A Mixed Cumulative Sum-Tukey’s Control Chart for Detecting Process Dispersion
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Abstract
The objective of this research is to propose a mixed Cumulative Sum-Tukey Control Chart (CUSUMTCC) for detecting process dispersion using the range, when the process is symmetric and asymmetric distributions.The performance of CUSUM-TCC is compared with Tukey’s Control Chart (TCC), Cumulative Sum Control Chart (CUSUM) and Exponentially Weighted Moving Average -Tukey Control Charts (EWMATCC), measured by the Average Run Length (ARL). The in control Average Run Length (ARL0) is given to 370 and 500. In order to approximate ARL, the Monte Carlo simulation method is used and the numerical results reveal that CUSUM-TCC is superior to TCC, CUSUM and EWMA-TCC for all cases of asymmetric distributions. However, for the case of ARL0 = 370 sample n = 1 and 5 and the process has laplace distribution, the performance of EWMA-TCC is superior to the mixed CUSUM-TCC and other control charts when the magnitudes of change in dispersion parameter δ ≤ 1.6. In addition, for the case of ARL0 = 500 sample n = 1 and 5 the EWMA-TCC performs better than the mixed CUSUM-TCC and other control charts for all magnitudes of change.
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