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제4제 제제제제 2012 . 03. 28 2012 . 03. 28 제제 제제제 제제제 제제제제 제제제제 제제 : 제 제 제제 1

제 4 강 통계기법

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제 4 강 통계기법. 2012 . 03. 28. 안산 대학교 디지털 정보학과 품질관리 담당 : 조 중 상 교수. 1. Harry&Schroeder(2000) -. 산업의 미래는 통계지식에 달려있다 , -. 미래를 보게 해주고 우리의 생활을 발전된 방향으로 변화하게 해준다 -. 기업들이 자료를 수집하고 , 정보로 전환한 뒤 , 직관 또는 과거의 경험이 아닌 사실에 근거하여 정보를 해석한다 - PowerPoint PPT Presentation

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  • 4 2012 . 03. 28 : *

  • 1. Harry&Schroeder(2000) -. , -. -. , , -. 2.Deming(1986) -. . -. .

  • 4.1 4.2 7 QC 4.3 7 QC 4.4 4.5 FMEA4.6

  • 4.1 : ? 1. -. -. -. .

    2. Barabba &Zaltman(1991) , -. -. . -. , (perception bias) : , ( ) , (interaction bias) : , :

  • (Statistical Thinking)1) .

    2) , ,

    3) : // *. *. *. *.

  • 4.2 7 QC 1. 2. 3. 4. 5. 6. 7. Ishikawa(1986)

    -. 7QC -. QC 7 -. : / -. / / / / / / / -. . : , )

  • Bowels & Hammond(1991)

    -. Ishikawa . , ,

  • 4.2 7 QC 1. 2. 3. 4. 5. 6. 7. Ishikawa(1986)

    -. 7QC -. QC 7 -. : / -. / / / / / / / -. . : , )

  • Kaoru Ishikawa (1915-1988)

    -. -. (1960 )-. -. -.

  • 4.2.11. (, CE(Cause-and-Effect), (fishbone diagram) Ishikawa **> 2. 3. : , , 4. : .()5. .

  • 1. 12

  • 2. 1 : 2 : 3 :

  • 4 : , , 5 : 6 : . . 7 : . ,

  • Cause & Effect Diagram

  • 3. , ,

  • -.

    -. ,

    4.2.2

  • 1. /Stratification4 , . (SQC) . .

  • 2. 5 , . AB

  • 3. /Stratification6 data data . () , , , , ,, , / , , , , , , , LOT, , , , , , LOT, , LINE

  • 4. /Stratification7 /, , ,, , , , , , , ,

  • 5. 8-. .-. .-. .-. -. .-. .-. .-. .

  • -.

    -.

    -. 4W(who, what, where, when) 1H(how)

    -. (check list) 4.2.3

  • 1. /Check Sheet13Data .

  • 2. 14 Data , .

  • , , , 3. 15

    0000000000000000000000000

    &A

    &P

    LIST

    LIST

    NO

    1 00436

    200440

    3 00442

    4 00447

    5VALEO COVER 00732

    6 00734

    7 00733

    8TRK 00880

    9TRK 00881

    10TRK VALEO COVER 00882

    M/C:PV-00 : .

    12345678910111213141516171819202122232425262728293031

    12345678910111213141516171819202122232425262728293031

    12345678910111213141516171819202122232425262728293031

    1999

    ()

    M/C:PV-00698 : ,

    12345678910111213141516171819202122232425262728293031

    1.51

    2101

    12345678910111213141516171819202122232425262728293031

    51

    12345678910111213141516171819202122232425262728293031

    .301

    S/W ON,OFF31

    S/W S/W ON,OFF41

    CHECK SHEET 2001 1

    ()

    M/C:PV-00845 : ,

    12345678910111213141516171819202122232425262728293031

    1,51

    2,31

    3.51

    12345678910111213141516171819202122232425262728293031

    12345678910111213141516171819202122232425262728293031

    1 21

    2 21

    3 21

    4 S/W ON,OFF51

    CHECK SHEET 2001 1

    ()

    M/C:PV-00846 : ,

    12345678910111213141516171819202122232425262728293031

    1 51

    2 51

    12345678910111213141516171819202122232425262728293031

    1 31

    2 31

    12345678910111213141516171819202122232425262728293031

    110bar max151

    2 5bar min151

    3 21

    CHECK SHEET 2001 1

    ()

