Effectiveness of Conventional CUSUM Control Chart for Correlated Observations

—Control charts, one of the important tools of quality control, are also known as Shewhart charts or process behavior charts. Page (1954) was the first, who introduced the Cumulative Sum (CUSUM) control charts for detection of process shifts and claimed that these charts are more efficient compared to Shewhart chart to detect small shifts in the process average. Various schemes of the CUSUM chart for autocorrelated data for sample size of 4 are developed and compared with the schemes of the Shewhart X chart for autocorrelated data. It is found that CUSUM chart outperforms the Shewhart X chart for all the shifts and at all the levels of correlation (Φ) for sample size (n) of four. So, the CUSUM control chart is much better option for faster detection in the process mean. NOMENCLATURE Following symbols have been used in this paper: μ o = Target mean xi = Observation, i n = Sample size ARL = Average Run Length UCL = Upper control limit = Shi(i) LCL = Lower control limit = Slo(i) Φ = Level of correlation h= decision interval for CUSUM chart k = slack variable for CUSUM chart

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