Title: An effective joint X-bar and R chart to monitor the process mean and variance

Authors: D.R. Prajapati, P.B. Mahapatra

Addresses: Department of Mechanical Engineering, Punjab Engineering College, Chandigarh – 160012, India. ' Department of Mechanical Engineering, Punjab Engineering College, Chandigarh – 160012, India

Abstract: When the shift occurs in both sample mean and standard deviation of a process, a joint X-bar and R charts can be used to monitor the process mean and variance. This paper deals with very simple and effective design of proposed X-bar and R charts to monitor the process mean and standard deviation. The concept of the proposed chart is based upon the sum of chi-square (χ²) to compute and compare Average Run Length values (ARLs). Although Variable Sample Size (VSS), Variable Sampling Interval (VSI) and Variable Sample Size and Sampling Interval (VSSI) joint charts are very useful to catch the small shifts in the mean or standard deviation, they make the chart more complex and very difficult to use at shop-floor level. The performance of the proposed chart has been compared with VSS, VSI and VSSI joint schemes proposed by Costa (1999).

Keywords: average run length; ARL; chi-square max; VSS; VSI; VSSI joint schemes; X-bar charts; R charts; control charts; SPC; statistical process control; variable sample size; variable sampling interval; process monitoring; process mean; variance; productivity; quality management; qaulity control.

DOI: 10.1504/IJPQM.2007.013339

International Journal of Productivity and Quality Management, 2007 Vol.2 No.4, pp.459 - 474

Available online: 21 Apr 2007 *

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