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: $$\begin{array} { c c c c c }
\text { Machine } &&{ \text { Measurements } } \
\hline \# 1 & 17 & 15 & 15 & 17 \
\# 2 & 16 & 25 & 18 & 25 \
\# 3 & 23 & 24 & 23 & 22
\end{array}$$
For upper and lower control limits of 23.29 and 16.71, which machine(s), if any, appear(s) to have an out-of-control process mean?
A) machine #1
B) machine #2
C) machine #3
D) all of the machines
E) none of the machines

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: $$\begin{array} { c c c c c } 
\text { Machine } &&{ \text { Measurements } } \
\hline \# 1 & 17 & 15 & 15 & 17 \
\# 2 & 16 & 25 & 18 & 25 \
\# 3 & 23 & 24 & 23 & 22
\end{array}$$
For upper and lower control limits of 23.29 and 16.71, which machine(s), if any, appear(s) to have an out-of-control process mean?
A) machine #1
B) machine #2
C) machine #3
D) all of the machines
E) none of the machines

Quizplus · Accepted Answer

To determine whether any machine is out of control, we need to calculate the mean and standard deviation of each machine's measurements.

Machine #1: 
Mean = (17+15+15+17)/4 = 16 
Standard deviation = 1

Machine #2: 
Mean = (16+25+18+25)/4 = 21 
Standard deviation = 4.44

Machine #3: 
Mean = (23+24+23+22)/4 = 23 
Standard deviation = 0.71

Using the given upper and lower control limits of 23.29 and 16.71, we can see that machine #1's mean of 16 falls outside the limits, indicating that it is out of control. The means of machines #2 and #3 fall within the control limits, so they appear to be in control.

Therefore, the best choice is A) Machine #1, which appears to have an out-of-control process mean.

A Quality Analyst Wants to Construct a Control Chart for Determining