Total Quality Management Question

Question 1 A finishing process packages assemblies into boxes. You have noticed variability in the boxes and desire to improve the process to fix the problem because some products fit too tightly into the boxes and others fit too loosely. Following are width measurements for the boxes. Sample S1 S2 S3 S4 S5 S6 X R Day1 Day2 Day3 68.51 68.94 68.66 68.46 68.20 68.44 68.54 68.54 68.55 68.34 68.56 68.77 68.46 68.70 68.70 68.46 68.70 68.64 68.46 0.20 68.61 0.74 68.63 0.33 Day4 Day5 Day6 Day7 68.64 68.34 68.99 68.49 68.94 68.63 68.42 68.56 68.62 68.99 68.62 68.32 68.02 68.95 68.93 68.69 68.34 68.03 68.94 68.96 68.56 68.24 68.47 68.97 68.95 68.64 0.45 68.47 0.40 68.38 0.97 68.94 68.95 68.96 0.05 Day8 68.92 68.91 68.97 68.94 0.06 a) Using the data in the table, compute the center line, the upper control limit, and lower control limit for the and R charts. (10 Marks) (Note: Refer to Appendix 1 for the formula) b) is the process in control? Interpret the charts. (6 Marks) c) If the specification is 68.5 0.25, compute the index process capability Cp and Cpk. Interpret the result. (4 Marks) Appendix 1 Factor for Control Limit A2 D3 1.88 0 1.023 0 0.729 0 0.577 0 0.483 0 0.419 0.076 0.373 0.136 0.337 0.184 n 2 3 4 5 6 7 8 9 Formula for control limit UCL = D. R R LCL = D, R R UCL = x + 4 R X LCL = x - A R X D4 3.268 2.574 2.282 2.114 2.004 1.924 2.704 1.864 2.847 1.816 2.97 d2 1.128 1.693 2.059 2.326 2.534 Formula for Process Capability Cpk USL - LSL 60 USL-x -LSL 30 30