SPC.XLS

Tools for Managers

Statistical Process ControlProfessor Stephen R. Lawrence

College of Business and AdministrationGraduate School of Business and Administration

University of ColoradoBoulder, CO 80303

303/[email protected]

© 1996-1999

Cpk

Process Name: Potato chip salterProcess Units: % salt

Ratio Value Process is: Specification Target: 1.00 % salt Cp: 1.33 capable

Lower Specification Limit: 0.98 % salt Cpk: 0.67 not capable (not centered)Upper Specification Limit: 1.02 % salt

Process Mean: 1.01 % salt Percent Under Spec: 0.00%Process Standard Deviation: 0.005 % salt Percent Over Spec: 2.28%

Percent Out of Spec: 2.28%

Chart Setup-0.50 0.96 0.0000 0.001 1.02-0.49 0.96 0.0000 0.001-0.48 0.96 0.0000 0.001-0.47 0.96 0.0000 0.001-0.46 0.96 0.0000 0.001-0.45 0.96 0.0000 0.001-0.44 0.96 0.0000 0.001-0.43 0.96 0.0000 0.001-0.42 0.96 0.0000 0.001-0.41 0.96 0.0000 0.001-0.40 0.96 0.0000 0.001-0.39 0.96 0.0000 0.001-0.38 0.96 0.0000 0.001-0.37 0.97 0.0000 0.001

PROCESS CAPABILITY INDEX -- Cpk

0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

Process Capability Chart

Quality Dimension

Pro

ce

ss

De

ns

ity

Cpk

-0.36 0.97 0.0000 0.001-0.35 0.97 0.0000 0.001-0.34 0.97 0.0000 0.001-0.33 0.97 0.0000 0.001-0.32 0.97 0.0000 0.001-0.31 0.97 0.0000 0.001-0.30 0.97 0.0000 0.001-0.29 0.97 0.0000 0.001-0.28 0.97 0.0000 0.001-0.27 0.97 0.0000 0.001-0.26 0.97 0.0000 0.001-0.25 0.97 0.0000 0.001-0.24 0.97 0.0000 0.001-0.23 0.97 0.0000 0.001-0.22 0.97 0.0000 0.001-0.21 0.97 0.0000 0.001-0.20 0.97 0.0000 0.001-0.19 0.97 0.0000 0.001-0.18 0.97 0.0000 0.001-0.17 0.97 0.0000 0.001-0.16 0.97 0.0000 0.001-0.15 0.97 0.0000 0.001-0.14 0.97 0.0000 0.001-0.13 0.97 0.0000 0.001-0.12 0.98 0.0000 0.001-0.11 0.98 0.0000 0.001-0.10 0.98 0.0000 0.001-0.09 0.98 0.0000 0.001-0.08 0.98 0.0000 0.001-0.07 0.98 0.0000 0.001-0.06 0.98 0.0000 0.001-0.05 0.98 0.0000 0.001-0.04 0.98 0.0000 0.001-0.03 0.98 0.0000 0.001-0.02 0.98 0.0000 0.001-0.01 0.98 0.0000 0.0010.00 0.98 0.0000 79.78850.01 0.98 0.0000 79.78850.02 0.98 0.0000 79.78850.03 0.98 0.0000 79.78850.04 0.98 0.0000 79.78850.05 0.98 0.0000 79.78850.06 0.98 0.0000 79.78850.07 0.98 0.0000 79.78850.08 0.98 0.0000 79.78850.09 0.98 0.0001 79.78850.10 0.98 0.0001 79.78850.11 0.98 0.0002 79.78850.12 0.98 0.0002 79.78850.13 0.99 0.0004 79.7885

