Measuring and managing project quality is one of the fundamental problems in project management. In this paper, once project is completed, we define the measure of task’s quality and the measure of overall project quality. We construct mathematical model of the process of quality improvement as the sequence of mutually dependent projects, where every project in the sequence is the revision of its previous one. We prove that it is possible, at certain point, to obtain a project with the highest quality measure and with failures less than the initially given level. The purpose of this paper is, to help companies to achieve the satisfying level of project quality by using the proposed model. According to our knowledge, paper offers an original connection between project management and measure theory potentially interesting to a reader for further research