    M/C:PV-01007 : ,

    12345678910111213141516171819202122232425262728293031

    1,31

    2PRINT,31

    3 51

    4

    12345678910111213141516171819202122232425262728293031

    11

    2

    3

    4

    12345678910111213141516171819202122232425262728293031

    1STYLUS31

    2RECORDING PEN31

    CHECK SHEET 2001 1

    ()

    M/C:PV-00513 : ,

    12345678910111213141516171819202122232425262728293031

    1 51

    2 51

    12345678910111213141516171819202122232425262728293031

    131

    12345678910111213141516171819202122232425262728293031

    11~10bar max151

    2 5bar min151

    CHECK SHEET 2001 1

    ()

    (2)

    M/C:PV-00734 : ,

    12345678910111213141516171819202122232425262728293031

    1 31

    2PC 32

    3 31

    4 51

    12345678910111213141516171819202122232425262728293031

    1 GUN31

    2ANGLE BAR GUN31

    3BALL GUIDE GUN31

    4BALL NUT GUN31

    12345678910111213141516171819202122232425262728293031

    1TORQUE CELL31

    2LIMIT 11

    3SERVO MOTER POM .31

    4 PC .21

    5AIR SYSTEMIN:5.5bar&31

    OUT:5bar

    CHECK SHEET 2001 1

    ()

    (2)

    M/C:PV-00733 : ,

    12345678910111213141516171819202122232425262728293031

    1 31

    2PC ,31

    3 (PC)31

    4 51

    12345678910111213141516171819202122232425262728293031

    1SHAFT 51

    2

    3

    4

    12345678910111213141516171819202122232425262728293031

    1JIG 31

    2 31

    3LOAD CELL1201

    4 SENSOR 601

    CHECK SHEET 2001 1

    ()

    M/C:PV-00844 : ,

    12345678910111213141516171819202122232425262728293031

    1,31

    2,31

    3,31

    4 51

    12345678910111213141516171819202122232425262728293031

    1SHAFT 51

    2 OIL GUN31

    3

    4

    12345678910111213141516171819202122232425262728293031

    1 31

    2 31

    CHECK SHEET 2001 1

    ()

    COVER

    VALEO COVER M/C:PV-00732 : ,

    12345678910111213141516171819202122232425262728293031

    1 ,101

    2PC ,51

    3 51

    4, 151

    12345678910111213141516171819202122232425262728293031

    1PUSH RING GUN31

    2PLATE RING GUN31

    3STARTING MACHINEPULLOIL GUN31

    12345678910111213141516171819202122232425262728293031

    1()0.7 bar & 31

    2()5.5 bar & 31

    3PLATE 601

    4PUSH 601

    5PULL 601

    6SENSOR BOX'0'TEST PC501

    7TEST 31

    CHECK SHEET 2001 1

    ()

    M/C:PV-00442 : ,

    12345678910111213141516171819202122232425262728293031

    1 ,31

    2,31

    3PRINT,31

    4 51

    12345678910111213141516171819202122232425262728293031

    1 SHAFT 1

    2

    3

    4

    12345678910111213141516171819202122232425262728293031

    1 51

    2

    3

    CHECK SHEET 2001 1

    ()

    (UTM)M/C:PV-01006 : ,

    12345678910111213141516171819202122232425262728293031

    1 ,31

    2,31

    3 51

    4

    12345678910111213141516171819202122232425262728293031

    1SHAFT 1

    2 1

    3

    4

    12345678910111213141516171819202122232425262728293031

    1MOTOR BELT 51

    2 51

    3 51

    CHECK SHEET 2001 1

    ()

    trk CO

    TRK VALEO COVER M/C:PV-00882 : ,

    12345678910111213141516171819202122232425262728293031

    1 ,101

    2PC ,51

    3 51

    4151

    12345678910111213141516171819202122232425262728293031

    1PUSH RING GUN31

    2PLATE RING GUN31

    3LM GUIDE GUN31

    12345678910111213141516171819202122232425262728293031

    1()0.7 bar & 31

    2()5.5 bar & 31

    3PLATE 601

    4PUSH 601

    5PULL 601

    6SENSOR BOX'0'TEST PC501

    7 SENSOR 1

    CHECK SHEET 2001 1

    ()

