Determine the Difference between Bias and Unbias Comparison in Economic Statistical Design of T^2_FRS and T^2_VSS Control Charts

The Hotelling s T^2 control chart, is the most widely used multivariate procedure for monitoring two or more related quality characteristics. Recently, the variable sampling sizes (VSS) control scheme has been proved to have a very good performance on detecting small to moderate shifts when it is compared to the fixed ratio sampling (FRS) T^2 control scheme. Moreover, it is shown that the VSS scheme is more economical than the FRS scheme. It is applied the cost model proposed by Lorenzen and vance (1986). Furthermore, it is assumed that the length of time that the process remains in control is exponentially distributed which allows applied the Markov chain approach for developing the cost model. It is applied genetic algorithm to determine the optimal values of model parameters by minimizing the cost function. This paper studies unbias comparison between Economic Statistical design T^2_FRS and T^2_VSS control charts with respect to the expected cost per unit time