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Journal of Korean Society for Quality Management 1994;22(1): 82-. |
| X Control Charts under the Second Order Autoregressive Process |
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| ABSTRACT |
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When independent individual measurements are taken both $S/c_4$ and $ar{R}/d_2$ are unbiased estimators of the process standard deviation. However, with dependent data $ar{R}/d_2$ is not an unbiased estimator of the process standard deviation. On the other hand $S/c_4$ is an asymptotic unbiased estimator. If there exists correlation in the data, positive(negative) correlation tends to increase(decrease) the ARL. The effect of using $ar{R}/d_2$ is greater than $S/c_4$ if the assumption of independence is invalid. Supplementary runs rule shortens the ARL of X control charts dramatically in the presence of correlation in the data. |
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