Course Project Figure (1) provides the details of a bracket assembly to hold a strut on an automobile in place. Welded to the auto body frame, the bracket cups the strut and secures it to the frame via a single bolt with a lock washer. Proper alignment is necessary for both smooth installation during assembly and future performance. For mounting purposes, the left side hole, A, must be aligned on center with the right-side hole, B. If the holes are centered directly opposite each other, in perfect alignment, then the angle between hole centers will measure 0. As the flowchart in Figure [2] shows, the bracket is created by passing coils of flat steel through a series of progressive dies. As the steel moves through the press, the bracket is stamped, pierced, and finally bent into the appropriate shape. Recently customers have been complaining about having difficulty securing the bracket closed with the bolt and lock washer. The bolts have been difficult to slide through the holes and then tighten. Assemblers complain of stripped bolts and snug fittings. Unsure of where the problem is, the management assembles a team consisting of representatives from process engineering, materials engineering, product design, and manufacturing. The team set a criterion to measure the performance as the percentage of the parts out of specification, both before and after applying a solution. Through the use of several cause-and-effect diagrams, the team determines that the most likely cause of the problems experienced by the customer is the alignment of the holes. At some stage in the formation process, the holes end up off-center. To confirm their suspicions, during the next production run, the bending press operator takes 20 subgroups of size 5 and measures the angle between the centers of the holes for each sample (Figure (3]). The specification of the angle between insert hole A and insert hole B is 0.00 with a tolerance of +0.30. The values recorded in Figure [3] represent the distance above (or when a minus sign is present, below) the nominal value of 0.00. Question 1 [4 Marks) a. Utilize the data to create a Histogram. Calculate the mean, median, mode, standard deviation, and range for all the data. b. Use the calculations for the area under the normal curve to determine the percentage of brackets created with misaligned holes. Remember the specifications for the angle between insert hole A and insert hole B are 0.00 with a tolerance of of + 0.30. You will need to determine the percentage of brackets outside each side of the tolerance. C. Follow the steps discussed in chapter 6 and use the data to create a set of X and R charts. You will need to calculate the mean and range for each subgroup. Describe the performance of the process. d. Describe the performance of the process. Using o = R/dz, calculate 6 .C and Cpk. Interpret the charts and these values. Do they tell you the same thing? Is the process capable of meeting specifications? Using the problem-solving method described in Chapter 3 (and followed in Case Study 3.2), the team has determined that the fixture that holds the flat bracket in place during the bending operation needs to be replaced. Now that the fixture has been replaced with a better one, the team would like to determine whether changing the fixture improved the process by removing a root cause of hole misalignment. Figure (4) presents the new data after replacing the fixture. Question 2 [4 Marks) a. Utilize the new data to create a Histogram. Calculate the mean, median, mode, standard deviation, and range for all the data. b. Use the calculations for the area under the normal curve to determine the percentage of brackets created with misaligned holes. Remember the specifications for the angle between insert hole A and insert hole B are 0.00 with a tolerance of of +0.30. You will need to determine the percentage of brackets outside each side of the tolerance. c. Follow the steps discussed in chapter 6 and use the data to create a set of X and R charts. You will need to calculate the mean and range for each subgroup. Describe the performance of the process. d. Describe the performance of the process. Using o = R/dz, calculate 6.C and Cpk. Interpret the charts and these values. Do they tell you the same thing? Is the process capable of meeting specifications? Question 3 (2 Marks] Describe the changes. How are they doing when you compare their measure of performance, percentage of the parts out of specification, both before and after the fixture is changed? 