A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results: $$\begin{array} { r }
{ \text { Service Life (hours) } }\
\begin{array} { l l l l l }
\text { Sample } & \
\hline 1 & 495 & 500 & 505 & 500 \
2 & 525 & 515 & 505 & 515 \
3 & 470 & 480 & 460 & 470
\end{array}\end{array}$$ If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control?
A) sample 1
B) sample 2
C) sample 3
D) both samples 2 and 3
E) all samples are in control

Question

A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results: $$\begin{array} { r } 
 { \text { Service Life (hours) } }\
\begin{array} { l l l l l } 
\text { Sample } & \
\hline 1 & 495 & 500 & 505 & 500 \
2 & 525 & 515 & 505 & 515 \
3 & 470 & 480 & 460 & 470
\end{array}\end{array}$$ If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control?
A) sample 1
B) sample 2
C) sample 3
D) both samples 2 and 3
E) all samples are in control

Quizplus · Accepted Answer

The lower control limit is 480 hours, and the upper control limit is 520 hours. Sample 3 has a mean of 470 hours, which is below the lower control limit. Therefore, service life appears to be out of control for sample 3.

A Design Engineer Wants to Construct a Sample Mean Chart