Cpk

0.14 0.99 0.0005 79.78850.15 0.99 0.0008 79.78850.16 0.99 0.0012 79.78850.17 0.99 0.0017 79.78850.18 0.99 0.0024 79.78850.19 0.99 0.0035 79.78850.20 0.99 0.0050 79.78850.21 0.99 0.0071 79.78850.22 0.99 0.0100 79.78850.23 0.99 0.0139 79.78850.24 0.99 0.0194 79.78850.25 0.99 0.0268 79.78850.26 0.99 0.0367 79.78850.27 0.99 0.0501 79.78850.28 0.99 0.0679 79.78850.29 0.99 0.0915 79.78850.30 0.99 0.1224 79.78850.31 0.99 0.1627 79.78850.32 0.99 0.2149 79.78850.33 0.99 0.2821 79.78850.34 0.99 0.3679 79.78850.35 0.99 0.4768 79.78850.36 0.99 0.6140 79.78850.37 0.99 0.7855 79.78850.38 1.00 0.9986 79.78850.39 1.00 1.2613 79.78850.40 1.00 1.5831 79.78850.41 1.00 1.9742 79.78850.42 1.00 2.4463 79.78850.43 1.00 3.0119 79.78850.44 1.00 3.6847 79.78850.45 1.00 4.4789 79.78850.46 1.00 5.4096 79.78850.47 1.00 6.4921 79.78850.48 1.00 7.7414 79.78850.49 1.00 9.1722 79.78850.50 1.00 10.7982 79.78850.51 1.00 12.6313 79.78850.52 1.00 14.6814 79.78850.53 1.00 16.9553 79.78850.54 1.00 19.4565 79.78850.55 1.00 22.1842 79.78850.56 1.00 25.1329 79.78850.57 1.00 28.2920 79.78850.58 1.00 31.6450 79.78850.59 1.00 35.1695 79.78850.60 1.00 38.8372 79.78850.61 1.00 42.6138 79.78850.62 1.00 46.4594 79.78850.63 1.01 50.3289 79.7885

Cpk

0.64 1.01 54.1728 79.78850.65 1.01 57.9383 79.78850.66 1.01 61.5703 79.78850.67 1.01 65.0125 79.78850.68 1.01 68.2092 79.78850.69 1.01 71.1065 79.78850.70 1.01 73.6540 79.78850.71 1.01 75.8061 79.78850.72 1.01 77.5233 79.78850.73 1.01 78.7737 79.78850.74 1.01 79.5335 79.78850.75 1.01 79.7885 79.78850.76 1.01 79.5335 79.78850.77 1.01 78.7737 79.78850.78 1.01 77.5233 79.78850.79 1.01 75.8061 79.78850.80 1.01 73.6540 79.78850.81 1.01 71.1065 79.78850.82 1.01 68.2092 79.78850.83 1.01 65.0125 79.78850.84 1.01 61.5703 79.78850.85 1.01 57.9383 79.78850.86 1.01 54.1728 79.78850.87 1.01 50.3289 79.78850.88 1.02 46.4594 79.78850.89 1.02 42.6138 79.78850.90 1.02 38.8372 79.78850.91 1.02 35.1695 79.78850.92 1.02 31.6450 79.78850.93 1.02 28.2920 79.78850.94 1.02 25.1329 79.78850.95 1.02 22.1842 79.78850.96 1.02 19.4565 79.78850.97 1.02 16.9553 79.78850.98 1.02 14.6814 79.78850.99 1.02 12.6313 79.78851.00 1.02 10.7982 79.78851.01 1.02 9.1722 0.0011.02 1.02 7.7414 0.0011.03 1.02 6.4921 0.0011.04 1.02 5.4096 0.0011.05 1.02 4.4789 0.0011.06 1.02 3.6847 0.0011.07 1.02 3.0119 0.0011.08 1.02 2.4463 0.0011.09 1.02 1.9742 0.0011.10 1.02 1.5831 0.0011.11 1.02 1.2613 0.0011.12 1.02 0.9986 0.0011.13 1.03 0.7855 0.001

