Monitoring of process mean and variance simultaneously by joint X and R chart for serial correlation

It is assumed that the presence of the assignable cause may shift either process mean or standard deviation from their target value. But in the design of joint X̄ and R charts, it is assumed that, both mean and standard deviation of the process change simultaneously. So, for simultaneous monitoring of the process mean and standard deviation, a modified joint X̄ and R chart is suggested in this paper, which can be more useful at the shop floor level. The design of modified joint X̄ and R chart is based upon the sum of chi-squares theory. The performance of joint chart is measured in terms of average run lengths (ARLs) and compared with the joint Shewhart chart and residuals charts, suggested by Karaoglan and Bayhan (2011) for sample size of ten. It is observed that the joint modified X̄ and R chart outperforms all the residual charts at the highest level of correlation, i.e., Φ = 0.95. The simplicity and robustness in the design of the modified joint X̄ and R chart makes it suitable for the industries where the data are highly correlated.