Darshan,
quality depends on many things, some more related to cost and time, some less. The design plays a key role, stakeholder engagement/customer expectation management influences the perceptions, experience and attitudes of project team members may create high quality and, yes, how you define and measure quality.
Anyhow, composing your team with quality-aware designers, developers, and tester will almost certain reducse cost and time of the project.
On the other hand, as a project manager, you should try to resist cost pressure. Your negotiation skills may help.