Cpk

1.14 1.03 0.6140 0.0011.15 1.03 0.4768 0.0011.16 1.03 0.3679 0.0011.17 1.03 0.2821 0.0011.18 1.03 0.2149 0.0011.19 1.03 0.1627 0.0011.20 1.03 0.1224 0.0011.21 1.03 0.0915 0.0011.22 1.03 0.0679 0.0011.23 1.03 0.0501 0.0011.24 1.03 0.0367 0.0011.25 1.03 0.0268 0.0011.26 1.03 0.0194 0.0011.27 1.03 0.0139 0.0011.28 1.03 0.0100 0.0011.29 1.03 0.0071 0.0011.30 1.03 0.0050 0.0011.31 1.03 0.0035 0.0011.32 1.03 0.0024 0.0011.33 1.03 0.0017 0.0011.34 1.03 0.0012 0.0011.35 1.03 0.0008 0.0011.36 1.03 0.0005 0.0011.37 1.03 0.0004 0.0011.38 1.04 0.0002 0.0011.39 1.04 0.0002 0.0011.40 1.04 0.0001 0.0011.41 1.04 0.0001 0.0011.42 1.04 0.0000 0.0011.43 1.04 0.0000 0.0011.44 1.04 0.0000 0.0011.45 1.04 0.0000 0.0011.46 1.04 0.0000 0.0011.47 1.04 0.0000 0.0011.48 1.04 0.0000 0.0011.49 1.04 0.0000 0.0011.50 1.04 0.0000 0.001

Cpk

not capable (not centered)

XR-chart

XR-Charts for Controlling Process Variables Data

Process: Potato chip slicer Obs MeanControl Variable: chip thickness 1 8.09

Measurement Unit: millimeters 2 7.633 11.07

Observations per Sample: 6 samples 4 12.97Average Sample Mean: 10.00 millimeters 5 10.04

Average Sample Range: 8.00 millimeters 6 8.667 9.50

X-chart R-chart 8 13.77Upper Control Limit: 13.87 16.03 millimeters 9 10.05Lower Control Limit: 6.13 0.00 millimeters 10 9.25

11 9.5112 10.6513 10.5214 9.3015 10.9116 8.3417 10.3118 10.3819 9.9720 9.4621 9.1522 9.9023 11.2324 10.4225 10.8826 10.6327 12.1228 11.6629 9.2730 9.2431 10.0632 9.6733 8.6534 9.9735 9.3436 9.7637 11.0438 10.0539 11.2740 9.8241 11.1042 11.4343 9.0244 8.8545 10.1346 10.49

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100

0

2

4

6

8

10

12

14

16

18

X-chart

Observation

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2

4

6

8

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12

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20R-chart

Observation

Sa

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XR-chart

47 9.4248 10.1649 9.5150 10.4351 13.8252 3.7653 9.5254 12.9655 15.6756 10.7657 7.1858 9.8859 10.2960 11.6961 13.7062 10.2163 14.3264 10.7265 10.0366 8.7367 7.0068 12.5869 9.3170 11.8571 7.3972 9.5073 16.0274 15.1075 15.0476 6.6077 11.9378 15.6279 8.3480 12.5581 13.8382 13.4883 7.3284 14.1185 10.4486 10.0687 16.3988 14.9089 13.6090 8.3891 15.2592 12.0993 10.2294 11.8195 9.3796 13.29

XR-chart

97 13.5398 9.0899 12.21

100 8.22

XR-chart

Data Control Chart FactorsX-chart R-chart

Range LCL UCL LCL UCL n d(2) d(3) A(2)8.11 6.1334 13.867 0 16.032 2 1.128 0.853 1.8814.97 6.1334 13.867 0 16.032 3 1.693 0.888 1.0239.24 6.1334 13.867 0 16.032 4 2.059 0.880 0.729

12.06 6.1334 13.867 0 16.032 5 2.326 0.864 0.5774.98 6.1334 13.867 0 16.032 6 2.534 0.848 0.483

11.10 6.1334 13.867 0 16.032 7 2.704 0.833 0.4198.29 6.1334 13.867 0 16.032 8 2.847 0.820 0.373

12.81 6.1334 13.867 0 16.032 9 2.970 0.808 0.3378.42 6.1334 13.867 0 16.032 10 3.078 0.797 0.3089.59 6.1334 13.867 0 16.032 11 3.173 0.787 0.285

