A Quality Analyst Wants to Construct a Sample Mean Chart

question 152

Essay

A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from past experience that the process standard deviation is two ounces. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below. $$\begin{array} { | l | l | l | l | l | } \hline & { \text { Weight } } \\\hline \text { Day } & \text { Package } 1 & \text { Package } 2 & \text { Package 3 } & \text { Package 4 } \\\hline \text { Monday } & 23 & 22 & 23 & 24 \\\hline \text { Tuesday } & 23 & 21 & 19 & 21 \\\hline \text { Wednesday } & 20 & 19 & 20 & 21 \\\hline \text { Thursday } & 18 & 19 & 20 & 19 \\\hline \text { Friday } & 18 & 20 & 22 & 20 \\\hline\end{array}$$ (a) Calculate all sample means and the mean of all sample means.
(b) Calculate upper and lower control limits that allow for natural variations.
(c) Is this process in control?

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Definitions:

Homolytically

Referring to homolytic cleavage, a process where a chemical bond is evenly split and each of the bonded atoms retains one of the shared electrons.

ΔS°

Represents the standard entropy change of a reaction, indicating the variation of randomness or disorder in a system at standard conditions.

Combustion

A chemical reaction where a substance combines with oxygen to release heat and often light.

Bond Dissociation Energies

The energy required to break a bond homolytically, resulting in two radical fragments, important for understanding reaction kinetics.