For the Statistical Process Control homework assignment, you will do $($from the book$)$

$1.$ Problem $15$ p$.129($Pine Crest Medical Clinic$)$

$2.$ Problem $18$ p$.130($Red Baron Airlines$)$

$-$ In problem $18,$ you should compute control limits using p$-$bar computed from the data.

$-$ DO NOT compute control limits using $\backslash ($ p $\backslash )-$bar $\backslash (=\mathrm{.}02\backslash )$ based on management's target of $\backslash (98\backslash \%\backslash )$ on$-$time performance. Despite the text's statement on p$.108,$ valid control limits are never based on "a target that managers would like the process to achieve." $($We don't need SPC philosophy to tell us whether we are or are not meeting some arbitrary target! We need SPC to tell us whether our process is in control vs$.$ out of control. Meeting some target established by management does not mean the process is $"$in control"! Not meeting such a target does not mean the process is "out of control"!$)$

In each problem you should compute the control limits$,$ construct the p$-$chart, and interpret what the chart is telling you. You may use Excel to construct the chart if you wish. The video below demonstrates how you can do this. $($Be sure you can also compute the control limits manually!$)$

$15.$ 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 data for $15$ samples.

a$.$ Assuming Janice Sanders is willing to use threesigma control limits$,$ construct a $\backslash ($ p $\backslash )-$chart.

b$.$ Based on your $\backslash ($ p $\backslash )-$chart and the data in the table, what can you conclude about the waiting time of the patients? $18.$ Red Baron Airlines serves hundreds of cities each day, but competition is increasing from smaller companies affiliated with major carriers. One of the key competitive priorities is on$-$time arrivals and departures. Red Baron defines on time as any arrival or departure that takes place within $15$ minutes of the scheduled time. To stay on top of the market, management set the high standard of $98$ percent on$-$time performance. The operations department was put in charge of monitoring the performance of the airline. Each week, a random sample of $300$ flight arrivals and departures was checked for schedule performance. Table $3\mathrm{.}6$ contains the numbers of arrivals and departures over the last $30$ weeks that did not meet Red Baron's definition of on$-$time service. Using three$-$sigma control limits based on $98$ percent on time arrivals or departures, what can you tell the management about the quality of service? Can you identify any nonrandom behavior in the process? If so$,$ what might cause the behavior? TABLE $3\mathrm{.}6\backslash (\backslash$mid $\backslash )$ SAMPLE DATA FOR RED BARON AIRLINES