11.59 6.1334 13.867 0 16.032 12 3.258 0.778 0.26611.51 6.1334 13.867 0 16.032 16 3.532 0.750 0.21211.78 6.1334 13.867 0 16.032 17 3.588 0.744 0.203

8.46 6.1334 13.867 0 16.032 18 3.640 0.739 0.1945.64 6.1334 13.867 0 16.032 19 3.689 0.734 0.1878.65 6.1334 13.867 0 16.032 20 3.735 0.729 0.180

11.64 6.1334 13.867 0 16.032 21 3.778 0.724 0.1735.14 6.1334 13.867 0 16.032 22 3.819 0.720 0.1678.60 6.1334 13.867 0 16.032 23 3.858 0.716 0.162

11.10 6.1334 13.867 0 16.032 24 3.895 0.712 0.1575.87 6.1334 13.867 0 16.032 25 3.931 0.708 0.1539.30 6.1334 13.867 0 16.0327.10 6.1334 13.867 0 16.0328.62 6.1334 13.867 0 16.0327.47 6.1334 13.867 0 16.032

12.95 6.1334 13.867 0 16.0327.31 6.1334 13.867 0 16.0326.43 6.1334 13.867 0 16.0325.70 6.1334 13.867 0 16.0326.19 6.1334 13.867 0 16.0328.86 6.1334 13.867 0 16.0327.47 6.1334 13.867 0 16.0328.96 6.1334 13.867 0 16.0326.80 6.1334 13.867 0 16.0329.89 6.1334 13.867 0 16.0325.34 6.1334 13.867 0 16.0323.39 6.1334 13.867 0 16.0328.12 6.1334 13.867 0 16.0328.34 6.1334 13.867 0 16.0329.41 6.1334 13.867 0 16.0328.95 6.1334 13.867 0 16.0327.49 6.1334 13.867 0 16.0323.85 6.1334 13.867 0 16.032

11.03 6.1334 13.867 0 16.0327.10 6.1334 13.867 0 16.0327.00 6.1334 13.867 0 16.032

XR-chart

11.09 6.1334 13.867 0 16.0329.19 6.1334 13.867 0 16.0323.84 6.1334 13.867 0 16.0322.91 6.1334 13.867 0 16.0323.25 6.1334 13.867 0 16.0322.80 6.1334 13.867 0 16.032

15.86 6.1334 13.867 0 16.0323.30 6.1334 13.867 0 16.0327.88 6.1334 13.867 0 16.0320.90 6.1334 13.867 0 16.0329.85 6.1334 13.867 0 16.032

16.23 6.1334 13.867 0 16.0327.59 6.1334 13.867 0 16.0323.15 6.1334 13.867 0 16.0323.54 6.1334 13.867 0 16.0322.35 6.1334 13.867 0 16.032

17.88 6.1334 13.867 0 16.03215.85 6.1334 13.867 0 16.032

6.46 6.1334 13.867 0 16.0329.53 6.1334 13.867 0 16.0324.11 6.1334 13.867 0 16.032

14.47 6.1334 13.867 0 16.03213.81 6.1334 13.867 0 16.032

0.94 6.1334 13.867 0 16.0326.88 6.1334 13.867 0 16.0329.87 6.1334 13.867 0 16.032

18.70 6.1334 13.867 0 16.03213.11 6.1334 13.867 0 16.032

5.53 6.1334 13.867 0 16.03218.36 6.1334 13.867 0 16.032

8.65 6.1334 13.867 0 16.03214.65 6.1334 13.867 0 16.03216.08 6.1334 13.867 0 16.03210.94 6.1334 13.867 0 16.03210.54 6.1334 13.867 0 16.03215.61 6.1334 13.867 0 16.032

4.71 6.1334 13.867 0 16.03217.62 6.1334 13.867 0 16.032

4.03 6.1334 13.867 0 16.0328.79 6.1334 13.867 0 16.0320.93 6.1334 13.867 0 16.032

12.13 6.1334 13.867 0 16.0324.42 6.1334 13.867 0 16.0328.76 6.1334 13.867 0 16.032

