OMIS $442$ SPC Homework Assignment $2$

Garcia's Garage desires to create some colorful charts and graphs to illustrate how reliably its

mechanics "get under the hood and fix the problem". The historical average for the proportion

of customers that return for the same repair within the $30-$day warranty period is $0\mathrm{.}10.$ Each

month, Garcia tracks $100$ customers to see whether they return for warranty repairs. The

results are plotted as a proportion to report progress toward the goal. Determine the control

limits for this chart. In March, $8$ of the $100$ customers in the sample group returned for

warranty repairs. Is the repair process in control? $(20$ points$)$

Janice Sanders, CEO of Pine Crest Medical Clinic, is concerned over the number of times

patients must wait more than $30$ minutes beyond their scheduled appointments. She asked her

assistant to take random samples of $64$ patients to see how many in each sample had to wait

more than $30$ minutes. Each instance is considered a defect in the clinic process. The table

below contains the date from $15$ samples.

a$.$ Assuming Janice Sanders is willing to use three$-$sigma control limits$,$ construct a p$-$chart.

points$)$

b$.$ Based on your p$-$chart and the data in the table, what can you conclude about the waiting

time of the patients? $(10$ points$)$