Question

You are working in a small, student-run company that sends out merchandise with university branding to alumni around the world. Every day, you take a sample of 50 shipments that are ready to be shipped to the alumni and inspect them for correctness. Across all days, the average percentage of incorrect shipments is 5 percent. What would be the upper control limit for a p-chart?

a. 0
b. 0.05
c. 0.03082207 d. 0.142466

Answer 1

d. \(0.142466\)

The \(p\) formula (for the proportion of nonconforming units from subgroups that can vary in size):

\(p=\frac{n p}{n}\)

\(\bar{p}=\frac{\sum n p}{\sum n}\)

Defects \(=5 / 100^{*} 50\) [ie \(\left.5 \%\right]\)

\(p=5 / 100 * 50 / 50=0.05\)

To calculate control limits for the \(p\)-chart:

\(\cup C L_{p}, L C L_{p}=\bar{p} \pm 3 \sqrt{\frac{\bar{p}(1-\bar{p})}{\bar{n}}}\)

Upper control limit \(=0.05+3 *\) Squareroot \(\left(0.05^{*}(1-0.05) / 50\right)=0.142466\)