Exam 10: Variables Control Charts

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The X-bar chart shows the accuracy of the data.
The R chart shows the precision of the data.
Using the R chart in combination with the X-bar chart is critical because together the charts show how the data is grouped (the measure of central tendency) and how the data is spread (the measure of dispersion of the individual values).

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a. 2/3 of the points are near the center value.
b. A few of the points are on or near the center value.
c. The points appear to float back and forth across the centerline.
d. The points are balanced on both sides of the centerline.
e. There are no points beyond the control limits.
f. There are no patterns or trends on the chart.

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Sum of x-bars = 66.34 Sum of R's = 3.5 n = 5
Point 4, X-bar = 9.92, R = 0.6 $$\begin{array} { l } \mathrm{XDB} \text { new }=-\frac{66.34-0.92}{7-1}=\frac{56.42}{6}=9.4\\\mathrm{R} \text { -barnew }=-\frac{3.5-0.6}{7-1}=\frac{2.9}{6}=0.5\\\text { Sigma }=-\frac{\text { Rbarnew }}{\text { d } 2}=-\frac{0}{2.326}=0.2\\U C L x = 9.4 + 1.324 ( 0.2 ) = 9.7 \\\operatorname { LCL } x = 9.4 - 1.324 ( 0.2 ) = 9.1 \\\text { UCLr } = 4.918 ( 0.2 ) = 0.98 \\\text { LCLr } = 0 \\\end{array}$$