Multivariate cumulative sum control chart and measure of process capability based on bivariate ranked set schemes

In this article we have proposed multivariate cumulative sum control chart based on bivariate ranked set schemes for quick identification of small variation in the process mean vector. Also, we have offered multivariate measure of process capability based on bivariate ranked set schemes for testing the customer requirements. In the construction of control chart, we have designed plotting statistic, and derived control limit. Regarding the multivariate measure of process capability, we have defined an estimator and then computed the critical values for inference purposes. In order to compare the performance of existing and proposed control charts, we have obtained various performance measures. Results reveal that performance of proposed control chart based on bivariate ranked set schemes depends on the choice of the factors such as sampling scheme, sample size, magnitude of association between concomitant variable and study variables, and size of the shift. Furthermore, comparative analysis shows that the performance of the proposed control chart based on bivariate ranked set schemes outperforms the existing methods. Finally, real life example is included in which we have applied proposed and existing control charts for monitoring calcium–magnesium and residual sodium contents in irrigation water. In addition, the implementation of the proposed multivariate measure of process capability ensures the level of calcium–magnesium and residual sodium contents in irrigation water to satisfy the requirements of customers or engineering tolerance.