Quality is everyone's job, and you can perceive it from different point of views.
The success rate of project is very low, as most of projects can not be delivered on value or reaching customer satisfaction. So how to manage project quality, and who shall take such responsibility?
You have to define what you mean by 'quality'. Then the required quality with all its aspects (product quality, quality of project management etc.) should be defined or described in the project start documents. Then you have to get support for project quality. If you get no support from management, then you will probably fail. There are so many things, outside of the project team, that can make a project fail, or affect the quality of a project. Even though management assigns a PM to a project, or incorporates a PO into the infrastructure, they are still responsible for the success of the project.
All stakeholders are responsible for quality. Everyone has some role in quality , but responsibility lies with PM. He/She is the one who should monitor the quality at every stage of project and take corrective actions whereever necessary. More specifically, quality is the main process of PM and when project is initialed, each needed deliverable has to have the named people in charge of the delivery and the named people in charge of the validation. Then, everybody becomes in charge of the quality with a responsibility for PM to follow-up deliveries and validations.
The PM should monitor quality and take corrective measures when necessary and possible. The PM manages his/her project on behalf of the owner of the business case/chairman of the steering committee/CIO. The Product Owner/Acceptant has a responsibility for the quality from a result point of view. The Production department has a responsibility for the quality in terms of manageability of the product/result. It’s PM's responsibility to manage the three most basic aspects of a project
SCOPE, cost and time. SCOPE management along with cost and time management (within budget and time limit completion of project may also be considered as external quality features of project) is the actual role of PM.
There’s idea of having separate quality anchor for the project; so that there is correct focus on quality parameters, while PM can track it. Having Quality manager work on the project will be best suitable for exceeding or meeting quality expectations on project. While everyone is playing their part, but still responsibility should lie with quality manager. In most companies the "project owner" is not concerned with the day to day development of the product, service or solution and as such will not have the skills required to assess quality, they are normally the "front guy" and more concerned with selling than developing. That is why you need a quality manager who understands the definition of quality as it applies to the product, service or solution and who has the power to make sure that the required quality is achieved. This is a vital role in modern business and one that is overlooked by many companies.
Quality is everyone's job, and you can see from different point of views, but the levels of authority and influence to get to quality are highly variable, project manager or the assigned quality manager should be in charge of overall quality of the project, from the quality plan, control till the final validation via a user integrated test. Beyond PM, there is project leader and PMO, who is in charge of the key decision making, and all members of the project should use qualitative methods and measures, but the responsibility lies with the product owner.