    trkDISC

    TRK M/C:PV-00880 : ,

    12345678910111213141516171819202122232425262728293031

    1 ,31

    2PC ,31

    3 32

    4 51

    12345678910111213141516171819202122232425262728293031

    1SHAFT 51

    2ANGLE BAR GUN31

    3

    4

    12345678910111213141516171819202122232425262728293031

    1JIG 31

    2TORQUE CELL201

    3 31

    4 31

    5 41

    CHECK SHEET 2001 1

    ()

    trkCU (4)

    TRK M/C:PV-00881 : ,

    12345678910111213141516171819202122232425262728293031

    1 31

    2PC ,31

    3 (PC)31

    4 51

    12345678910111213141516171819202122232425262728293031

    1JIG 31

    2 31

    3LOAD CELL 1201

    4 SENSOR 601

    CHECK SHEET 2001 1

    ()

  • 4. 16

  • 5. 17

    Sheet1

    3/33/43/53/63/73/8

    S/Pin //////////////////

    F/C /////////////

    CU/P /-///-/

    T/Spring//////////////// ////////

    F/Washer//////////////////

  • 6. 18

    0000000000000000000000000

    &A

    &P

    LIST

    LIST

    NO

    1 00436

    200440

    3 00442

    4 00447

    5VALEO COVER 00732

    6 00734

    7 00733

    8TRK 00880

    9TRK 00881

    10TRK VALEO COVER 00882

    M/C:PV-00 : .

    12345678910111213141516171819202122232425262728293031

    12345678910111213141516171819202122232425262728293031

    12345678910111213141516171819202122232425262728293031

    1999

    ()

    M/C:PV-00698 : ,

    12345678910111213141516171819202122232425262728293031

    1.51

    2101

    12345678910111213141516171819202122232425262728293031

    51

    12345678910111213141516171819202122232425262728293031

    .301

    S/W ON,OFF31

    S/W S/W ON,OFF41

    CHECK SHEET 2001 1

    ()

    M/C:PV-00845 : ,

    12345678910111213141516171819202122232425262728293031

    1,51

    2,31

    3.51

    12345678910111213141516171819202122232425262728293031

    12345678910111213141516171819202122232425262728293031

    1 21

    2 21

    3 21

    4 S/W ON,OFF51

    CHECK SHEET 2001 1

    ()

    M/C:PV-00846 : ,

    12345678910111213141516171819202122232425262728293031

    1 51

    2 51

    12345678910111213141516171819202122232425262728293031

    1 31

    2 31

    12345678910111213141516171819202122232425262728293031

    110bar max151

    2 5bar min151

    3 21

    CHECK SHEET 2001 1

    ()

    M/C:PV-01007 : ,

    12345678910111213141516171819202122232425262728293031

    1,31

    2PRINT,31

    3 51

    4

    12345678910111213141516171819202122232425262728293031

    11

    2

    3

    4

    12345678910111213141516171819202122232425262728293031

    1STYLUS31

    2RECORDING PEN31

    CHECK SHEET 2001 1

    ()

    M/C:PV-00513 : ,

    12345678910111213141516171819202122232425262728293031

    1 51

    2 51

    12345678910111213141516171819202122232425262728293031

    131

    12345678910111213141516171819202122232425262728293031

    11~10bar max151

    2 5bar min151

    CHECK SHEET 2001 1

    ()

    (2)

    M/C:PV-00734 : ,

    12345678910111213141516171819202122232425262728293031

    1 31

    2PC 32

    3 31

    4 51

    12345678910111213141516171819202122232425262728293031

    1 GUN31

    2ANGLE BAR GUN31

    3BALL GUIDE GUN31

    4BALL NUT GUN31

    12345678910111213141516171819202122232425262728293031

    1TORQUE CELL31

    2LIMIT 11

    3SERVO MOTER POM .31

    4 PC .21

    5AIR SYSTEMIN:5.5bar&31

    OUT:5bar

    CHECK SHEET 2001 1

    ()

    (2)

