A Multiobjective Optimization for the Ewma and Mewma Quality Control Charts

The Multivariate EWMA control chart, MEWMA, Lowry, Woodall, Champ and Ridgon [1] and its univariate version EWMA, may be designed to efficiently detect small shifts in the mean vector of a set of p quality characteristics of a production process. However, this work presents a method for the optimal design of MEWMA and EWMA charts parameters to control processes where it is not convenient to detect small magnitude shifts and, at the same time, powerful enough to detect shifts considered important. This problem can be considered as a multiobjective optimization. Woodall [2] studied the statistical design of control charts and recommended choosing the magnitude of the shift that it is important to detect as a design criterion for control charts. For this purpose, he suggested defining three regions: incontrol, indifferent, and out-of-control. These regions will be delimited by two values (A and B). The main objective of this paper is to find the best MEWMA and EWMA quality control charts given the previous regions, where the requirements for each region has to be balanced to decide which solution is better. For this purpose, friendly Windows software has been developed to optimize this problem, using Genetic Algorithms. A comparison is made among the EWMA chart designed employing this software, the typical design of a EWMA chart and the Shewhart control chart. Results show that the design using our approach outperforms the other designs.