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

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  • D.R. Prajapati
  • Sukhraj Singh

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.

Suggested Citation

  • D.R. Prajapati & Sukhraj Singh, 2014. "Statistical design of X charts for autocorrelated processes for different sample sizes," International Journal of Productivity and Quality Management, Inderscience Enterprises Ltd, vol. 14(4), pages 387-407.
    • Handle: RePEc:ids:ijpqma:v:14:y:2014:i:4:p:387-407
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