Bias and Unbias Comparison between Economic Statistical Design T2-VSI and T2-FRS Control Charts

The Hotelling's  control chart, is the most widely used multivariate procedure for monitoring  two or more related quality characteristics, but it’s power lacks the desired performance in detecting small to moderate shifts. Recently, the variable sampling intervals (VSI) control scheme in which the length of successive sampling intervals is determined upon the preceding values 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) control scheme. Moreover, it is shown that the VSI scheme is more economical than the FRS scheme. It is applied the cost model proposed by Lorenzen and vance (1986). This model considers the cost of producing out of control and in of control items, the cost of sampling and testing, the cost of false alarms and the cost of finding and repairing an assignable cause. 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 bias and unbias comparison between Economic Statistical design T2-VSI and T2-FRS control charts with respect to the expected cost per unit time.