How can a project manager be sure that he

or she has chosen the correct metrics to assess project performance? I need a few examples please.

The focus ought to be on cost, schedule, and quality performance. In my experience, cost follows schedule. So if the focus is on getting the job done right, on time, cost will fall in line.

Schedule is best served by monitoring task completion on a critical path or PERT analysis at task level. Getting requisite supplies in on time is managed following the same PERT analysis. Performance to quality standary is again monitoring task level by QA (indpendent of workers) on the PERT task level.

I have also used GAANT, but for complex tasks, PERT analysis is very valuable.