12.34 6.1334 13.867 0 16.03214.70 6.1334 13.867 0 16.032

6.75 6.1334 13.867 0 16.03213.30 6.1334 13.867 0 16.032

6.97 6.1334 13.867 0 16.0321.12 6.1334 13.867 0 16.032

XR-chart

10.65 6.1334 13.867 0 16.03214.14 6.1334 13.867 0 16.03217.99 6.1334 13.867 0 16.03214.56 6.1334 13.867 0 16.032

XR-chart

D(3) D(4)0.000 3.2690.000 2.5740.000 2.2820.000 2.1140.000 2.0040.076 1.9240.136 1.8640.184 1.8160.223 1.7770.256 1.7440.284 1.7160.363 1.6370.378 1.6220.391 1.6090.403 1.5970.414 1.5860.425 1.5750.434 1.5660.443 1.5570.452 1.5480.460 1.540

P-chart

P-Chart for Controlling Proportion Defective - fixed sample size DataProportion

Product: Potato Chips ObsType of Defect: bad seals 1

Unit of Measure: bags/case 23

Observations per Sample: 10 samples 4Average Proportion Defective: 0.05 5

6P-Chart 7

Upper Control Limit: 0.26 proportion defective 8Lower Control Limit: 0.00 proportion defective 9

1011121314151617181920212223242526272829303132333435363738394041424344454647484950

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Proportion Defective: p-chart

Observation

Pro

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efe

cti

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P-chart

51525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899

100

P-chart

DataProportion p-chart

Defective LCL UCL0.09253 0 0.2567610.10868 0 0.2567610.05035 0 0.2567610.08077 0 0.2567610.06033 0 0.2567610.15734 0 0.2567610.06364 0 0.2567610.07007 0 0.2567610.14873 0 0.2567610.20329 0 0.2567610.07540 0 0.2567610.07513 0 0.2567610.24734 0 0.2567610.14323 0 0.2567610.22196 0 0.2567610.13867 0 0.2567610.11513 0 0.2567610.17660 0 0.2567610.10341 0 0.2567610.25693 0 0.2567610.09935 0 0.2567610.10017 0 0.2567610.12806 0 0.2567610.20086 0 0.2567610.11924 0 0.2567610.17768 0 0.2567610.13688 0 0.2567610.12675 0 0.2567610.22205 0 0.2567610.11072 0 0.2567610.12354 0 0.2567610.23591 0 0.2567610.07589 0 0.2567610.20914 0 0.2567610.10952 0 0.2567610.07291 0 0.2567610.23323 0 0.2567610.09593 0 0.2567610.02382 0 0.2567610.11771 0 0.2567610.06839 0 0.2567610.13516 0 0.2567610.14381 0 0.2567610.20993 0 0.2567610.13161 0 0.2567610.17808 0 0.2567610.16249 0 0.2567610.12605 0 0.2567610.14302 0 0.2567610.09709 0 0.256761

P-chart

0.33120 0 0.2567610.15042 0 0.2567610.12549 0 0.2567610.14107 0 0.2567610.21983 0 0.2567610.12608 0 0.2567610.10019 0 0.2567610.13875 0 0.2567610.07411 0 0.2567610.19570 0 0.2567610.15075 0 0.2567610.29414 0 0.2567610.11336 0 0.2567610.17203 0 0.2567610.14482 0 0.2567610.08999 0 0.2567610.14575 0 0.2567610.11608 0 0.2567610.18928 0 0.2567610.12980 0 0.2567610.12730 0 0.2567610.16084 0 0.2567610.11382 0 0.2567610.14107 0 0.2567610.20099 0 0.2567610.18023 0 0.2567610.09851 0 0.2567610.09579 0 0.2567610.13145 0 0.2567610.14101 0 0.2567610.11575 0 0.2567610.11159 0 0.2567610.10010 0 0.2567610.17852 0 0.2567610.19909 0 0.2567610.10481 0 0.2567610.16939 0 0.2567610.19420 0 0.2567610.13870 0 0.2567610.04071 0 0.2567610.17289 0 0.2567610.20765 0 0.2567610.15625 0 0.2567610.12332 0 0.2567610.05869 0 0.2567610.15604 0 0.2567610.08851 0 0.2567610.13906 0 0.2567610.08544 0 0.2567610.07672 0 0.256761