    M/C:PV-00733 : ,

    12345678910111213141516171819202122232425262728293031

    1 31

    2PC ,31

    3 (PC)31

    4 51

    12345678910111213141516171819202122232425262728293031

    1SHAFT 51

    2

    3

    4

    12345678910111213141516171819202122232425262728293031

    1JIG 31

    2 31

    3LOAD CELL1201

    4 SENSOR 601

    CHECK SHEET 2001 1

    ()

    M/C:PV-00844 : ,

    12345678910111213141516171819202122232425262728293031

    1,31

    2,31

    3,31

    4 51

    12345678910111213141516171819202122232425262728293031

    1SHAFT 51

    2 OIL GUN31

    3

    4

    12345678910111213141516171819202122232425262728293031

    1 31

    2 31

    CHECK SHEET 2001 1

    ()

    COVER

    VALEO COVER M/C:PV-00732 : ,

    12345678910111213141516171819202122232425262728293031

    1 ,101

    2PC ,51

    3 51

    4, 151

    12345678910111213141516171819202122232425262728293031

    1PUSH RING GUN31

    2PLATE RING GUN31

    3STARTING MACHINEPULLOIL GUN31

    12345678910111213141516171819202122232425262728293031

    1()0.7 bar & 31

    2()5.5 bar & 31

    3PLATE 601

    4PUSH 601

    5PULL 601

    6SENSOR BOX'0'TEST PC501

    7TEST 31

    CHECK SHEET 2001 1

    ()

    M/C:PV-00442 : ,

    12345678910111213141516171819202122232425262728293031

    1 ,31

    2,31

    3PRINT,31

    4 51

    12345678910111213141516171819202122232425262728293031

    1 SHAFT 1

    2

    3

    4

    12345678910111213141516171819202122232425262728293031

    1 51

    2

    3

    CHECK SHEET 2001 1

    ()

    (UTM)M/C:PV-01006 : ,

    12345678910111213141516171819202122232425262728293031

    1 ,31

    2,31

    3 51

    4

    12345678910111213141516171819202122232425262728293031

    1SHAFT 1

    2 1

    3

    4

    12345678910111213141516171819202122232425262728293031

    1MOTOR BELT 51

    2 51

    3 51

    CHECK SHEET 2001 1

    ()

    trk CO

    TRK VALEO COVER M/C:PV-00882 : ,

    12345678910111213141516171819202122232425262728293031

    1 ,101

    2PC ,51

    3 51

    4151

    12345678910111213141516171819202122232425262728293031

    1PUSH RING GUN31

    2PLATE RING GUN31

    3LM GUIDE GUN31

    12345678910111213141516171819202122232425262728293031

    1()0.7 bar & 31

    2()5.5 bar & 31

    3PLATE 601

    4PUSH 601

    5PULL 601

    6SENSOR BOX'0'TEST PC501

    7 SENSOR 601

    CHECK SHEET 2001 1

    ()

    trkDISC

    TRK M/C:PV-00880 : ,

    12345678910111213141516171819202122232425262728293031

    1 ,31

    2PC ,31

    3 32

    4 51

    12345678910111213141516171819202122232425262728293031

    1SHAFT 51

    2ANGLE BAR GUN31

    3

    4

    12345678910111213141516171819202122232425262728293031

    1JIG 31

    2TORQUE CELL201

    3 31

    4 31

    5 41

    CHECK SHEET 2001 1

    ()

    trkCU (4)

    TRK M/C:PV-00881 : ,

    12345678910111213141516171819202122232425262728293031

    1 31

    2PC ,31

    3 (PC)31

    4 51

    12345678910111213141516171819202122232425262728293031

    1SHAFT 51

    2LM GUIDE 51

    3

    4

    12345678910111213141516171819202122232425262728293031

    1JIG 31

    2 31

    3LOAD CELL 1201

    4 SENSOR 601

    CHECK SHEET

    ()

  • 4.2.4 -. (Histogram) -.

