Optimal Design of a Revised Double Sampling X ̅ Chart Based on Median Run Length

Fachrur Rozi, Udjianna S. Pasaribu, Utriweni Mukhaiyar, Dradjad Irianto

Abstract

In process control, it is very important to have a tool that is able to detect small shifts of a process mean. The revised double sampling  chart is more effective than a standard Shewhart chart in detecting small to moderate shifts of a process mean. To optimize this type of chart, the average run length is widely used because of its simplicity and consistency. Nevertheless, the skewness of the run length distribution changes along with the process mean shift. Furthermore, its average is confusing and not necessarily a good representation of control chart performance. Because this distribution is highly right-skewed, especially when the shift is small, it is argued that its median provides a more intuitive and fair representation of the central tendency of the distribution. Based on an in-control median run length and average sample size, this paper investigates the behavior of control limit parameters to obtain the optimal parameters with a minimized out-of-control median run length. The parameters obtained were used to construct an example of this chart that was illustrated with real data.

 

Keywords: median run length, process mean shift, revised double sampling  chart, run length distribution.


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References


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