Session 8 Homework Problems 1- The following data are the production units from a manufacturing line for the past 8 weeks. The manager wants to know if the process is stable and in control. Produce Xbar and R charts and comment on the process Week Monday Tuesday Wednesday Thursday Friday 1 12 15 8 7 10 2 6 9 11 13 7 3 15 11 9 6 12 4 8 7 6 11 14 5 20 12 10 5 14 6 13 10 9 8 12 7 10 14 11 8 5 8 10 15 17 11 9 2- A project manager at Q Corporation has a commitment to deliver 200 cylinders to a customer. The internal diameter of these cylinders must be 60 centimeters. The tolerance is +1 and -0.5 centimeter. If the mean value of the production process is 60.4 and the standard deviation is 0.5, a- Calculate the process capability index (CP and CPk) and indicate if the process is capable. b- How many cylinders the PM should plan to produce in order for 200 of them to meet specification. c- What should be the standard deviation in order for the process to become capable? Note the process is not centered. 3- A product has specification limits of 18 to 20. If the process mean is 19.2 and the standard deviation is 0.6, calculate a. The process capability for this production line. b. Is the process Cable? c. What % of the products are out of specs if any? d. What should be the process standard deviation in order for the process to become capable? 2 UMGC/MHFallah 4- An IT organization has a service level agreement (SLA) with a major customer requiring that tier 1 calls/problems be resolved within 12 hours. There is a penalty of $150 for each call that takes more than 12 hours to resolve. The IT manager has developed the following data: Average Daily volume of tier one calls is 30 with a standard deviation of 8 calls Mean processing time in the center is 10 hours with a standard deviation of 1.1 hour a- Calculate the % daily tier 1 problems that misses the SLA. b- Estimate the annual penalty cost to the center. c- If you were the manger, would you add another technician to help desk to avoid the penalty cost. Why or why not. Use your own estimate and rationale.