Case Study III: A production system specializes in sheet metal fabrication. A wide variety of parts are fabricated for assembly. One simple part involves shearing a small flat blank from coil stock. The material is fed to a stop and then the shear is engaged to cut the length dimension. Next, the sheared strip is moved to a second shear and placed against the stop, the second shear is engaged, and the cut to width is produced. The sheared-off metal is recycled. The part is then moved to the next operation, a break operation for a bend. The sheet metal part specifications and targets are as follows: Length specifications: 7+ 0.04 inches. Width specifications: 5+ 0.05 inches. Length target: 7.001 inches. Width target: 4.990 inches. Data were collected in sub-groups of four parts, where each part is measured for both length and width (see Tables 2 and 3). (A) Construct appropriate control charts for the measured characteristics, assume assignable causes can be eliminated and revise the limits. (B) Calculate the process capability indices: Cp, Cpk and Com. Any suggestions for process improvement? (C) If a 5% reduction in the variability of the width or the length are possible under current budget, which one would you recommend? Table 2: Length Data (Inches) Observation Observation Subgroup Subgroup 6.994 7.007 6.988 7.008 7.027 7.004 26 7.002 6.995 6.994 27 7.016 7.005 7.026 6.986 28 6.984 6.999 6.993 6.996 7.012 29 6.987 7.013 30 6.987 6.99 6.998 7.013 7.017 31 6.981 6.994 7.016 6.969 7.003 6.997 32 6.977 6.985 7.021 6.994 6.956 6.982 7.025 6.993 33 7.004 7.028 7.053 34 6.998 7.006 6.995 7.016 6.997 6.998 7.005 35 7.015 7.008 6.993 11 7.029 36 6.977 12 6.985 7.019 6.99 37 6.993 6.992 7.013 7.044 38 7.027 7.011 6.993 6.997 6.993 7.004 39 6.993 7.012 15 7.002 7.032 7.007 6.996 16 7.017 7.025 7.023 6.992 6.997 7.012 7.004 7.05 6.996 7.038 7.008 6.996 19 6.973 7.012 7.006 7.004 44 6.99 6.975 20 6.98 6.989 45 21 6.997 46 6.973 7.002 6.996 47 7.028 7.011 7.004 7.019 6.989 7.008 48 6.998 7.005 7.003 7.015 24 6.995 7.011 25 6.998 Table 3: Width Data (Inches) Observation Subgroup 5.022 4.983 4.992 26 4.995 5.018 5.007 5.005 5.003 27 4.972 5.017 5.004 28 5.004 5.003 5.013 5.012 5.007 4.981 29 4.986 5.002 5.049 4.985 30 5.004 4.993 5.035 31 5.012 4.987 1.98 5.008 5.011 5.008 4.98 4.985 4.982 5.029 33 5.008 4.989 4.972 5.012 5.005 34 5.026 4.995 4.974 35 4.978 11 5.019 36 5.013 5.005 4.979 12 5.006 5.004 37 4.984 4.982 5.016 38 5.029 4.994 4.98 4.99 39 5.013 4.972 15 5.013 5.005 4.998 40 5.009 5.004 16 5.019 4.983 5.011 41 4.977 4.998 5.017 5.008 42 5.012 5.014 43 5.013 5.01 5.011 5.003 44 5.003 20 4.979 5.005 45 21 5.004 5.006 5.006 5.028 5.005 4.997 46 5.012 22 5.022 47 5.001 4.947 23 4.98 4.997 4.984 48 24 4.989 4.984 49 5 4.995 4.995 50