Construct an R Chart and Determine Whether the Process Variation $\text { Control Chart Constants }$

question 89

Essay

Construct an R chart and determine whether the process variation is within statistical control. $\text { Control Chart Constants }$
$\quad$$\quad$$\quad$$\quad$$\quad$$\bar{x}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$ $\boldsymbol{s}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$ $\boldsymbol{R}$
$\begin{array}{ccccccc}\hline n & A_{2} & A_{3} & B_{3} & B_{4} & D_{3} & D_{4} \\\hline 2 & 1.880 & 2.659 & 0.000 & 3.267 & 0.000 & 3.267 \\3 & 1.023 & 1.954 & 0.000 & 2.568 & 0.000 & 2.574 \\4 & 0.729 & 1.628 & 0.000 & 2.266 & 0.000 & 2.282 \\5 & 0.577 & 1.427 & 0.000 & 2.089 & 0.000 & 2.114 \\6 & 0.483 & 1.287 & 0.030 & 1.970 & 0.000 & 2.004 \\7 & 0.419 & 1.182 & 0.118 & 1.882 & 0.076 & 1.924 \\8 & 0.373 & 1.099 & 0.185 & 1.815 & 0.136 & 1.864 \\9 & 0.337 & 1.032 & 0.239 & 1.761 & 0.184 & 1.816 \\10 & 0.308 & 0.975 & 0.284 & 1.716 & 0.223 & 1.777 \\\hline\end{array}$
A machine that is supposed to produce ball bearings with a diameter of 7 millimeters yields the following data from a test of 5 ball bearings every 20 minutes.
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Ball Bearing Diameter }(\mathrm{mm} \text { ) }$
$\begin{array}{c|ccccc|c|c|}\text { Sample } &&&&& & \bar{x} & \text { Range } \\\hline 1 & 6.3 & 6.8 & 6.9 & 6.8 & 6.9 & 6.74 & 0.6 \\2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0 & 6.56 & 0.7 \\3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.80 & 0.5 \\4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.80 & 0.3 \\5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4 & 6.62 & 0.4 \\6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9 & 6.66 & 0.6 \\7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0 & 7.28 & 0.4 \\8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1 & 7.08 & 0.3 \\9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.40 & 0.5 \\10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.40 & 0.5 \\11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0 & 7.16 & 0.4 \\12 & \quad7.5 \quad& 7.4 & 7.4 & 7.6 & \quad 7.1 \quad& 7.40 & 0.5\end{array}$

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Definitions:

Sold

The completion of a transaction where goods or services are exchanged for money.

Conversion Cost

The combined costs of direct labor and manufacturing overhead required to convert raw materials into finished products.

November

The eleventh month of the year in the Gregorian calendar, usually consisting of 30 days.

Variable Cost

Outlays that fluctuate based on the level of a business's activity.