The following information is collected by a Six Sigma team during the define phase of a Six Sigma project implemented in a car repair shop.

The repair shop's customers have an arrival of 80 cars per day during the weekdays and 100 cars per day during the weekends. Every arriving customer first fills out a form and then waits for service. Waiting for service is usually longer than filling-out the form. There are 3 mechanics fixing cars with the following information.

1 st mechanic's service (fixing car) rate is = 10 cars per day.

2 nd mechanicís service (fixing car) rate is 16 cars out of 20 cars per day.

3 rd mechanicís service (fixing car) rate is = 25 cars per day.

The first mechanic talks to the customers, gets information from each customer, and drives the customersícars to the shop as a part of his job while the second and the third mechanics talk to the customers even though it is not a part of their duty. There can be several outcomes after the mechanicsícomplete their service to the customers:

(i) mechanic may not be able to fix the car at all and the customer may not return to the repair shop;

(ii) car is partially repaired but the car must return to the shop for a complete fixture after parts are purchased;

(iii) car repair is complete and customer doesn't return to the shop.

The first mechanic goes to the waiting area and talks to the customers and explains what is done to the car in the shop and reschedules a visit if there has to be a return to the shop. If the service is complete then the customer pays to the mechanic before leaving the repair shop. Your observations indicated customers parking farther from the shop before service, waiting too long in the waiting room, and the 2 nd and 3 rd mechanics talk to the customers. It is observed during a particular week that 50% of the cars' repair is completed, 10% of the cars repair cannot be completed at all, and 40% of the cars have to revisit the shop for repair.

(a) Draw a flow diagram for the car repair scenario explained above.

(b) Determine the number of cars that are fixed with no return to the shop.

(c) What type of additional observations and data might be necessary to determine areas of improvement for the car fixing process? What areas of the process can be improved with the existing information?

(d) At the end of the week, considering the repair capability of the mechanics, how many cars are expected to revisit the shop?