C-chart

C-Chart for Defects per Unit Data

ObsProduct: Potato chip cooking oil 1

Type of Defect: particles of burned potato 2Unit of Measure: quart 3

4Mean Number Defects per Unit: 10.00 defects per quart 5

6C-Chart 7

Upper Control Limit: 19.49 defects per quart 8Lower Control Limit: 0.51 defects per quart 9

1011121314151617181920212223242526272829303132333435363738394041424344454647484950

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5

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Defects per Unit: c-chart

Observation

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C-chart

51525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899

100

C-chart

DataCount p-chart

Defective LCL UCL13 0.513167 19.48683 101 0.513167 19.486837 0.513167 19.486836 0.513167 19.48683

12 0.513167 19.4868311 0.513167 19.486837 0.513167 19.486838 0.513167 19.48683

10 0.513167 19.4868320 0.513167 19.4868315 0.513167 19.4868312 0.513167 19.486835 0.513167 19.486830 0.513167 19.48683

11 0.513167 19.486837 0.513167 19.48683

14 0.513167 19.486831 0.513167 19.486838 0.513167 19.486831 0.513167 19.48683

12 0.513167 19.486832 0.513167 19.48683

18 0.513167 19.4868313 0.513167 19.486832 0.513167 19.48683

11 0.513167 19.4868312 0.513167 19.486837 0.513167 19.48683

13 0.513167 19.486832 0.513167 19.48683

11 0.513167 19.4868313 0.513167 19.486836 0.513167 19.48683

10 0.513167 19.4868310 0.513167 19.486835 0.513167 19.486834 0.513167 19.486834 0.513167 19.48683

11 0.513167 19.4868316 0.513167 19.486838 0.513167 19.48683

11 0.513167 19.4868310 0.513167 19.486832 0.513167 19.48683

10 0.513167 19.4868312 0.513167 19.4868314 0.513167 19.4868311 0.513167 19.4868312 0.513167 19.4868310 0.513167 19.48683

C-chart

12 0.513167 19.486839 0.513167 19.486834 0.513167 19.48683

11 0.513167 19.486834 0.513167 19.486830 0.513167 19.48683

12 0.513167 19.486837 0.513167 19.486830 0.513167 19.486839 0.513167 19.48683

11 0.513167 19.486835 0.513167 19.48683

13 0.513167 19.4868319 0.513167 19.4868317 0.513167 19.4868321 0.513167 19.4868311 0.513167 19.4868313 0.513167 19.486839 0.513167 19.486833 0.513167 19.48683

10 0.513167 19.4868313 0.513167 19.486830 0.513167 19.48683

10 0.513167 19.486833 0.513167 19.486832 0.513167 19.48683

14 0.513167 19.4868314 0.513167 19.486837 0.513167 19.48683

10 0.513167 19.486837 0.513167 19.48683

12 0.513167 19.486835 0.513167 19.48683

12 0.513167 19.486834 0.513167 19.48683

12 0.513167 19.4868313 0.513167 19.4868318 0.513167 19.486837 0.513167 19.48683

19 0.513167 19.486833 0.513167 19.48683

13 0.513167 19.486838 0.513167 19.486835 0.513167 19.486838 0.513167 19.486831 0.513167 19.486836 0.513167 19.48683

10 0.513167 19.4868310 0.513167 19.4868311 0.513167 19.48683

Example 1Process Capability

Control Chart for Pro

Instructions: 1. Clear data in XR-chart spreadsheet 2. Calculate sample means X-bar below 3. Calculate samples ranges R below 4. Calculate average sample mean (mean of X-bar ) – enter in XR-chart spreadsheet 5. Calculate average of range R-bar – enter in XR-chart spreadsheet Control limits now established... 6. Enter new data in XR-chart spreadsheet and track

Process Capability. Venture Electronics manufactures a line of MP3 audio players. One of the components manufactured by Venture and used in its players has a nominal output voltage of 8.0 volts. Specifications allow for a variation of plus or minus 0.6 volts. An analysis of current production shows that mean output voltage for the component is 8.054 volts with a standard deviation of 0.192 volts. Is the process "capable: of producing components that meet specification? What fraction of components will fall outside of specification? What can management do to improve this fraction?

