A Computer Optimization of a Set of EWMA Quality Control Charts EUGENIO EPPRECHT 1 , FRANCISCO APARISI 2 , MARCO A. DE LUNA 3 , ANDRÉS CARRIÓN 2 1 Departamento de Engenharia Industrial Pontificia Universidade Católica de Río de Janeiro Río de janeiro, BRASIL eke@puc3rio.br 2 Departamento de Estadística e Investigación Operativa Aplicadas y Calidad. Universidad Politécnica de Valencia Valencia, SPAIN faparisi@eio.upv.es, acario@eio.upv.es 3 Departamento de Inegeniaría Industrial y Mecánica ITESM, Campus Guadalajara Guadalajara, MÉXICO. mdeluna@itesm.mx   Two main approaches are possible when several correlated variables must be monitored: one multivariate quality control chart or a set of univariate charts. This paper deals with the optimal design of a set of EWMA control charts to monitor the mean of several quality variables simultaneously. A specific Markov’s chain model has been developed to compute the ARL of a set of  EWMA charts. An optimization is carried out using Genetic Algorithms in order to find the optimal parameters of the EWMA charts, implemented in friendly software. The result of the optimization are the values of the parameters of the EWMA charts that minimize the out3of3control ARL for a specified shift, while respecting the constraint of a specified in3control ARL.        ! 1 Introduction The simultaneous statistical control of several correlated quality variables has been widely studied [1]. Essentially, two main approaches can be employed: 1) To control each variable with one control chart. For example, a set of " control charts, CUSUM or EWMA charts. 2) To employ a single multivariate control chart. Multivariate control charts have the advantage of allowing setting easily the false3alarm rate. On the other hand, some disadvantages are found. The main disadvantage is that the use of multivariate charts is more complicated in comparison with univariate control charts. Another issue is the interpretation of the out3of3control signal. The multivariate chart signals, but there is no indication of the variable(s) that have changed. However, some research has been done to overcome this problem [2, 3, 4, 5, 6]. When comparing the performance of both schemes (multivariate vs. multiple) no clear winner is found. One scheme will be better than the other in some circumstances. For example, for a given shift in the process to be monitored a multivariate chart may be the best option. However, for a different shift a well designed set of univariate charts may outperform the equivalent multivariate chart. Therefore, there is interest in a good design of a set of univariate charts, because for some industries/processes this will be the best option. A most usual measure of performance of a control charting procedure is the average run length (ARL). It is defined as the expected number of samples (points on the chart) until an out3of3control signal. The out3of3 control ARL (ARL1) is the average number of samples until a true alarm; the in3control ARL (ARL0) is the average number of samples until a false alarm. A good design of a process control scheme is one that keeps the in3control ARL at an acceptable level and achieves small out3of3control ARLs for shifts that are considered relevant and should be quickly detected. This paper deals with the design of a set of EWMA control charts for the statistical control of the mean vector of a set of correlated variables. The first work has been developing a Markov’s chain model to obtain the ARL of a set of EWMA control charts. When the model was finished, the optimization of the parameters Proceedings of the 9th WSEAS International Conference on APPLICATIONS of COMPUTER ENGINEERING ISSN: 1790-5117 93 ISBN: 978-960-474-166-3