6 mm 11 mm 22 mm 10 mm + B 10 mm 45 mm 2 mm 28 mm 60 mm Figure 1: Bracket Stamp pierce Uncoil stool Straighten stool Quality check Bond at bracket Quality check Transor Quality check Figure 2: Flowchart of Bracket Fabrication Process Subgroup imple 1 0.31 0.29 0.30 0.28 0.23 2 0.27 0.23 0.31 0.23 0.29 3 0.30 0.30 0.28 0.24 0.32 4 0.30 0.20 0.21 0.23 0.25 5 0.25 0.20 0.19 0.26 0.25 6 0.18 0.26 0.18 0.24 0.17 7 0.26 0.27 0.12 0.20 0.23 8 0.15 0.21 0.24 0.27 0.30 9 0.30 0.24 0.26 0.27 0.26 10 0.31 0.25 0.25 0.28 0.25 11 12 0.18 0.22 0.16 0.30 0.21 0.21 0.29 0.24 0.27 0.26 13 0.19 0.28 0.26 0.29 0.24 14 0.14 0.27 0.25 0.28 0.16 15 0.29 0.23 0.27 0.24 0.23 Figure 3: Hole A, B Alignment; Angle Above (+) or Below (-) Nominal Subgroup 17 19 0.22 0.24 18 0.33 0.30 0.22 0.26 0.26 0.32 0.27 0.28 0.19 0.31 0.22 0.20 0.17 0.26 0.31 0.24 0.24 0.28 0.15 0.27 0.19 30 Subgroup Sample 1 2 3 4 5 1 2 0.03 0.06 0.08 0.08 -0.03 -0.01 0.07 0.08 -0.02 0.02 3 0.06 0.08 0.05 -0.03 0.03 4 5 0.03 -0.04 0.00 -0.07 0.05 0.00 -0.01 -0.01 0.07 -0.01 6 7 -0.02 -0.05 0.06 -0.07 0.02 0.11 0.12 -0.03 -0.07 0.03 8 9 0.06 0.00 0.03 0.06 0.04 0.02 0.03 -0.02 0.01 0.00 10 11 -0.02 -0.02 -0.01 0.06 0.00 -0.02 -0.10 0.02 -0.04 0.09 12 0.06 0.02 -0.01 -0.02 0.03 13 0.07 -0.04 0.08 0.01 -0.04 14 0.10 0.05 0.03 0.04 0.06 15 0.02 -0.05 0.04 0.05 -0.05 Figure 4: Alignment Following Process Improvement; Above (+) or Below (-) Subgroup Sample 16 -0.05 0.00 0.06 -0.02 -0.01 17 -0.06 -0.02 0.04 0.07 -0.04 18 -0.04 -0.02 -0.01 0.03 -0.02 19 -0.05 0.00 0.00 0.03 0.04 20 -0.01 0.02 0.05 0.04 0.03 Course Project Figure (1) provides the details of a bracket assembly to hold a strut on an automobile in place. Welded to the auto body frame, the bracket cups the strut and secures it to the frame via a single bolt with a lock washer. Proper alignment is necessary for both smooth installation during assembly and future performance. For mounting purposes, the left side hole, A, must be aligned on center with the right-side hole, B. If the holes are centered directly opposite each other, in perfect alignment, then the angle between hole centers will measure 0. As the flowchart in Figure [2] shows, the bracket is created by passing coils of flat steel through a series of progressive dies. As the steel moves through the press, the bracket is stamped, pierced, and finally bent into the appropriate shape. Recently customers have been complaining about having difficulty securing the bracket closed with the bolt and lock washer. The bolts have been difficult to slide through the holes and then tighten. Assemblers complain of stripped bolts and snug fittings. Unsure of where the problem is, the management assembles a team consisting of representatives from process engineering, materials engineering, product design, and manufacturing. The team set a criterion to measure the performance as the percentage of the parts out of specification, both before and after applying a solution. Through the use of several cause-and-effect diagrams, the team determines that the most likely cause of the problems experienced by the customer is the alignment of the holes. At some stage in the formation process, the holes end up off-center. To confirm their suspicions, during the next production run, the bending press operator takes 20 subgroups of size 5 and measures the angle between the centers of the holes for each sample (Figure (3]). The specification of the angle between insert hole A and insert hole B is 0.00 with a tolerance of +0.30. The values recorded in Figure [3] represent the distance above (or when a minus sign is