) 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 Then, based on your samples, answer the following questions Find the subgroup averages and subgroup ranges Then, compute the average of averages, , and average range, According to your findings in (a), plot an chart and an R chart 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) Suppose it was possible to find an assignable cause for all of the outliers in the chart and R chart Then, what should be the revised central line and the control limits for the two charts Suppose that the product specifications for the drill bits is 3 30 5 What can you say about the capability of the manufacturing process (Hint Estimate the process standard deviation by the formula d 2 , where is the final average range value and d 2 is to be found from Table B ) Production Hour 1 2 3 4 5 6 2,7 4,3 2,9 2,6 4,1 4,3 2,8 4,1 2,7 2,7 7 8 9 10 11 12 13 14 3,3 3,1 3,4 3,6 3,3 3,8 3,4 3,4 3,2 3,3 3,3 3,2 3,4 3,3 3,3 3,5 3,4 3,4 3,2 3,3 3,4 3,6 3,3 3,4 3,4 3,6 4,5 3,6 4,1 3,7 4,1 2,7 3,8 3,1 3,8 3,3 4,5 2,6 3,5 4,2 3,3 4,2 4,3 2,9 2,7 3,6 3,3 3,6 4,3 3,1 2,7 2,6 4,2 3,6 4,2 3,1 3,6 3,1 2,9 4,3 2,7 3,4 2,9 4,0 4,1 2,5 3,4 2,7 3,7 3,2 2,5 3,9 3,7 3,3 4,2 Products 2,7 2,8 2,7 3,4 4,2 3,3 2,8 2,7 3,6 4,3 2,7 3,5 3,4 4,3 3,4 3,4 2,9 4,5 4,3 3,8 3,7 3,9 3,1 3,0 4,0 3,1 2,5 3,2 3,2 2,8 4,2 2,7 4,0 3,8 4,3 3,6 3,0 3,5 3,1 4,2 2,6 4,3 2,8 3,4 3,2 2,6 2,9 3,3 3,3 3,5 2,5 4,2 3,2 2,8 3,3 2,6 3,9 3,5 3,6 3,0 4,3 3,3 4,3 4,4 3,2 3,5 4,1 2,7 3,1 3,2 3,0 3,0 3,2 2,6 4,2 3,4 3,2 2,7 3,4 2,9 3,4 4,1 3,7 3,8 4,0 4,3 4,1 3,6 2,7 3,1 4,3 4,3 3,9 3,5 3,4 3,9 3,6 3,6 2,5 4,1 2,6 2,6 3,4 4,0 4,0 4,4 3,9 2,9 4,4 3,0 3,6 2,6 2,6 4,5 2,9 3,3 3,2 3,5 3,3 3,4 3,5 3,4 3,3 3,4 3,4 3,6 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 3,3 3,8 3,3 3,2 3 3,6 3,4 3,4 3,3 3,5 3,3 3,8 3 3,3 3,5 3,6 3,3 3,4 3,4 3,4 3,3 3,3 3,3 3,6 3,3 15 16 17 18 19 20 21 22 23 24 25

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Question: ) For this question, refer to the Excel file named Data for HW1. A manufacturing company produces drill bits and has to control the thickness

) 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. Then, based on your samples, answer the following questions.

Find the subgroup averages and subgroup ranges. Then, compute the average of averages, , and average range, .
According to your findings in (a), plot an chart and an R chart.
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).
Suppose it was possible to find an assignable cause for all of the outliers in the chart and R chart. Then, what should be the revised central line and the control limits for the two charts?
Suppose that the product specifications for the drill bits is 3.30.5. What can you say about the capability of the manufacturing process? (Hint: Estimate the process standard deviation by the formula: = /d₂, where is the final average range value and d₂ is to be found from Table B.)

Production Hour 1 2 3 4 5 6 2,7 4,3 2,9 2,6 4,1 4,3 2,8 4,1 2,7 2,7 7 8 9 10 11 12 13 14 3,3 3,1 3,4 3,6 3,3 3,8 3,4 3,4 3,2 3,3 3,3 3,2 3,4 3,3 3,3 3,5 3,4 3,4 3,2 3,3 3,4 3,6 3,3 3,4 3,4 3,6 4,5 3,6 4,1 3,7 4,1 2,7 3,8 3,1 3,8 3,3 4,5 2,6 3,5 4,2 3,3 4,2 4,3 2,9 2,7 3,6 3,3 3,6 4,3 3,1 2,7 2,6 4,2 3,6 4,2 3,1 3,6 3,1 2,9 4,3 2,7 3,4 2,9 4,0 4,1 2,5 3,4. 2,7 3,7 3,2 2,5 3,9 3,7 3,3 4,2 Products 2,7 2,8 2,7 3,4 4,2 3,3 2,8 2,7 3,6 4,3 2,7 3,5 3,4 4,3 3,4 3,4 2,9 4,5 4,3 3,8 3,7 3,9 3,1 3,0 4,0 3,1 2,5 3,2 3,2 2,8 4,2 2,7 4,0 3,8 4,3 3,6 3,0 3,5 3,1 4,2 2,6 4,3 2,8 3,4 3,2 2,6 2,9 3,3 3,3 3,5 2,5 4,2 3,2 2,8 3,3 2,6 3,9 3,5 3,6 3,0 4,3 3,3 4,3 4,4 3,2 3,5 4,1 2,7 3,1 3,2 3,0 3,0 3,2 2,6 4,2 3,4 3,2 2,7 3,4 2,9 3,4 4,1 3,7 3,8 4,0 4,3 4,1 3,6 2,7 3,1 4,3 4,3 3,9 3,5 3,4 3,9 3,6 3,6 2,5 4,1 2,6 2,6 3,4 4,0 4,0 4,4 3,9 2,9 4,4 3,0 3,6 2,6 2,6 4,5 2,9 3,3 3,2 3,5 3,3 3,4 3,5 3,4 3,3 3,4 3,4 3,6 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 3,3 3,8 3,3 3,2 3 3,6 3,4 3,4 3,3 3,5 3,3 3,8 3 3,3 3,5 3,6 3,3 3,4 3,4 3,4 3,3 3,3 3,3 3,6 3,3 15 16 17 18 19 20 21 22 23 24 25

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