A manufacturer of lightbulbs picks 10 lightbulbs at random each day for quality control. The mean 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. Construct an R chart to determine whether the process is in statistical control. $$\begin{array} { c | c | c | c }
\text { Day } & \overline { \boldsymbol { x } } & \text { Range } & \boldsymbol { s } \
\hline 1 & 201.1 & 3.4 & 1.2 \
2 & 203.4 & 4.7 & 1.7 \
3 & 200.9 & 3.1 & 0.9 \
4 & 205.6 & 6.2 & 2.3 \
5 & 201.3 & 4.7 & 1.3 \
6 & 200.5 & 3.7 & 1.7 \
7 & 205.8 & 5.8 & 2.1 \
8 & 203.7 & 6.2 & 2.9 \
9 & 199.8 & 2.1 & 0.8 \
10 & 202.7 & 4.4 & 1.6 \
11 & 200.0 & 2.7 & 0.7 \
12 & 204.6 & 7.8 & 3.0
\end{array}$$
A) The process is not within statistical control.
B) The process is within statistical control.

Question

A manufacturer of lightbulbs picks 10 lightbulbs at random each day for quality control. The mean 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. Construct an R chart to determine whether the process is in statistical control. $$\begin{array} { c | c | c | c } 
\text { Day } & \overline { \boldsymbol { x } } & \text { Range } & \boldsymbol { s } \
\hline 1 & 201.1 & 3.4 & 1.2 \
2 & 203.4 & 4.7 & 1.7 \
3 & 200.9 & 3.1 & 0.9 \
4 & 205.6 & 6.2 & 2.3 \
5 & 201.3 & 4.7 & 1.3 \
6 & 200.5 & 3.7 & 1.7 \
7 & 205.8 & 5.8 & 2.1 \
8 & 203.7 & 6.2 & 2.9 \
9 & 199.8 & 2.1 & 0.8 \
10 & 202.7 & 4.4 & 1.6 \
11 & 200.0 & 2.7 & 0.7 \
12 & 204.6 & 7.8 & 3.0
\end{array}$$ 
A) The process is not within statistical control. 
B) The process is within statistical control.

Quizplus · Accepted Answer

To construct the R chart, we first calculate the average range and plot the range values for each day. From the chart below, we can see that all the plotted points are within the control limits, indicating that the process is in statistical control.

![image.png](attachment:image.png)

Therefore, the correct choice is B), the process is within statistical control.

A Manufacturer of Lightbulbs Picks 10 Lightbulbs at Random Each