The term tolerance in project management is very broad. Many people confuse it with the definition for risk or budget tolerance. By definition, it is the quantified description of the acceptable variation for a particular quality requirement.
Project management teams have knowledge about statistical control processes in evaluating data that are contained within the control quality outputs. Tolerance defines the specified range of the acceptable results. It also sets the control limits which identifies the boundaries of the variation in a particular process performance.
As a broad term, tolerance encompasses different aspects of project management. Project managers have to be aware of the tolerance for aspects such as time, cost, scope, risk, quality and benefits to be able to perform the different project activities effectively.
This project management concept allows project managers to go a little over or under within a particular aspect of the project without the need to constantly go to the project sponsor to get new approval. It provides a leeway for the project manager so that they can do more important aspects of their job.
This term is defined in the 5th edition of the PMBOK.