Improving Bivariate Ranked Set Sampling with Application to Chi-Square Control Chart
Ranked set sampling (RSS) is useful for data collection if observations can be ranked cheaply without actual measurement. RSS has been studied widely but not enough, especially in case of collecting independent interested variables by using multivariate ranked set sampling. There are many problems in the sample selection for this case. One important problem is called “Incomplete Ranked Set Sampling (InRSS)”, which causes bias in estimating mean. Hence, in this study, modified incomplete ranked set sampling (M-InRSS) is proposed for dealing with InRSS in one cycle bivariate RSS for independent bivariate normal distribution. Analytical results reveal that problems of bias and mean square error (MSE) in InRSS can be solved by using M-InRSS. Moreover, how to apply M-InRSS to chi-square control chart is shown with the numerical example of bivariate chi-square control chart based on M-InRSS. The results show that the charts based on M-InRSS are better than based on SRS.