Control limits are one of the main elements of control charts. Generally speaking, a control chart is the graphical display of a statistic regarding the quality characteristic of interest, computed from a sample randomly drawn from a process at different time instances. As natural variability is always present in a process, we expect some variability on the control chart. Excessive variability, owing to special cause events, is referred to as being due to an assignable cause. Otherwise, when only chance causes – also called common causes of variation – are operating, the process is said to be in statistical control. In order to make a decision about the status of the process, control limits are typically positioned so that under the hypothesis of no deviation in the process, a type I probability error corresponds to an economically acceptable average run length. In this article, we discuss in a general manner how to compute control limits, and give some remarks on how limits should be computed so as to reduce false out of control signals.
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