Question (f) and (g)

4. The data set refers to the ball shear strengths (X) of a product at a bonding temperature of 240C: Mon 1 2 3 66.3 67.5 68.1 69.2 Tue 5 6 7 8 9 10 Wed ONS IS SI S7 S2 S2 SI SI S2 S2 SI S/ S2 S2 S/ SI S2 S2 SI SI S2 S2 S/ SI S2 S2 86.5 68.0 84,0 75.7 56.4 62.9 71.9 66.2 63.1 73.7 60.8 51.6 69.9 52.6 745 IN 875 80.1 77.6 75.8 88.7 74.8 83.7 79.8 88.8 76.9 82.6 85.7 66.9 83.4 76.9 64.1 80.1 73.3 75.3 82.1 73.7 73.5 73.5 87.0 12 13 14 15 16 17 18 19 20 21 22 23 24 73.1 842 60.0 67.8 67.6 70.1 77.6 54.5 74.6 59.4 78.4 57.3 71.4 74.9 70.6 59.0 65.3 62.5 79.0 75,6 63.6 54,0 78,1 57.3 62.7 61.1 58.9 56.3 58,3 65.5 65.5 71.4 54.1 69.4 63.8 66,5 67.1 84.2 66.4 69.2 76.4 64.0 74.6 69.2 Thu 69.4 87.5 68.1 65.4 63,8 58.4 70.1 52.0 75.6 70.1 67.6 60.0 64.0 35.1 74.8 60,7 65.5 62.8 61.8 69.5 70,0 59.2 693 80.6 Fri 68.5 67.0 77.5 71.8 742 67.1 71.5 63.1 Sat wode Ceghted States (1) From the data/results in (a), (d) and (e), show empirically whether the following relationships hold: 0 = 0,7m 0, R/d2 What is the practical significance of the relationships in SPC? (g) Assume that the process mean shifts to 78. For the X chart in (d), what is the probability of not detecting the shift in the first sample plotted after the shift? What is the ARL in this case? Use only sensitizing rule 1. Answers: 81%, about 5