The role of quality engineering is not a hardware technology but a software technology to find just one numerical number to measure the distance of functionability of hardware from the ideal function.
Discussed here is to use Mahalanobis distance as a numerical number to measure the distance of any input-pattern from each nominal pattern for pattern recognition.
This type of soft technology would be one of the most important areas in future engineering fields.
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.