Construct An $\bar { x }$ Chart
Control Chart Constants A Machine Is Supposed to Fill Boxes to a Weight

question 89

Essay

Construct an $\bar { x }$ chart.
Control Chart Constants
$\begin{array}{ccccccc}&\bar{x}&&s&&R\\\hline n & A_{2} & A_{3} & B_{3} & B_{4} & D_{3} & D_{4} \\\hline 2 & 1.880 & 2.659 & 0.000 & 3.267 & 0.000 & 3.267 \\3 & 1.023 & 1.954 & 0.000 & 2.568 & 0.000 & 2.574 \\4 & 0.729 & 1.628 & 0.000 & 2.266 & 0.000 & 2.282 \\5 & 0.577 & 1.427 & 0.000 & 2.089 & 0.000 & 2.114 \\6 & 0.483 & 1.287 & 0.030 & 1.970 & 0.000 & 2.004 \\7 & 0.419 & 1.182 & 0.118 & 1.882 & 0.076 & 1.924 \\8 & 0.373 & 1.099 & 0.185 & 1.815 & 0.136 & 1.864 \\9 & 0.337 & 1.032 & 0.239 & 1.761 & 0.184 & 1.816 \\10 & 0.308 & 0.975 & 0.284 & 1.716 & 0.223 & 1.777 \\\hline\end{array}$

A machine is supposed to fill boxes to a weight of 50 pounds. Every 30 minutes a sample of four boxes is tested; the results are given below.
$\begin{array} { c | c c c c | c | c } \text { Sample } &&& { \text { Beight (lb) } } && \overline { \boldsymbol { x } } & \text { Range } \\\hline 1 & 49 & 38 & 39 & 45 & 42.75 & 11 \\2 & 52 & 51 & 43 & 61 & 51.75 & 18 \\3 & 56 & 60 & 32 & 52 & 50.00 & 28 \\4 & 44 & 59 & 46 & 49 & 49.50 & 15 \\5 & 51 & 61 & 48 & 45 & 51.25 & 16 \\6 & 45 & 50 & 46 & 48 & 47.25 & 5 \\7 & 52 & 51 & 45 & 55 & 50.75 & 10 \\8 & 40 & 50 & 53 & 48 & 47.75 & 13 \\9 & 48 & 67 & 60 & 51 & 56.50 & 19 \\10 & 43 & 50 & 50 & 47 & 47.50 & 7 \\11 & 48 & 30 & 38 & 39 & 38.75 & 18 \\12 & 50 & 46 & 48 & 53 & 49.25 & 7 \\13 & 50 & 58 & 56 & 64 & 57.00 & 14 \\14 & 47 & 52 & 47 & 49 & 48.75 & 5 \\15 & 52 & 57 & 58 & 52 & 54.75 & 6\end{array}$

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Definitions:

Liquidation

The process of closing a business and distributing its assets to claimants.

Noncash Assets

Assets that cannot be easily converted to cash, such as property, equipment, and investments, often used for operational purposes.

Income Ratios

Financial metrics that compare different aspects of a company's income to other figures, typically used to assess financial performance and efficiency.

Liabilities

Financial obligations or debts that are owed by a business to another entity, which are settled over time through the transfer of economic benefits including money, goods, or services.