(Situation A) To construct a p-chart for a manufacturing process, 20 samples of size 100 were selected. The results are shown below: $$\begin{array} { c c c c c c }
\hline \text { Sample } & \text { Sample Size } & \text { Defectives } & \text { Sample } & \text { Sample Size } & \text { Defectives } \
\hline 1 & 100 & 10 & 11 & 100 & 8 \
2 & 100 & 8 & 12 & 100 & 8 \
3 & 100 & 9 & 13 & 100 & 5 \
4 & 100 & 6 & 14 & 100 & 9 \
5 & 100 & 7 & 15 & 100 & 7 \
6 & 100 & 3 & 16 & 100 & 9 \
7 & 100 & 8 & 17 & 100 & 11 \
8 & 100 & 6 & 18 & 100 & 4 \
9 & 100 & 11 & 19 & 100 & 6 \
10 & 100 & 10 & 20 & 100 & 8 \
\hline
\end{array}$$
-Calculate the upper and lower control limits for the p-chart.
A) $\bar { p } \pm .1783$
B)$\bar { p } \pm .0797$
C) $\bar { p } \pm .0532$
D) $\bar { p } \pm .0266$

Question

(Situation A) To construct a p-chart for a manufacturing process, 20 samples of size 100 were selected. The results are shown below: $$\begin{array} { c c c c c c } 
\hline \text { Sample } & \text { Sample Size } & \text { Defectives } & \text { Sample } & \text { Sample Size } & \text { Defectives } \
\hline 1 & 100 & 10 & 11 & 100 & 8 \
2 & 100 & 8 & 12 & 100 & 8 \
3 & 100 & 9 & 13 & 100 & 5 \
4 & 100 & 6 & 14 & 100 & 9 \
5 & 100 & 7 & 15 & 100 & 7 \
6 & 100 & 3 & 16 & 100 & 9 \
7 & 100 & 8 & 17 & 100 & 11 \
8 & 100 & 6 & 18 & 100 & 4 \
9 & 100 & 11 & 19 & 100 & 6 \
10 & 100 & 10 & 20 & 100 & 8 \
\hline
\end{array}$$
-Calculate the upper and lower control limits for the p-chart. 
A) $\bar { p } \pm .1783$
B)$\bar { p } \pm .0797$
C) $\bar { p } \pm .0532$
D) $\bar { p } \pm .0266$

Quizplus · Accepted Answer

The average proportion defective $\bar{p}$ is calculated as the total number of defectives divided by the total number of samples. The standard deviation for the p-chart is $\sqrt{\frac{\bar{p}(1-\bar{p})}{n}}$, where $n$ is the sample size. The control limits are $\bar{p} \pm 3 \times \text{standard deviation}$.

(Situation A) to Construct a P-Chart for a Manufacturing Process