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A simple method for optimal X-chart design

A simple but efficient method has been developed for the design of <img border=0 id="_x0000_i1029" src="/img/revistas/gp/v5n3/a04img01.gif">-charts. The solutions provided are optimal in terms of the ratio between the number of items inspected per unit time and the detection speed (defined as the inverse of the average time to signal a shift in the mean). The method is superior to design procedures based exclusively on statistical properties of the chart (such as the ARL), and does not have the implementation drawbacks of economical design models. The results obtained differ from some results widely reported in the literature, which are shown to be sub-optimal as a consequence of their underlying model not considering some important aspects of the problem. An additional contribution of the method is the explicit treatment of optional constraints on the sample size and/or on the interval between samples. The ease of use of the method makes its implementation straightforward in any environment, and also makes it suitable for the classroom.

<img border=0 id="_x0000_i1030" src="/img/revistas/gp/v5n3/a04img01.gif">-chart; Shewhart charts; control chart design; semi-economic design; statistical process control; statistical quality control


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