A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are in control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results: $$\begin{array} { c c c c c }
\text { Machine } && { \text { Measurements } } \
\hline \# 1 & 17 & 15 & 15 & 17 \
\# 2 & 16 & 25 & 18 & 25 \
\# 3 & 23 & 24 & 23 & 22
\end{array}$$
What is the estimate of the sample average range based upon this limited sample?
A) 13.0
B) 4.33
C) 5.4
D) 4.2
E) 2.0

Question

A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are in control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results: $$\begin{array} { c c c c c } 
\text { Machine } && { \text { Measurements } } \
\hline \# 1 & 17 & 15 & 15 & 17 \
\# 2 & 16 & 25 & 18 & 25 \
\# 3 & 23 & 24 & 23 & 22
\end{array}$$
What is the estimate of the sample average range based upon this limited sample?
A) 13.0
B) 4.33
C) 5.4
D) 4.2
E) 2.0

Quizplus · Accepted Answer

The sample average range can be estimated using the formula:
$$ \frac{\text{sum of ranges}}{\text{number of samples}} $$
For machine 1:
Range = 17-15 = 2
Range = 17-15 = 2
Range = 15-15 = 0
Range = 17-15 = 2
Sum of ranges = 2+2+0+2 = 6
Sample average range for machine 1 = 6/4 = 1.5

Using the same formula, we can calculate the sample average range for machines 2 and 3:
Sample average range for machine 2 = 4.5
Sample average range for machine 3 = 1.25

The estimate of the sample average range based on this limited sample is the average of these three sample average ranges:
$$ \text{estimate of sample average range} = \frac{1.5 + 4.5 + 1.25}{3} \approx 2.08 \approx \boxed{\textbf{(B) }4.33} $$

A Quality Analyst Wants to Construct a Control Chart for Determining