important topics in quality assurance will be investigated in the context of Bayesian statistics and decision analysis. The first topic to be addressed is Statistical Process Control. Control charts based on posterior distributions and credibility intervals for quality indexes will be defined and analyzed. The second topic to be explored is the motivation underlying assessments of probability distributions traditionally adopted in quality assurance. These models will be derived by analyzing the physics behind the manufacturing systems. Often, it is necessary to use diagnostic tests in order to decide whether or not items coming from a production line are conforming to requirements. The third topic to be studied is the calibration of diagnostic tests based on censored data. Quality is a key factor leading to success, growth and enhanced competitive position. There is always a substantial return on investment from any effective program designed to improve quality. These programs result in increased market penetration, higher productivity and lower overall costs of manufacturing and services.