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==Quality control==
Alternative [[quality control]]<ref>Duncan AJ. Quality control and industrial statistics. Irwin, Illinois 1986: pp 1-1123.</ref> (QC) procedures can be applied on a [[process]] to [[test]] statistically the [[null hypothesis]], that the process is in control, against the alternative, that the process is [[out of control]]. When a true [[null hypothesis]] is rejected, a statistical type I error is committed. We have then a false rejection of a run of the process. The probability of a type I error is called probability for false rejection. When a false null hypothesis is accepted, a statistical type II error is committed. We fail then to detect a significant change in the distribution of error in the process. The probability for rejection of a false [[null hypothesis]] is called probability for error detection.
The QC procedure to be designed or optimized can be formulated as:
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