• Proceedings of the Korean Statistical Society Conference
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• 2003.10a
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• pp.97-103
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• 2003

Shewhart-type control charts have historically been used for attribute data, though they have ARL biased property and even are unable to detect the improvement of a process with some process parameters. So far most efforts have been made to improve the performance of attribute control charts in terms of faster detection of special causes without increasing the rates of false alarm. In this paper, control limits are proposed that yield an ARL (nearly) unbiased chart for attributes. Optimal design is also proposed for attribute control charts under a natural sense of criterion.

• Journal of Korean Society for Quality Management
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• v.22 no.1
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• pp.82-95
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• 1994

When independent individual measurements are taken both $S/c_4$ and $\bar{R}/d_2$ are unbiased estimators of the process standard deviation. However, with dependent data $\bar{R}/d_2$ 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 $\bar{R}/d_2$ 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.