Performance Comparison of Numerical Integral Equation Methods on DMEWMA Control Chart for Moving Average Process Order q

The study's purpose is to approximate average run length (ARL) by using numerical integral equation (NIE) method on double modified EWMA (DMEWMA) control chart for moving average process order q (MA(q)) for checking the least time consuming. The four quadrature or integral rules namely composite midpoint rule, composite trapezoidal rule, composite Simpson's rule, and Gauss-Legendre rule were applied to solve the integral equation. A comparison of the effectiveness of DMEWMA control chart with EWMA control chart and MEWMA control chart are determined. The results show that the Midpoint rule took the least computational time for every shift size of either q=1 or q=2. Furthermore, the DMEWMA control chart performance is better than EWMA and MEWMA control charts except when A is too small where shift size is greater than 0.5.