Instructions: 1. Enter upper and lower specification limits in Cpk spreadsheet 2. Enter mean and standard deviation of actual voltages 3. Read capability index number 4. Read percent outside of specification limits

Example 3Control Chart for Proportion Defective

Initial Data New DataSample # Defects Fraction Sample # Defects

1 10 1 132 5 2 183 10 3 44 12 4 75 11 5 46 9 6 187 22 7 348 4 8 139 12 9 7

10 24 10 411 12 11 1812 15 12 1613 8 13 1514 14 14 615 4 15 616 10 16 1617 11 17 718 11 18 1019 26 19 820 13 20 421 10 21 1422 9 22 2923 11 23 424 12 24 8

Mean: 25 1026 1927 2028 829 1030 2

Control Chart for Pro


Control Chart for Proportion Defective. Chic Clothing is an upscale mailorder clothing company selling merchandise to successful business women. The company sends out thousands of orders five days a week. In order to monitor the accuracy of its order fulfillment process, 200 orders are carefully checked every day for errors. Initial data for 24 days is shown below when the order fulfillment process was thought to be "in control."

Instructions: 1. Clear data in P-chart spreadsheet 2. Calculate fraction defects below 3. Calculate mean fraction defective -- enter in P-chart spreadsheet 4. Enter obserbations per sample in P-chart spreadsheet Control limits now established... 3. Enter new data in P-chart spreadsheet and track

31 1632 1433 1134 1835 536 1637 1238 1139 840 441 842 1343 1244 845 446 3547 548 1249 1750 551 2452 1053 1454 355 456 1857 1458 2659 960 461 1462 1463 1264 765 266 1667 1668 1169 670 971 672 1673 2474 875 6

Example 4Control Chart for Defective per Unit

Initial Data New DataSample # Defects Sample # Defects

1 4 1 92 6 2 103 10 3 164 3 4 65 6 5 46 7 6 67 8 7 138 5 8 59 2 9 4

10 5 10 311 9 11 312 4 12 1213 3 13 1014 4 14 715 13 15 616 9 16 417 10 17 418 11 18 719 15 19 420 12 20 3

Mean: 21 422 1323 1424 425 426 1027 528 1629 630 12

Control Chart for Defective per Unit. Dave's is a restaurant chain that employs independent evaluators to visit its restaurants as secret shoppers to the asses the quality of service. The company evaluates restaurants in two categories, food quality, and service (promptness, order accuracy, courtesy, friendliness, etc.) The evaluator considers not only his/her order experiences, but also evaluations throughout the restaurant. Following are the results of one evaluator's 20 visits to one particular restaurant over a four month period. The data show the number of "defects" shown in the service category.

Instructions: 1. Clear data in C-chart spreadsheet 2. Calculate mean number of defects below -- enter in C-chart spreadsheet Control limits now established... 3. Enter new data in C-chart spreadsheet and track

31 732 533 534 835 536 737 638 1239 540 641 242 543 344 345 646 747 448 549 750 551 652 853 354 755 356 857 658 459 960 561 562 663 664 465 566 367 568 569 470 571 572 673 574 575 3

Example 2Control Charts for Continuous Variables

Initial DataSample # Readings (in ohms) X-bar R

1 1010 991 985 9862 995 996 1009 9943 990 1003 1015 10084 1015 1020 1009 9985 1013 1019 1005 9936 994 1001 994 10057 989 992 982 10208 1001 986 996 9969 1006 989 1005 1007

10 992 1007 1006 97911 996 1006 997 98912 1019 996 991 101113 981 991 989 100314 999 993 988 98415 1013 1002 1005 992

