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

question 45

Essay

Construct an R chart and determine whether the process variation is within statistical control.
Control Chart Constants $\text { Control Chart Constants }$

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

A machine that is supposed to fill small bottles to contain 20 milliliters yields the following data from a test of 4 bottles every hour.

$\begin{array}{c|cccc|c|l}\text { Sample } &&&{\text { bottle Volume (oz) }} && \overline{\boldsymbol{x}} & \text { Range } \\\hline 1 & 19.9 & 20.1 & 20.2 & 20.3 & 20.125 & 0.4 \\2 & 20.4 & 20.0 & 20.3 & 20.3 & 20.250 & 0.4 \\3 & 20.0 & 20.7 & 20.4 & 20.3 & 20.350 & 0.7 \\4 & 20.4 & 20.1 & 20.1 & 19.9 & 20.125 & 0.5 \\5 & 19.9 & 19.8 & 19.6 & 19.5 & 19.700 & 0.4 \\6 & 19.4 & 19.4 & 19.6 & 19.7 & 19.525 & 0.3 \\7 & 19.8 & 19.4 & 19.6 & 19.7 & 19.625 & 0.4 \\8 & 19.9 & 19.8 & 20.0 & 20.0 & 19.925 & 0.2 \\9 & 20.2 & 20.3 & 20.1 & 20.3 & 20.225 & 0.2 \\10 & 20.0 & 20.3 & 20.0 & 20.2 & 20.125 & 0.3 \\11 & 20.3 & 20.5 & 20.1 & 20.2 & 20.275 & 0.4 \\12 & 20.1 & 19.9 & 19.8 & 19.7 & 19.875 & 0.4 \\13 & 19.5 & 19.8 & 19.7 & 19.6 & 19.650 & 0.3 \\14 & 19.4 & 19.8 & 19.8 & 19.4 & 19.400 & 0.4 \\15 & 19.5 & 19.6 & 19.6 & 19.9 & 19.650 & 0.4\end{array}$

Analyze the effects of selling noncash assets and settling liabilities on the partnership’s final cash distribution.

Comprehend the concept of safe payments and how they are determined during the liquidation process.

Apply the profit and loss sharing ratios to determine individual partners' shares of profits, losses, and liquidation proceeds.

Evaluate the liquidation process, including the preparation and interpretation of the Statement of Liquidation.

---

Definitions:

Event A

A specified outcome or set of outcomes of a random experiment.

Random Variable

A variable whose values are numerical and result from randomness.

Probability Distribution

A function in mathematics that offers the chances of various outcomes happening in an experiment.

Average Profit

The mean amount of profit earned, calculated by dividing the total profit by the number of units sold or the period over which the profit was earned.