Title: Effect of warning limits on the performance of the X chart under autocorrelation

Authors: Sukhraj Singh; D.R. Prajapati

Addresses: Department of Mechanical Engineering, PEC University of Technology, Chandigarh-160012, India ' Department of Mechanical Engineering, PEC University of Technology, Chandigarh-160012, India

Abstract: X charts for variables are one of the outstanding charts of statistical quality control (SQC), used to detect larger shifts in the process mean. In actual practice, many processes are autocorrelated and if these charts are used, their performance is deteriorated. The performance of the chart is measured in terms of the average run length (ARL), which is the average number of samples before getting an out-of-control signal. The ARLs at various sets of parameters of the X chart are computed by simulation, using MATLAB. An attempt has been made to counter autocorrelation by designing the X chart using warning limits. Various optimal schemes are proposed for different levels of correlation (Φ). Moreover these optimal schemes of modified X chart are compared with Derman-Ross's (Derman and Ross, 1997) and Klein's (2000) schemes at various levels of correlation (Φ). It is concluded that the modified X scheme outperforms the Derman-Ross's (2 of 2) scheme.

Keywords: traditional X charts; warning limits; average run length; ARL; independent data; identically distributed data; autocorrelation; MATLAB; control charts; statistical quality control; SQC.

DOI: 10.1504/IJPQM.2014.059175

International Journal of Productivity and Quality Management, 2014 Vol.13 No.2, pp.235 - 250

Published online: 17 May 2014 *

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