Economic Design of T² Control Charts to Maintain Current Control of a Process

An approximate cost model for a quality control procedure for two or more related variables is investigated. A method is presented to determine the optimal sample size, interval between samples, and critical region parameter for the Hotelling T² control chart. This model is a multivariate analog of several well-known models for the univariate X\bar -chart. It is assumed that only one assignable cause of variation exists and the time between occurrences is exponentially distributed. Numerical results are provided in a particular bivariate case for several values of the cost coefficients. The behavior of the model to variation of the model parameters is discussed.