Control charts for monitoring process variability, such as the R-chart and S-chart, do not have symmetric probability limits as the distribution of the sample variability is not normal. Hence, the usual zone rules can not be applied although it is still desirable to be able to use the information from more than one point in decision making. In this paper, a modified S-chart based on an optimal normalizing transformation of the sample variance is first introduced. The new chart is shown to have approximate symmetric probability limits and hence can be interpreted in the same way as that of a ¯ X chart. This modified chart is shown to be comparable with the probability S-chart and have a much better performance than the usual Shewhart S-chart for the cases of known and estimated limits. The effect of parameter estimation is investigated. The optimal normalizing transformation is a simple power transformation. The power parameter depends only on the sample size and approaches 1/3 as the sample size increases. Hence, the transformation S-chart can be easily implemented and integrated into any SPC system.
Monitoring process variability with symmetric control limits. (2002). 1-22. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/2064
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