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

question 121

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$$\quad$ $\boldsymbol{R}$
$\begin{array}{ccccccc}\hline n & A_{2} & A_{3} & B_{3} & B_{4} & D_{3} & D_{4} \\\hline 2 & 1.880 & 2.659 & 0.000 & 3.267 & 0.000 & 3.267 \\3 & 1.023 & 1.954 & 0.000 & 2.568 & 0.000 & 2.574 \\4 & 0.729 & 1.628 & 0.000 & 2.266 & 0.000 & 2.282 \\5 & 0.577 & 1.427 & 0.000 & 2.089 & 0.000 & 2.114 \\6 & 0.483 & 1.287 & 0.030 & 1.970 & 0.000 & 2.004 \\7 & 0.419 & 1.182 & 0.118 & 1.882 & 0.076 & 1.924 \\8 & 0.373 & 1.099 & 0.185 & 1.815 & 0.136 & 1.864 \\9 & 0.337 & 1.032 & 0.239 & 1.761 & 0.184 & 1.816 \\10 & 0.308 & 0.975 & 0.284 & 1.716 & 0.223 & 1.777 \\\hline\end{array}$
A machine is supposed to fill cans that contain 12 ounces. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below.
$\text { Sample }\mid$ $\quad \text { ~~~Can Volume (oz) } \quad\mid$$\quad\overline{\boldsymbol{~~x}} \quad\mid$$\text { Range }$
$\begin{array}{c|cccc|c|c}\hline 1& 11.2 & 11.7 & 11.8 & 11.7 & 11.600 & 0.6 \\ 2 & 11.8 & 11.3 & 11.6 & 11.6 & 11.575 & 0.5 \\3 & 11.3 & 12.0 & 11.8 & 11.7 & 11.700 & 0.7 \\4 & 12.1 & 11.6 & 12.1 & 12.0 & 11.950 & 0.5 \\5 & 11.8 & 11.8 & 11.9 & 11.9 & 11.850 & 0.1 \\6 & 12.0 & 11.9 & 11.8 & 11.7 & 11.850 & 0.3 \\7 & 11.6 & 12.0 & 11.9 & 11.8 & 11.825 & 0.4 \\8 & 11.5 & 12.1 & 11.9 & 12.0 & 11.875 & 0.6 \\9 & 12.1 & 12.1 & 11.7 & 11.9 & 11.950 & 0.4 \\10 & 11.7 & 12.0 & 11.6 & 11.9 & 11.800 & 0.4 \\11 & 12.1 & 12.4 & 11.9 & 12.2 & 12.150 & 0.5 \\12 & 12.5 & 12.0 & 12.4 & 12.3 & 12.300 & 0.5 \\13 & 12.5 & 12.0 & 12.1 & 12.1 & 12.175 & 0.5 \\14 & 12.4 & 12.0 & 12.0 & 12.4 & 12.200 & 0.4 \\ \quad15 \quad& 12.4 & 12.4 & 12.6 & 12.1 & 12.375 & 0.5\end{array}$

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Definitions:

Net Present Value

A calculation that compares the value of money now with the value of that money in the future, accounting for inflation and returns.

Lockbox System

A service offered by banks to companies for the receipt of payment from customers, involving the collection and processing of cheque payments at a secure location.

Collection Time

The average period a company takes to collect payments owed by its customers.

Lockbox Fee

A charge by banks for the service of collecting payments through a secured post office box and processing them for the account holder.