ARL1 of the Attribute c Control Chart with Estimated Parameter

International audience

<p>In this paper, the out of control average run length (ARL1) of the c control chart with estimated parameter is computed for various shifts in the average number of nonconformities. In spite of the discrete nature of this chart, it is proved that a target in-control average run length (ARL0) can be obtained when the average number of nonconformities is estimated. This is a good starting point for comparing the performances of the c control chart with those of other attribute control charts with estimated parameters. Based on the computational results obtained, it is showed that the ARL1 of the c control chart with estimated parameter can be approximated by using a polynomial expression.</p>