Among innovations and improvements occurred in the past two decades on the techniques and tools used for statistical process control (SPC), adaptive control charts have shown to substantially improve the statistical and/or economical performances. Variable sampling intervals (VSI) control charts are one of the most applied types of the adaptive control charts and have shown to be faster than traditional Shewhart control charts in identifying small changes of concerned quality characteristics.

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... ile in the designing procedure of the VSI control charts the data or measurements are assumed independent normal observations, in real situations, the validity of these assumptions is under question in many processes. This paper develops an economic-statistical design of a VSI X-bar control chart under non-normality and correlation. Since the proposed design consists of a complex nonlinear cost model that cannot be solved using a classical optimization method, a genetic algorithm (GA) is employed to solve it. Moreover, to improve the performances, response surface methodology (RSM) is employed to calibrate GA parameters. The solution procedure, efficiency, and sensitivity analysis of the proposed design are demonstrated through a numerical illustration at the end. 1 Corresponding author substantially faster than their FSI versions in detecting small shifts (e.g., Reynolds et al., 1988; Park & Reynolds, 1999) . Following Chiu's (1975) cost model, Bai & Lee (1998) presented the economic design of the VSI X control charts. Chen (2003) used Bai & Lee's model (1998) and employed the Burr distribution for developing an economic-statistical design of VSI X control charts with symmetric control limits. Chen (2004) presented the economic model of VSI X control charts with asymmetric control limits. For correlated samples, Chen and Chiou (2005) developed the economic model of the VSI X control charts with a combination of the multivariate normal distribution model given by Yang & Hancock (1990) and the cost model of Bai & Lee (1998). Recently Torng et al. (2010) evaluated the performances of the double sampling VSI X control charts under non-normality. Finally, Chen & Yeh (2010) developed an economic design of the VSI X control charts for non-normal data with Burr distribution under gamma failure models. In this research, an economic-statistical design for VSI X control charts in presence of correlation and non-normality is proposed to not only be applicable to closer to reality environments, but also to have desire economic and statistical performances as well. Since the obtained cost function is a complex nonlinear model, a genetic algorithm (GA) is used to solve it and obtain the optimal values of the design parameters. As the quality of a solution obtained by GA usually depends on its control parameters, the response surface methodology (RSM) is used for calibration. The remainder of the paper is organized as follows. In the next section, the concept of the VSI control charts is briefly discussed. In Section 3, the Burr distribution that is used to model non-normal process data is briefly introduced. The model assumptions along with model development come in Section 4. The effects of correlation and non-normality are discussed in