Ten samples of size four were taken from a process, and their weights measured. The sample averages and sample ranges are in the following table. Construct and plot an x-bar and R-chart using this data. Is the process in control?
$120.010.45219.980.67320.250.30419.900.30520.350.36619.230.49720.010.53819.980.40920.560.951019.970.79\begin{array} { |l | l | l | } \hline \text { Sample } & \text { Mean } & \text { Range } \\\hline 1 & 20.01 & 0.45 \\\hline 2 & 19.98 & 0.67 \\\hline 3 & 20.25 & 0.30 \\\hline 4 & 19.90 & 0.30 \\\hline 5 & 20.35 & 0.36 \\\hline 6 & 19.23 & 0.49 \\\hline 7 & 20.01 & 0.53 \\\hline 8 & 19.98 & 0.40 \\\hline 9 & 20.56 & 0.95 \\\hline 10 & 19.97 & 0.79 \\\hline\end{array}$

Question

Ten samples of size four were taken from a process, and their weights measured. The sample averages and sample ranges are in the following table. Construct and plot an x-bar and R-chart using this data. Is the process in control?

120.010.45219.980.67320.250.30419.900.30520.350.36619.230.49720.010.53819.980.40920.560.951019.970.79\begin{array} { |l | l | l | } \hline \text { Sample } & \text { Mean } & \text { Range } \\\hline 1 & 20.01 & 0.45 \\\hline 2 & 19.98 & 0.67 \\\hline 3 & 20.25 & 0.30 \\\hline 4 & 19.90 & 0.30 \\\hline 5 & 20.35 & 0.36 \\\hline 6 & 19.23 & 0.49 \\\hline 7 & 20.01 & 0.53 \\\hline 8 & 19.98 & 0.40 \\\hline 9 & 20.56 & 0.95 \\\hline 10 & 19.97 & 0.79 \\\hline\end{array}

ARSHDEEP SINGH · Accepted Answer

Final Answer :   X-bar   Range   X-doublebar value  20.024  R bar  0.524  Uper control limit  20.406 1.196  Center line  20.024 0.524  Lower control limit  19.642 0 \begin{array} { | l | l | l | } \hline  &  	ext { X-bar }  &  	ext { Range } \\hline 	ext { X-doublebar value }  &  20.024  &  \\hline  &   &  \\hline  	ext { R bar }  &  0.524  &  \\hline &   &  \\hline 	ext { Uper control limit }  &  20.406  &  1.196 \\hline 	ext { Center line }  &  20.024  &  0.524 \\hline	ext { Lower control limit } & 19.642 & 0\\hline\end{array}  X-doublebar value   R bar   Uper control limit   Center line   Lower control limit  ​  X-bar  20.024 0.524 20.406 20.024 19.642 ​  Range  1.196 0.524 0 ​ ​     The x-bar chart is out of control because samples 6 and 9 are outside of the control limit, and therefore the process is out of control.

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