Quality assurance through statistical methods is a key component in a manufacturing organization where TQM generally starts by sampling a random selection selection of the product. The sample can then be tested for things that matter most to the end users. The causes of any failures of any failures are isolated secondary measures of the production process are designed, and then the cause of the failure are corrected. The statistical distributions of important measurements are tracked. When parts measures drift into a defined error band teh process is fixed. The error band is usually a tighter distribution than the failure band so that the production process is fixed before failing parts can be produced.
It took people a while to develop tests to find emergent problems. One popular testis a life test in which the sample product is operated until a part fails. Another popular testis called shake and bake in which the product is mounted on a vibrator in an environmental oven, and operated at progressively more extreme vibration and temperatures until something fails. The failures is then isolated and engineers design an improvement.