Why Eliminate Quality Inspection?
I think everyone has their own different interpretation of Deming's 14 principles. I believe the only nation who really master and truly understand these principle was Japan. Throughout time, the Japanese developed these principles as today world's most admired management tools - Lean Manufacturing. The ideology behind the 14 principles is having a positive impact on Quality, Cost, & Delivery.
Some people challenge why Dr.Deming suggested to eliminate quality inspection?
Because data collection or additional inspection of quality is what end customer want? Why didn't companies build their product with quality in mind in the first place?
Think deeper: Inspection incurs additional touch; every touch incurs additional cost and risk. This is what exactly Lean Manufacturing quotes as "muda" (waste in Japanese).