Cost Optimization Models for Multivariate Control Charts

The ability of businesses and industries to produce high quality products and services at a low cost is becoming increasingly important in determining the success and sustainability of businesses and industries. Thus, management is always keen to find ways to reduce the cost of improving quality. Control charts are one of the important tools used in monitoring and controlling quality based on statistical principles. However, the cost of implementing control charts can be high. Thus, this paper proposes cost optimization models which minimize the cost of implementing various multivariate control charts. Multivariate control charts are applied in a lot of processes where several variables need to be controlled concurrently in order to properly monitor the output quality of a production process or product. The multivariate control charts considered in this paper are the synthetic T 2 , Hotelling's T 2 and Multivariate Exponentially Weighted Moving Average (MEWMA) charts. The cost optimization models involve the formulation of the cost function and the algorithms to minimize the cost function. Through the cost optimization models proposed in this paper, the optimal design parameters of the various charts, i.e. the chart parameters which minimize the cost of implementing the control chart, are obtained. Comparison among the three charts show that the synthetic T 2 chart is the most economical to be implemented, followed by the MEWMA and Hotelling's T 2