(Situation E) a Machine at K-Company Fills Boxes with Bran

question 77

Essay

(Situation E) A machine at K-Company fills boxes with bran flake cereal. The target weight for the filled boxes is 24 ounces. The company would like to use control charts to monitor the performance of the machine. The company decides to sample and weigh 10 consecutive boxes of cereal at randomly selected times over a two-week period. Twenty measurement times are selected and the following information is recorded. $$\begin{array} { c c c c c c } \hline \text { Time } & \text { Mean (oz) } & \text { Range (oz) } & \text { Time } & \text { Mean (oz) } & \text { Range (oz) } \\\hline 1 & 23.8 & 1.05 & 11 & 24.5 & 1.21 \\2 & 24.5 & 0.85 & 12 & 24.7 & 0.65 \\3 & 23.9 & 1.12 & 13 & 24.0 & 0.55 \\4 & 24.2 & 0.95 & 14 & 25.5 & 3.21 \\5 & 23.7 & 1.22 & 15 & 24.2 & 1.25 \\6 & 23.5 & 1.42 & 16 & 24.4 & 1.35 \\7 & 24.2 & 1.02 & 17 & 24.5 & 0.98 \\8 & 24.4 & 1.10 & 18 & 25.0 & 1.30 \\9 & 24.1 & 0.75 & 19 & 24.1 & 0.88 \\10 & 24.2 & 0.60 & 20 & 24.2 & 1.01\end{array}$$
-Calculate the centerline of the $\mathrm { R } - \text { chart }$

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Definitions:

True Power

The actual power consumed by a circuit, calculated as the product of the voltage, current, and the cosine of the phase angle between them in a resistive load, measured in watts.

Series RL Circuit

An electrical circuit composed of resistors (R) and inductors (L) connected in a series configuration, affecting the phase and amplitude of the circuit's response.

Inductive Reactance

The resistance offered by an inductor to alternating current, which varies with the frequency of the current and the inductance, also measured in ohms.

Power Factor

A dimensionless number between 0 and 1 that represents the ratio of the real power flowing to the load to the apparent power in the circuit.