Title: Statistical design of X charts for autocorrelated processes for different sample sizes

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: The X charts for variables are widely used in industries to detect the shift in the process mean. As in actual practice, some process outputs are correlated and conventional charts may not be effective in such situation. The performance of the chart is measured in terms of the average run length (ARL) that is the average number of samples before getting an out-of-control signal. Ultimately the performance of the chart is suspected due to the effect of correlation. 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 of modified X chart are proposed for various sample sizes (n) at the levels of correlation (Φ) of 0.00, 0.475 and 0.95. These optimal schemes of modified X chart are compared with the double sampling (DS) X chart, suggested by Costa and Claro (2008). It is concluded that the modified X chart outperforms the DS chart at various levels of correlation (Φ) and shifts in the process mean. The simplicity in the design of modified X chart makes it versatile for many industries.

Keywords: quality control; sample size; warning limits; average run length; ARL; double sampling charts; X-bar charts; level of correlation; statistical process control; SPC; simulation; control charts; control chart design; statistical design.

DOI: 10.1504/IJPQM.2014.065550

International Journal of Productivity and Quality Management, 2014 Vol.14 No.4, pp.387 - 407

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 29 Oct 2014 *

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