present, below) the nominal value of 0.00. Question 1 [4 Marks) a. Utilize the data to create a Histogram. Calculate the mean, median, mode, standard deviation, and range for all the data. b. Use the calculations for the area under the normal curve to determine the percentage of brackets created with misaligned holes. Remember the specifications for the angle between insert hole A and insert hole B are 0.00 with a tolerance of of + 0.30. You will need to determine the percentage of brackets outside each side of the tolerance. C. Follow the steps discussed in chapter 6 and use the data to create a set of X and R charts. You will need to calculate the mean and range for each subgroup. Describe the performance of the process. d. Describe the performance of the process. Using o = R/dz, calculate 6 .C and Cpk. Interpret the charts and these values. Do they tell you the same thing? Is the process capable of meeting specifications? Using the problem-solving method described in Chapter 3 (and followed in Case Study 3.2), the team has determined that the fixture that holds the flat bracket in place during the bending operation needs to be replaced. Now that the fixture has been replaced with a better one, the team would like to determine whether changing the fixture improved the process by removing a root cause of hole misalignment. Figure (4) presents the new data after replacing the fixture. Question 2 [4 Marks) a. Utilize the new data to create a Histogram. Calculate the mean, median, mode, standard deviation, and range for all the data. b. Use the calculations for the area under the normal curve to determine the percentage of brackets created with misaligned holes. Remember the specifications for the angle between insert hole A and insert hole B are 0.00 with a tolerance of of +0.30. You will need to determine the percentage of brackets outside each side of the tolerance. c. Follow the steps discussed in chapter 6 and use the data to create a set of X and R charts. You will need to calculate the mean and range for each subgroup. Describe the performance of the process. d. Describe the performance of the process. Using o = R/dz, calculate 6.C and Cpk. Interpret the charts and these values. Do they tell you the same thing? Is the process capable of meeting specifications? Question 3 (2 Marks] Describe the changes. How are they doing when you compare their measure of performance, percentage of the parts out of specification, both before and after the fixture is changed? 6 mm 11 mm 22 mm 10 mm + B 10 mm 45 mm 2 mm 28 mm 60 mm Figure 1: Bracket Stamp pierce Uncoil stool Straighten stool Quality check Bond at bracket Quality check Transor Quality check Figure 2: Flowchart of Bracket Fabrication Process Subgroup imple 1 0.31 0.29 0.30 0.28 0.23 2 0.27 0.23 0.31 0.23 0.29 3 0.30 0.30 0.28 0.24 0.32 4 0.30 0.20 0.21 0.23 0.25 5 0.25 0.20 0.19 0.26 0.25 6 0.18 0.26 0.18 0.24 0.17 7 0.26 0.27 0.12 0.20 0.23 8 0.15 0.21 0.24 0.27 0.30 9 0.30 0.24 0.26 0.27 0.26 10 0.31 0.25 0.25 0.28 0.25 11 12 0.18 0.22 0.16 0.30 0.21 0.21 0.29 0.24 0.27 0.26 13 0.19 0.28 0.26 0.29 0.24 14 0.14 0.27 0.25 0.28 0.16 15 0.29 0.23 0.27 0.24 0.23 Figure 3: Hole A, B Alignment; Angle Above (+) or Below (-) Nominal Subgroup 17 19 0.22 0.24 18 0.33 0.30 0.22 0.26 0.26 0.32 0.27 0.28 0.19 0.31 0.22 0.20 0.17 0.26 0.31 0.24 0.24 0.28 0.15 0.27 0.19 30 Subgroup Sample 1 2 3 4 5 1 2 0.03 0.06 0.08 0.08 -0.03 -0.01 0.07 0.08 -0.02 0.02 3 0.06 0.08 0.05 -0.03 0.03 4 5 0.03 -0.04 0.00 -0.07 0.05 0.00 -0.01 -0.01 0.07 -0.01 6 7 -0.02 -0.05 0.06 -0.07 0.02 0.11 0.12 -0.03 -0.07 0.03 8 9 0.06 0.00 0.03 0.06 0.04 0.02 0.03 -0.02 0.01 0.00 10 11 -0.02 -0.02 -0.01 0.06 0.00 -0.02 -0.10 0.02 -0.04 0.09 12 0.06 0.02 -0.01 -0.02 0.03 13 0.07 -0.04 0.08 0.01 -0.04 14 0.10 0.05 0.03 0.04 0.06 15 0.02 -0.05 0.04 0.05 -0.05 Figure 4: Alignment Following Process Improvement; Above (+) or Below (-) Subgroup Sample 16 -0.05 0.00 0.06 -0.02 -0.01 17 -0.06 -0.02 0.04 0.07 -0.04 18 -0.04 -0.02 -0.01 0.03 -0.02 19 -0.05 0.00 0.00 0.03 0.04 20 -0.01 0.02 0.05 0.04 0.03