Determine the Bias value in Comparison of Economic Statistical Design of T^2_FRS and T^2_VSICL Control Schemes using Genetic Algorithm

The Hotelling s T^2 control chart, a direct analog of the univariate Shewhart X ̅ chart, is perhaps the most commonly used tool in industry for simultaneous monitoring of several quality characteristics. Recent studies have shown that using variable sampling intervals and control limits (VSICL) schemes results in charts with more statistical power when detecting small to moderate shifts in the process mean vector when it is compared to the fixed ratio sampling (FRS) T^2 control scheme. Moreover, it is shown that the VSICL 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_VSICL control charts with respect to the expected cost per unit time.