Question

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: 6+ 0.04 inches.
Width specifications: 4+ 0.05 inches.
Length target: 6.001 inches.
Width target: 3.990 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 Cpm. 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 26 27 28 29 30 6.008 6.027 6.004 5.997 5.994 5.993 5.992 5.975 6.016 6.005 6.026 5.996 6.012 5.9865.993 6.019 6.0176.013 5.974 5.991 5.998 6.013 6.017 5.996 5.969 6.003 5.997 5.956 5.982 6.025 5.993 5.973 6.015 5.997 6.023 6.016 5.997 5.998 6.005 6.029 6.011 6.0045.996 5.985 6.019 5.990 6.008 6.013 5.9935.995 6.044 5.997 5.993 6.017 6.004 6.011 6.002 6.032 6.007 5.987 6.0176.025 5.986 5.9955.9976.012 5.997 5.996 6.038 6.008 6.007 5.973 6.012 6.006 6.004 6.006 5.9915.980 5.989 5.967 5.9976.013 6.023 6.002 6.028 5.986 6.019 5.989 6.008 6.007 5.9955.999 6.006 6.011 5.998 5.985 5.996 6.001 5.994 6.007 6.022 5.988 6.002 5.995 6.0256.009 5.9895.982 6.0005.991 5.9975.9845.9995.993 6.001 5.995 5.9876.015 5.9855.992 5.987 5.990 5.981 5.981 5.9946.016 5.9775.985 6.021 6.004 6.028 6.053 6.007 5.998 6.006 5.995 5.999 6.015 6.008 5.9936.008 5.977 6.001 5.9935.994 6.027 6.018 6.011 5.993 6.002 6.001 5.987 6.000 5.996 6.012 5.9825.987 5.988 6.007 6.023 5.992 6.001 6.004 6.003 6.050 5.997 6.034 6.014 5.9966.005 5.99 5.991 6.021 6.001 5.9975.973 6.002 5.964 6.028 6.011 5.9986.005 6.003 6.015 5.986 4 32 5.994 34 35 36 37 38 39 40 6.003 6.005 5.992 5.991 6.000 13 5.976 15 42 43 6.007 20 45 46 47 48 49 50 6.012 5.975 6.038 5.996 5.996 23 24 25 6.004 6.017 Table 3: Width Data (Inches) Observation Observation Subgroup 1 Subgroup 1 4 4.023 3.983 3.992 4.007 3.999 4.001 4.017 4.012 3.993 4.049 3.987 4.035 3.991 3.980 3.971 3.982 3.998 3.991 3.974 10 4.001 4.029 4.016 3.993 12 4.006 3.986 3.987 3.998 3.99 4.013 3.992 4.019 3.993 3.998 4.015 3.992 4.014 4.003 4.015 3.979 4.005 4.028 4.005 3.994 4.026 3.980 3.992 3.990 4.018 4.000 3.995 3.981 4.005 3.992 3.986 4.004 4.0073.981 4.024 3.985 3.9894.006 3.986 4.008 4.029 3.983 4.012 4.005 3.974 4.019 4.019 3.993 4.004 3.979 4.016 3.976 4.015 4.004 3.998 3.994 3.983 4.011 4.008 3.990 4.014 3.993 3.996 4.015 4.004 4.006 3.997 4.002 4.028 4.022 3.997 3.984 3.9893.984 4.003 3.995 26 4.016 4.002 4.022 4.003 3.995 3.981 4.018 4.012 4.003 3.998 3.972 3.981 4.004 3.985 4.0004.003 4.007 3.981 4.013 4.028 4.004 3.986 4.002 4.006 4.0043.998 3.9933.986 4.012 3.985 3.9943.987 4.0114.008 3.988 3.985 4.008 4.018 3.9893.972 4.0263.982 3.985 3.995 3.978 3.984 3.993 3.995 4.013 4.005 3.9793.984 3.984 4.006 3.9823.996 4.0294.000 3.9943.980 4.013 3.972 3.9983.995 4.0053.995 4.009 4.004 3. 28 29 31 32 34 3.991 40 17 43 993 3.9813.997 3.973 .977 3.9893.982 4.017 3.991 4.007 4.0124.013 4.013 4.010 4.015 4.011 4.003 3.997 3.9983.983 4.006 4.002 4.019 3.978 3.979 4.001 3.998 3.993 3.947 20 23 24 25 48 49 50 4.012 4.012 4.001

Answer 1

Sine we kno that fo a function r ch 2.