To have quality built into a new product is very important. Here are a few processes that people have used or are using to try to ensure quality. Some of them have come more from a manufacturing perspective, rather than a design perspective, and so may have to be adapted to be suitable for product development.
Total Quality Management.
Lean Six Sigma
Design for Six Sigma
Advanced Product Quality Planning. Big in the automotive industry
Methodology developed by Taguchi.
Failure Mode Avoidance
Method for avoiding failures by better design