A Proctor and Gamble Factory Process Fills Boxes with Detergent

question 41

Essay

A Proctor and Gamble factory process fills boxes with detergent. Construct an appropriate set of control charts to monitor the process. Historical data for fill weight (in ounces) of eight samples is presented below. A sample size of eight was used. $$\begin{array} { | c | c | c | } \hline \text { Sample } & \text { Sample Mean } & \text { Sample Range } \\\hline 1 & 15.80 & 0.42 \\\hline 2 & 16.10 & 0.38 \\\hline 3 & 16.02 & 0.08 \\\hline 4 & 15.95 & 0.15 \\\hline 5 & 16.12 & 0.42 \\\hline 6 & 16.18 & 0.23 \\\hline 7 & 15.87 & 0.36 \\\hline 8 & 16.20 & 0.40 \\\hline\end{array}$$
a.Compute the limits for both an R-chart and x-bar chart. Compare the sample results to the limits of the charts.
b.Briefly explain what the quality control charts tell you. What actions, if any, would you take?

---

Definitions:

Losses

Financial reductions resulting from the operation of a business, particularly when expenses exceed revenues.

Shut Down

In economics, shut down refers to a short-term decision by a firm to cease production because operating costs exceed the revenue generated, particularly when prices fall below variable costs.

Increasing-Cost Industry

An industry in which costs of production increase as output is increased, often due to factors like limited resources or higher input prices.

LRAC Curve

Stands for Long-Run Average Cost curve, which shows the lowest average cost of producing different levels of output when all inputs, including capital, are variable.