DATA FOR QUESTION 1 Production Hour 2 3 4 7 8 9 10 1 2.7 3.3 3.3 3,6 4,5 2,1 3,1 2 3 3,6 2,9 3,3 4 5 3,8 3 3,6 6 3,3 3.1 3,4 3,6 3,3 3,8 3,4 3,4 3.2 3,3 3 3,2 3,4 7 8 4,1 3,7 4,5 2.7 3,8 3.1 3,8 2,3 4,5 2,6 3,5 4,2 3,3 2,6 4,1 4,3 2.8 4.1 2,7 2.7 2,2 2,7 2,2 4.2 3,6 4.2 3.1 3.6 3,1 2.9 4.3 2,2 3.4 2,9 4,0 9 3.5 2.9 2.7 4,3 3.2 3,0 3,0 3.2 2.6 4.2 2.8 3.2 2,7 3,4 2,9 3.4 4.2 Products 5 6 2,7 3.1 2.8 2,5 2.7 3.2 3.4 3,2 4.2 2.8 4,7 4,3 3.3 3.5 2,7 4,0 3.6 3.8 4,3 4.3 2.7 3.6 3.5 3,0 3.4 3,5 4,3 3,1 3,4 4,2 3.4 2.6 2.9 4,3 4,5 2.8 4,3 3.4 3,8 3.2 3,7 2.6 3,9 2,9 3.1 3,0 3,3 4,0 3,5 3.2 2,8 3,3 4,7 3.9 4,3 2,3 3,9 4,2 3.4 3.9 3,6 3,6 2.5 4.1 2.6 2,6 3,4 4,0 4,0 4,9 3.9 2,9 4,4 3,0 3,6 2.6 2,6 4,5 2.91 3,4 3,3 3.5 4,8 3,8 3 3,3 3,5 3,6 3,3 3,2 3,5 4,3 3,4 3,5 3,4 3,3 3.4 3,4 3,1 3.1 3,5 3,6 3,7 3,4 3,4 3,3 3,4 3,1 3,5 3,3 3,4 3,6 3,2 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 4.2 4.1 3,5 3,4 3.3 3,5 3,4 3.4 3.2 3,3 3.4 3,6 3,3 3,4 3,4 4,3 2,9 2.7 3,6 3.3 3,6 4,3 3,1 3,6 3,0 4,3 3,3 2.2 3,4 2.7 3,7 3.2 2.5 3.9 3,7 3.3 4.2 3,7 3.8 4,0 4,3 4.1 3,6 2.7 3.1 3,4 3,4 3,3 3,3 4,3 3.3 SHIM Se 3,6 3,3 3.2 1. (40 points) For this question, refer to the Excel file named "Data for HW1". A manufacturing company produces drill bits and has to control the thickness of the tips produced. In each production hour, a random sample of 4 units need to be selected Please first prepare samples of 4 out of the given 10 products produced in each hour. (Always use the same 4 products in your samples. The product selection will depend on the last digits of the student numbers of the people in your group. For instance: If you are working on this HW as two students with student numbers 2192302020 and 2192302025 select product 10 and 5, and two more products of your choice. If you are working on this HW as four students with student numbers 20182304032, 20182305034, 20162304047, 20201705323 select 4 products 2, 3, 4, 7. If you are working on this HW alone, select the product of your student number's last digit + 3 more products of your choice Etc. Then, based on your samples, answer the following questions. a) Find the subgroup averages and subgroup ranges. Then, compute the average of averages.. and average range, b) According to your findings in (a), plot an chart and an R chart. c) Find the central line and control limits for both charts (Hint: Use Table B on the last page). Which observations are outliers? (Calculate the UCL and LCL up to two decimal places) d) Suppose it was possible to find an assignable cause for all outliers in the chart and R chart. Then, what should be the revised central line and the control limits for the two charts? c) Suppose that the product specifications for the drill bits is 3.3+0.5. What can you say about the capability of the manufacturing process? (Hint: Estimate the process standard deviation by the formula: 0 - d. where is the final average range value and dis to be found from Table B.)
