economically designed Hotelling's T2 control chart using VSICL scheme

The Hotelling's T² control chart, is the most widely used multivariate procedure for 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 T² values has been proved to have a very good performance on detecting small to moderate shifts when it is compared to the original T² control chart. Moreover, it has been shown that the VSI scheme is more economical than the classical one. This paper studies the economic consequences of a new control scheme named variable sampling intervals and control limits (VSICL) in that the sampling interval h and control limit k vary between minimum and maximum values while keeping the sample size fixed over time. We apply the cost model proposed by Costa and Rahim [8]. Furthermore, we assume that the length of time that the process remains in control is exponentially distributed which allows us to apply the Markov chain approach for developing the cost model. We apply genetic algorithm to determine the optimal values of model parameters by minimizing the cost function. Finally, both VSI and VSICL T² control charts are compared with respect to the expected cost per unit time.