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

Authors: D.R. Prajapati; Sukhraj Singh

Addresses: Department of Mechanical Engineering, PEC University of Technology, Chandigarh-160012, India ' Department of Mechanical Engineering, BBSBEC, Fatehgarh Sahib, 140407, Punjab, India

Abstract: 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 X 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 X and R chart is suggested in this paper, which can be more useful at the shop floor level. The design of modified joint X 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 X 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 X and R chart makes it suitable for the industries where the data are highly correlated.

Keywords: quality control; x-bar charts; R charts; sample size; warning limit; level of correlation; process mean; process variance; process monitoring; simultaneous monitoring; control charts; statistical process control; SPC.

DOI: 10.1504/IJPQM.2015.070193

International Journal of Productivity and Quality Management, 2015 Vol.16 No.1, pp.70 - 91

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 21 May 2015 *

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