The Blue Star Bus Company $($BSBC$)$ is a bus service that recently began offering its

services to a new city, Timely Town. BSBC was able to strike a deal with Timely Town

because they offered discounted rates to all city employees. A main requirement imposed

by Timely Town$$s city council was the buses had to stick to their announced schedule

and run $18$ hours a day, which would mean each route would have three shifts.

BSBC started its operations without any major mishaps. Timely Town was very satisfied

with the bus service. Unfortunately, six months after BSBC started its operations, they

began receiving complaints about excessive wait times at the hospital$$s bus stop. This

problem needed to be addressed in order for BSBC to keep their contract with Timely

Town. Having a superior record in the other cities where their buses run, BSBC had never

felt the need to consider formal process control approaches. However, after receiving a

phone call from the Mayor of Timely Town, Rachelle, the manager of BSBC$$s Timely

Town$$s office, suspected that the growing popularity and increased passenger volumes

were affecting their wait times.

The owner of BSBC decided to hire a third party company, Mystery Riders, Inc., to ensure

the fulfillment of the company$$s contract with the City of Timely Town. Given the culture

of the city, the contract specified that buses are not to run more than $2$ minutes late, with

a tolerance of $0\mathrm{.}125$ minutes. Therefore, the upper and lower specifications are

LSL$=1\mathrm{.}875$ minutes and USL$=2\mathrm{.}125$ minutes. Given that the buses run multiple times an

hour, Mystery Riders, Inc. recommended inspecting the hospital bus stop during five

consecutive loops in the middle of each of three daily shifts, over a $10-$day period. The

wait time at the bus stop would be recorded. Table $1$ shows the data collected for each

route and shift over the $10$ day period. In this initial study, Rachelle wants to have the

following questions answered:

$$ Is the bus route in a state of statistical control? Why or why not?

$$ If the bus route is out of control, what might be the likely cause$($s$)?$ What

recommendations might you make to improve the situation $$ i$.$e$.,$ reduce or

eliminate the cause$($s$)?$

$$ Finally, is BSBC capable of meeting the specifications given? Why or why

not?

After taking into consideration the results of the initial study, Rachelle decided to

implement your suggestions. Because of the success in using control charts, BSBC

decided to continue using them on their daily operations, at multiple bus stops. After

establishing control of the hospital bus route, additional samples were taken over the next

$20$ shifts, shown in Table $2.$ Rachelle now wants to know:

$$ Has the process changed?

$$ Is the process capable?