Computation of ARL for Combined Individual Measurement and Moving Range Charts

Summary: A numerical procedure is presented for the tabulation of average run lengths (ARLs) of a control chart for individual measurements in combination with a moving range chart based on two consecutive measurements. An exact expression for the ARL is given in terms of an integral equation, approximated using numerical quadrature. ARLs are given for various settings of the control limits and shifts in the nominal level of the process mean and standard deviation. A control chart design strategy is presented.