A hybrid Nelder–Mead simplex and PSO approach on economic and economic-statistical designs of MEWMA control charts

Economic design of a control chart involves determining its basic parameters such that a cost function is minimized. This design when statistical performance measures are also considered is referred to as the economic-statistical design. In this paper, a simplex-based Nelder–Mead algorithm is used in combination with a particle swarm meta-heuristic procedure to solve both the economic and economic-statistical designs of a MEWMA control chart. The application results on extensive simulation experiments show that the particle swarm can lead the Nelder–Mead algorithm to better results. Furthermore, a comparative study is performed on the performances of three different algorithms of the Nelder–Mead, the particle swarm optimization (PSO), and the hybrid PSO and Nelder–Mead (PSO–NM). In this study, five different performance measures are taken into consideration and the results for both the economic and the economic-statistical models are reported at the end.