Calculate the process capability statistics for the outside diameters of the bot

Question

Calculate the process capability statistics for the outside diameters of the bottles made on the injection molding machine at the Moby Molding Co. Use 0.12 as the upper tolerance limit and - 0.10 as the lower tolerance limit for this important measure of process performance. What recommendation would you make to management concerning the process, based on these findings?

Sample Observations Head 1 Head 2 Head 3 Head 4 1 0.06 0.03 0.05 0.03 2 -0.07 -0.01 0.05 0.02 3 -0.01 0.05 0.04 0.03 4 -0.08 0.02 0.03 0.07 5 -0.10 -0.02 0.02 0.07 6 -0.03 -0.01 0.03 0.07 7 -0.04 0.00 0.05 0.02 8 -0.03 0.04 0.05 0.05 9 -0.03 -0.04 -0.02 0.03 10 -0.03 -0.08 0.04 0.07 11 -0.05 -0.05 0.05 0.06 12 -0.06 -0.02 -0.01 0.04 13 -0.05 -0.06 0.01 0.00 14 -0.03 0.01 0.03 0.04 15 -0.04 0.01 0.02 0.02 16 -0.04 -0.04 0.04 0.10 17 -0.03 -0.04 0.01 0.11 18 -0.04 0.01 0.03 -0.02 19 -0.05 0.06 0.05 0.05 20 -0.03 -0.03 -0.03 0.07 21 0.04 0.03 0.06 -0.07 22 0.03 0.07 0.03 -0.01 23 0.02 0.06 0.07 -0.08 24 0.03 0.04 0.07 -0.10 25 0.05 0.00 0.07 -0.03 26 0.05 0.04 0.02 -0.04 27 -0.02 0.02 -0.01 -0.03 28 0.04 0.10 0.00 -0.03 29 0.05 0.11 0.04 -0.03 30 0.01 -0.06 -0.02 -0.03

Explanation / Answer

UCL=0.12

LCL=-0.10

Standard Deviation can be found from below

Overall variance is 0.00245.

SD = SQRT(0.00245)=0.0495

Process Capability Cp = (UCL-LCL)/6SD

=0.22/(6*0.0495)=0.74.

Hence,This process is not capable

Sample Observations Mean Variance Head 1 Head 2 Head 3 Head 4 1 0.06 0.03 0.05 0.03 0.04 0.0002 2 -0.07 -0.01 0.05 0.02 0.00 0.0026 3 -0.01 0.05 0.04 0.03 0.03 0.0007 4 -0.08 0.02 0.03 0.07 0.01 0.0041 5 -0.1 -0.02 0.02 0.07 -0.01 0.0052 6 -0.03 -0.01 0.03 0.07 0.02 0.0020 7 -0.04 0 0.05 0.02 0.01 0.0014 8 -0.03 0.04 0.05 0.05 0.03 0.0015 9 -0.03 -0.04 -0.02 0.03 -0.02 0.0010 10 -0.03 -0.08 0.04 0.07 0.00 0.0046 11 -0.05 -0.05 0.05 0.06 0.00 0.0037 12 -0.06 -0.02 -0.01 0.04 -0.01 0.0017 13 -0.05 -0.06 0.01 0 -0.03 0.0012 14 -0.03 0.01 0.03 0.04 0.01 0.0010 15 -0.04 0.01 0.02 0.02 0.00 0.0008 16 -0.04 -0.04 0.04 0.1 0.02 0.0046 17 -0.03 -0.04 0.01 0.11 0.01 0.0047 18 -0.04 0.01 0.03 -0.02 -0.01 0.0010 19 -0.05 0.06 0.05 0.05 0.03 0.0027 20 -0.03 -0.03 -0.03 0.07 -0.01 0.0025 21 0.04 0.03 0.06 -0.07 0.02 0.0034 22 0.03 0.07 0.03 -0.01 0.03 0.0011 23 0.02 0.06 0.07 -0.08 0.02 0.0047 24 0.03 0.04 0.07 -0.1 0.01 0.0057 25 0.05 0 0.07 -0.03 0.02 0.0021 26 0.05 0.04 0.02 -0.04 0.02 0.0016 27 -0.02 0.02 -0.01 -0.03 -0.01 0.0005 28 0.04 0.1 0 -0.03 0.03 0.0032 29 0.05 0.11 0.04 -0.03 0.04 0.0033 30 0.01 -0.06 -0.02 -0.03 -0.03 0.0008 Overall 0.01 0.00245

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