A quality analyst wants to construct a control chart for determining whether four machines, all producing the same product, are under control with regard to a particular quality attribute. Accordingly, she inspected 1,000 units of output from each machine in random samples, with the following results: $$\begin{array} { l c }
\text { Machine } & \text { Total Defectives } \
\hline \# 1 & 23 \
\# 2 & 15 \
\# 3 & 29 \
\# 4 & 13
\end{array}$$ What are the control chart upper and lower control limits for an alpha risk of .05?
A) .0272 and .0128
B) .0287 and .0113
C) .029 and .013
D) .0303 and .0097
E) .0332 and .0068

Question

A quality analyst wants to construct a control chart for determining whether four machines, all producing the same product, are under control with regard to a particular quality attribute. Accordingly, she inspected 1,000 units of output from each machine in random samples, with the following results: $$\begin{array} { l c } 
\text { Machine } & \text { Total Defectives } \
\hline   \# 1 & 23 \
\# 2 & 15 \
\# 3 & 29 \
\# 4 & 13
\end{array}$$ What are the control chart upper and lower control limits for an alpha risk of .05?
A) .0272 and .0128
B) .0287 and .0113
C) .029 and .013
D) .0303 and .0097
E) .0332 and .0068

Quizplus · Accepted Answer

The control limits for a p-chart are calculated using the formula: $ \bar{p} \pm Z \sqrt{\frac{\bar{p}(1-\bar{p})}{n}} $, where $ \bar{p} $ is the average proportion defective, $ Z $ is the Z-value for the desired confidence level (1.96 for 95%), and $ n $ is the sample size. Here, $ \bar{p} = \frac{23+15+29+13}{4000} = 0.02 $. Plugging in the values, the control limits are approximately 0.0287 and 0.0113.

A Quality Analyst Wants to Construct a Control Chart for Determining