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example 6.2 Construction of a p Chart with Variable Sample Sizes A large aerospace operation is evaluating purchase orders placed with the com- pany's suppliers. The sample sizes in Table 6.3 are the total number of purchase orders issued each week. A nonconforming unit is a purchase order with an error such as specifying an incorrect part number, wrong delivery date, or wrong sup- plier information. Create a p chart using these data using variable and average sample sizes. Table 6.3 Purchase Order Data with Variable Sample Sizes Standard Deviation 5. =| (0.096)(0.904) Sample Number, 1 Number of Nonconforming Units, D 12 Sample Size, ni 100 Control Limits LCL UCL 0.009 0.183 0.195 2 80 8 Sample Nonconforming P = D,In 0.120 0.100 0.075 0.090 0.091 8 0 3 80 6 0 0.195 4 100 9 0.009 0.183 0.180 5 110 0.029 0.033 0.033 0.029 0.028 0.028 0.029 0.029 0.031 10 6 110 12 0.109 0.180 N 100 11 0.110 0.012 0.012 0.009 0.009 0.003 0.183 8 100 16 0.183 0.160 0.110 9 90 10 0.189 10 90 6 0.067 0.189 11 20 12 15 110 120 120 120 0.182 0.125 0.075 0.067 0.031 0.028 0.027 0.027 0.027 0.003 0.012 0.015 0.015 0.015 0.180 0.177 0.177 0.177 13 9 14 8 (Continued) Table 6.3 Continued Sample Number, i Number of Nonconforming Units, D; Sample Size, ni 110 Sample Nonconforming, P = D, 0.055 qp Standard Deviation (0.096)(0.904) ni 0.028 Control Limits LCL UCL 15 6 0.012 0.180 16 80 8 0.100 0.033 0 0.195 17 80 10 0.125 0.033 0 0.195 18 80 7 0.088 0.033 0 0.195 19 90 5 0.056 0.031 0.003 0.189 20 100 8 0.080 0.029 0.009 0.183 21 100 5 0.050 0.029 0.009 0.183 22 100 8 0.080 0.029 0.009 0.183 23 100 10 0.100 0.029 0.009 0.183 24 90 6 0.067 0.031 0.003 0.189 25 90 9 0.100 0.031 0.003 0.189 2450 234 2.383