Q1. (10 points) Consider the following figure: LSL USL 30 99.73% 2200 605 1036 20 -le per 10 20 30 e 5o 60 Spes. Lim Percent lesie Specs Defective 1 Sigma 68 27 317300 +2 Sigma 95.45 45500 3 Sigma 99.73 4 Sigma 99.9937 15 Sigma 99999943 0:57 t6 Sigma 99.9999998 0.002 (a) Normal distribution centered at the target (7) 1.50 1.50 LSL USL -60 -50 40 -30 20-lo T+20 -30 -40 -58 -50 Spec. Link Percent inside specs Detective 1 Sigma 3023 697700 +2 Sigma 60.13 608700 1:3 Sigma 92.32 66810 14 Sigma 99.3790 6210 15 Sigma 99.97670 200 46 Sigma 90.999.60 (b) Normal distribution with the mean shifted by +1.50 from the target 1. (2 points) Show that the ppm for #3sigma is 2700 ppm in figure (a)? 2. (2 points) Show that the ppm for #3sigma is 66810 ppm in figure (b)? 3. (2 points) A process was working on +3sigma in figure (a) before being improved. After improvement, the process is working on sigma in figure (b). What is the percentage of improvement does the process have after improvement? 4. (4 points) Suppose that your business is operating at the five-sigma quality level, assuming the 1.5 sigma shift in the mean that is customary with six-sigma applications). If projects have an average improvement rate of 5%monthly, how many years will it take to achieve six-sigma quality assuming 1.5 sigma shift in the mean Q1. (10 points) Consider the following figure: LSL USL 30 99.73% 2200 605 1036 20 -le per 10 20 30 e 5o 60 Spes. Lim Percent lesie Specs Defective 1 Sigma 68 27 317300 +2 Sigma 95.45 45500 3 Sigma 99.73 4 Sigma 99.9937 15 Sigma 99999943 0:57 t6 Sigma 99.9999998 0.002 (a) Normal distribution centered at the target (7) 1.50 1.50 LSL USL -60 -50 40 -30 20-lo T+20 -30 -40 -58 -50 Spec. Link Percent inside specs Detective 1 Sigma 3023 697700 +2 Sigma 60.13 608700 1:3 Sigma 92.32 66810 14 Sigma 99.3790 6210 15 Sigma 99.97670 200 46 Sigma 90.999.60 (b) Normal distribution with the mean shifted by +1.50 from the target 1. (2 points) Show that the ppm for #3sigma is 2700 ppm in figure (a)? 2. (2 points) Show that the ppm for #3sigma is 66810 ppm in figure (b)? 3. (2 points) A process was working on +3sigma in figure (a) before being improved. After improvement, the process is working on sigma in figure (b). What is the percentage of improvement does the process have after improvement? 4. (4 points) Suppose that your business is operating at the five-sigma quality level, assuming the 1.5 sigma shift in the mean that is customary with six-sigma applications). If projects have an average improvement rate of 5%monthly, how many years will it take to achieve six-sigma quality assuming 1.5 sigma shift in the mean