In every other field, the model of "have a dysfunctional process, test every output piece, throw out or rework 5-30% of the pieces" is discredited. General Motors could get away with it before they got Japanese competition, but not after.
Post Deming we know the way you get quality is build it into your process. Formal methods are part of that (hopefully will be a bigger on in the future) but there is a lot you can do to build quality in from day one.
Software is different in certain ways, but it is the same more than people think. There is a contradiction between "trying to do something fast and cheap" and quality, but not a contradiction between "completing the project economically" and quality -- look at your own experience and you will see that screwing up is very expensive.