Means:

New DataSample # Readings (in ohms)

1 998.49 992.77 1001.12 987.962 1003.05 1000.57 1016.15 1001.193 1008.29 982.09 997.52 1003.194 994.50 1009.35 1014.88 1007.965 992.71 996.19 1007.84 1015.356 981.52 989.77 975.61 1000.03

Control Charts for Continuous Variables. Resistors for electronic circuits are being manufactured on a high-speed automated machine. The machine is set up to produce a large run of resistors of 1,000 ohms each. To create a control chart to be used throughout the run, 15 samples were taken with four resistors in each sample. Develop X-bar and R charts and plot the values. From the charts, what comments can you make about the process?


7 1006.48 1023.13 1005.08 1012.038 1009.91 1003.51 983.55 998.139 1001.57 994.43 991.74 989.16

10 1005.87 996.05 1005.79 974.4111 1011.67 1000.61 991.28 996.5712 1006.77 1009.62 995.56 986.3913 999.70 997.03 1003.64 1002.2514 999.16 987.16 984.18 1022.5815 1006.49 991.90 992.85 1008.2616 978.00 997.13 1000.88 974.8017 1005.52 998.84 993.38 990.9818 996.76 998.04 986.45 994.2119 994.87 1006.69 1009.50 997.3520 982.81 978.07 1003.57 994.5521 988.11 1002.57 1000.58 1014.5122 973.84 991.41 989.94 985.7923 1001.03 985.67 996.59 1016.4224 981.31 1005.89 995.72 984.9125 1011.55 1000.71 996.39 1016.2126 978.95 990.52 997.35 1002.0227 1009.61 1011.46 984.41 1019.9828 986.79 993.72 980.46 979.5329 991.47 1003.85 1016.63 1013.0630 981.58 981.02 995.41 996.2831 1006.87 994.91 1004.43 1001.0532 1016.19 991.04 1005.32 1003.7533 1006.24 1005.40 992.83 996.9734 1029.71 999.35 1006.78 999.9835 999.37 1002.64 1005.04 1017.4836 984.08 983.87 1017.35 985.1037 1022.32 993.17 986.18 1000.9638 1000.80 1013.38 989.32 989.4339 1002.59 1003.20 1005.48 1006.6740 1006.81 994.36 992.66 1004.6541 994.07 994.12 993.71 1005.6142 982.78 1006.37 982.98 991.0743 981.94 1008.07 988.36 988.2144 1007.17 1010.70 1003.20 997.1945 1008.43 1007.93 998.83 997.2846 1006.94 989.31 1010.94 993.1947 973.22 989.73 1001.70 1003.8948 994.14 1006.93 1024.82 993.5749 992.94 990.43 988.95 1009.9850 1013.03 996.87 1033.28 1017.6651 968.01 998.21 1005.02 982.4052 1029.58 1012.02 1004.48 998.2753 1004.27 989.19 991.22 1003.5054 1004.26 999.95 1007.31 988.3455 1008.02 1016.35 993.23 1021.5956 1009.91 1005.19 988.20 1032.6557 1014.53 1028.93 1040.51 991.12

58 1010.02 1005.74 1006.76 1000.7859 990.46 985.46 991.93 981.2360 1041.56 1007.71 1037.21 995.6961 1003.06 997.29 1001.75 1000.7262 1001.58 982.89 1013.49 1006.4363 1009.89 1016.33 992.85 1020.4564 1006.14 1023.92 1016.08 979.3665 998.66 1019.54 1026.30 975.1066 988.63 1001.15 1013.26 1017.1267 1020.23 1018.33 987.81 985.9768 1005.66 993.27 1001.47 1022.9669 996.37 1004.50 1033.79 1000.2670 1005.81 984.47 1026.08 1011.4771 1018.79 987.54 1011.47 934.5972 993.61 1026.24 1026.39 1003.2173 977.94 1022.89 1001.85 1010.6374 1003.68 1005.90 1016.45 992.2775 1022.02 1010.33 998.33 988.74

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