Statistical Process Control
1. Ford Motor Co. is concerned about the length of the body frame for its new line of cars. It is important that the car frames are uniform in length, as hundreds of parts will be added to the frame to produce the final product.
Ford collects data from a sample for each day.
Monday mean = 180.00 inches
Tuesday mean = 180.04 inches
Wednesday mean = 179.88 inches
Thursday mean = 180.02 inches
Friday mean = 179.94 inches
If each day's sample mean is found from taking a sample of 10 car frames (n=10), find the upper and lower control limits for the mean. Assume that the population standard deviation for frames is 0.02 inches. Use a three standard deviation allowance for the control limits. (this problem is similar to problem #1 in the SPC handout, as it has a KNOWN standard deviation)
Plot your results and comment on your findings.
2. If the sample means are consistently acceptable (in control), can you explain how it may be possible that a product suffers from a uniformity problem? What test, in addition to the mean test, should you use to test for uniformity of product? (think about Sam's game-by-game scoring example from class, as he was supposed to score 46 points every game...or use the refrigerator example, as each was supposed to hold 46 degrees.)
3. Using the data from question #1 above, suppose you also had data on the range of each daily sample set.
Monday range = 0.08 inches
Tuesday range = 0.10 inches
Wednesday range = 0.00 inches
Thursday range = 0.10 inches
Friday range = 0.08 inches
Find the upper and lower control limits for the range. Plot each day's range on your chart. Comment on the results.
Wednesday appears to have been a great day for production variability, as there was none. What does your control chart suggest about Wednesday? What, if anything, should you do? (we discussed this issue in respect to the scale in my house, and the radar gun being used by the police, etc.)
Reliability & Process Design
4. In order to complete a production process successfully, all 9 steps in the process must be completed in order for the entire process to achieve success. If each step has a reliability of 0.90, what is the overall reliability of the entire process? If three of the steps are provided with a redundant step, also with a 0.90 reliability, what is the new overall reliability of the entire process? If all nine of the steps are provided with a redundant step (one redundant step for each part of the process), all with a 0.90 reliability, what is the new overall reliability of the entire process?
5. A one-step process has a reliability of 0.80. A manufacturer wants to increase the reliability of the process by either: (a) paying $32,000 for a training program to hopefully increase reliability to .96, or (b) paying $30,000 for new employee who also has a reliability of 0.80, and will act as a supervisor for the one-step process above. If the goal is to have an overall reliability of 0.96, which method is preferred? Explain.
6. Using problem #5 as an example, discuss the theory behind providing redundancy to a process in place of trying to increase the reliability of each individual step in the process.
7. A) What is the reliability of a process that has six steps with the following reliabilities for each step?
Step #1 = 0.80
Step #2 = 0.90
Step #3 = 0.80
Step #4 = 0.90
Step #5 = 0.80
Step #6 = 0.90
B) If Steps #1,#3, and #5 are provided with a redundancy (also with reliability = 0.80), what is the new overall reliability of the entire process?
C) If Steps #1, #3, and #5 are provided with two backup steps (double redundancy), with each backup step also with reliability = 0.80, what is the overall reliability of the entire process?
Inventory Costs and Economic Order Quantity (EOQ)
8. A Home Depot store faces annual demand for one of its floor tiles of 500,000 units. If it costs the store $20 per order, and the holding costs = $0.05/tile, what is the optimal order quantity?
9. Show the total order and total storage costs from problem #8. Also show that a higher order quantity would not be preferred (show by example). Also show that a lower order quantity would not be preferred (show by example).
10. Explain the relationship between ordering and storage costs. Include an illustration in your explanation.
Multiple Regression & Qualitative Variables
11. Using your own data set (site your source), develop a model that has at least one quantitative variable, and at least one qualitative variable requiring at least two (2) variables to describe it. Find the multiple regression equation, and state the results in WORDS, explaining the meaning of each coefficient term. (examples: the four seasons of the year will require three variables, the seven days of the week will require six variables, etc)