Is there a conflict between Quality and Cost control?

the better the quality, the lowest the cost.

cost control is an activity or process to control cost, in general quality affect in anything to get the optimal solution, and best cost.

the relation between quality and cost, not cost control is quality reduce cost, as the target of quality to detect problems early and solve it, but without quality the problem may be detected at the end, so it will require to restart from the beginning, so it will costs what has been done twice, ....

it is a Reverse process