A Control Chart for Monitoring Variation and Center Can Be $\overline {s}$

question 77

Essay

A control chart for monitoring variation and center can be based on standard deviations instead of on ranges.
An s chart for monitoring variation is made by plotting sample standard deviations with a centerline at $\overline {s}$ (the
mean of the sample standard deviations) and control limits at $\mathrm { B } _ { 4 } \overline { \mathrm { s } } \text { and } \mathrm { B } _ { 3 } \overline { \mathrm { s } }$ , where $\mathrm { B } _ { 4 } \text { and } \mathrm { B } _ { 3 }$ are found in the
Control Chart Constants table. Construct an s chart for the data below.
A manufacturer of lightbulbs picks 10 lightbulbs at random each day for quality control. The mean, standard
deviation, and range (in hours) of the lifetimes of the 10 lightbulbs are calculated. The results for 12 consecutive
days are shown in the table below. $$\begin{array} { c | c | c | c } \text { Day } & \bar { x } & \text { Range } & \mathrm { s } \\\hline 1 & 201.1 & 3.4 & 1.2 \\2 & 203.4 & 4.7 & 1.7 \\3 & 200.9 & 3.1 & 0.9 \\4 & 205.6 & 6.2 & 2.3 \\5 & 201.3 & 4.7 & 1.3 \\6 & 200.5 & 3.7 & 1.7 \\7 & 205.8 & 5.8 & 2.1 \\8 & 203.7 & 6.2 & 2.9 \\9 & 199.8 & 2.1 & 0.8 \\10 & 202.7 & 4.4 & 1.6 \\11 & 200.0 & 2.7 & 0.7 \\12 & 204.6 & 7.8 & 3.0\end{array}$$

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Definitions:

Syllogism

A kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.

Unflattering View

An opinion or perspective that is not favorable or complimentary.

Human Reasoning

The process through which individuals draw conclusions and make decisions based on information, past experiences, and logical thinking.

Syllogism's Conclusion

The final part of a syllogism, consisting of a statement that logically follows from the two premises.