(25 points) Problem 1 - Chapter 6 Consider the piston ring data in the following Table. 1- Using formulas in chapter 6, find the trial centerline and upper and lower control limit for Xbar and R. Clearly mention what values from tables you have used. 2- Using Minitab (or if you prefer, manually), draw the two charts of Xbar and R and insert it here first. Then if there are outliers, assume you know the assignable cause of them, so remove them in second step and draw the revised plots and find the centerline, UCL and LCL and insert your new plots again. 3- Based on the result of revised control lines, estimate the potential and actual process capability assuming that specifications are 130.0 20.0 mm. da y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 X1 X2 X3 X4 X5 135.2 134.8 131.5 139.8 133.4 136.4 135 139.6 138.3 138.7 138.6 138.9 139.7 135.2 124.6 138.2 132.8 138.3 138.7 138.6 138.9 139.7 135.2 124.6 138.2 121 138.3 133.1 168.3 120 136.2 125.4 137.9 130.2 121.8 139 135.3 127.3 132.8 131 126.4 124 130.2 121.8 139 135.3 127.3 132.8 131 126.4 134.6 129.6 128.5 164 131.6 134.7 139.1 131.1 130.4 139.5 131.9 131.5 130.5 136.1 128.8 124.4 135 130.4 139.5 131.9 131.5 130.5 136.1 128.8 124.4 130.2 151.8 133.2 188.1 138.4 137.1 138.3 133.7 132.4 123.3 130.2 137.9 129 131 137.5 137.1 135 132.4 123.3 130.2 137.9 129 131 137.5 137.1 127.3 132.7 131.6 153.1 134.2 173.2 130.4 120.5 135.1 131.8 131.1 135 130.5 129.2 131.6 127.5 135.8 135.1 131.8 131.1 135 130.5 129.2 131.6 127.5