There are misunderstandings on the philosophy and approaches in quality engineering. These are causes by the confusion of mathematical statistics with quality engineering.
For example, the way of treating a statistic such as standard deviation in mathematical statistics is based on the distribution of a population. In engineering application however, it is almost impossible in most cases to conjecture the distribution. Because of this, the statistic must be treated based on a measured value something that is physically measurable.
This paper states the role of mathematical statistics in quality engineering and clarifies the differences between the two through the cases of process control, product inspection, the diagnosis of human health, the role of orthogonal arrays and new product development.