    -. ,

    ex)502mm

    ex)

    ex)

    4F4F

    3F3F

    2F2F

    1F1F

    &C

    &C

    ()

    (/)

    50mm

    52mm

    48mm

    LOT

    DATA

    LOT

    DATA

    Sampling

    Sampling

    ()

    ()

    1

    2

    R = X max - X min

    100 ~ 250

    7 ~1210 ~ 20

    ex)X min = 10.02

    X max = 10.08

    0.750.75

    ex)

    5.56.05.96.15.96.35.66.46.46.0-0.80-0.30-0.40-0.20-0.400.00-0.700.100.10-0.30-0.000.090.160.040.1600.490.010.010.09

    5.86.06.66.06.16.06.56.27.66.7- SPEC-0.50-0.300.30-0.30-0.20-0.300.20-0.101.300.400.250.090.090.090.040.090.040.011.690.16

    6.36.55.56.17.16.06.96.86.36.16.2 1.50.000.20-0.80-0.200.80-0.300.600.500.00-0.2000.040.640.040.640.090.360.2500.04

    6.96.05.86.26.56.06.95.85.96.20.60-0.30-0.50-0.100.20-0.300.60-0.50-0.40-0.100.360.090.250.010.040.090.360.250.160.01

    5.66.05.35.76.06.37.46.66.36.7- X max= 7.7-0.70-0.30-1.00-0.60-0.300.001.100.300.000.400.490.0910.360.0901.210.0900.16

    7.16.86.37.06.36.06.26.07.66.3- X min = 5.30.800.500.000.700.00-0.30-0.10-0.301.300.000.640.2500.4900.090.010.091.690

    6.06.06.66.46.16.36.77.75.66.0- k = 10-0.30-0.300.300.10-0.200.000.401.40-0.70-0.300.090.090.090.010.0400.161.960.490.09

    6.46.66.26.47.07.65.66.76.06.20.100.30-0.100.100.701.30-0.700.40-0.30-0.100.010.090.010.010.491.690.490.160.090.010.231922

    6.96.76.05.95.96.05.86.76.26.50.600.40-0.30-0.40-0.40-0.30-0.500.40-0.100.200.360.160.090.160.160.090.250.160.010.04

    5.86.76.56.35.86.46.06.85.66.2-0.500.430.200.00-0.500.10-0.300.50-0.70-0.100.250.18490.0400.250.010.090.250.490.01

    -0.70.3-2.3-0.9-0.3-0.10.62.70.5-0.1-0.3

    NoX (U)fXfX

    15.25 ~ 5.455.3611

    25.45 ~ 5.655.5578

    35.65 ~ 5.855.75715

    45.85 ~ 6.055.952439

    56.05 ~ 6.256.151453

    66.25 ~ 6.456.351669

    76.45 ~ 6.656.55877

    86.65 ~ 6.856.751188

    96.85 ~ 7.056.95593

    107.05 ~ 7.257.15295

    117.25 ~ 7.457.35196

    127.45 ~ 7.657.55399

    137.65 ~ 7.857.751100

    100

    NoX (U)fXfX

    15.25 ~ 5.455.3611-3-39

    25.45 ~ 5.655.5578-2-14285.95 + ((167/100) X 0.2)

    35.65 ~ 5.855.75715-1-77= 6.284

    45.85 ~ 6.055.952439000

    56.05 ~ 6.256.15145311414

    66.25 ~ 6.456.35166923264

    76.45 ~ 6.656.5587732472

    86.65 ~ 6.856.751188444176

    96.85 ~ 7.056.95593525125

    107.05 ~ 7.257.1529561272

    117.25 ~ 7.457.351967749

    127.45 ~ 7.657.55399824192

    137.65 ~ 7.857.7511009981

    10010039167889

    U =

    U = 0.0021 X 1,000,000 = 2,100 PPM

    U =

    U = 0.00066 X 1,000,000 = 660 PPM

    U = 2,100 + 660 = 2,760PPM

    Cp =

    = AVERAGE(Xi : Xn)

    &C

    &C

    SU - X

    s

    fX

    n

    R

    (k)

    * h =

    ...

    ...

    2

    *

    .

    * ( )

    .

    *

    . ( )

    *

    .

    ( )

    2

    2

    2

    2

    * k =

    n

    fX

    n

    * s = h

    2

    2

    = 0.2

    889

    100

    167

    100

    2

    = 0.2

    8.89 - 2.79

    = 0.2

    6.1

    = 0.494

    2

    2

    2

    (Xi)

    - s =

    "=STDEVP (X1 : Xn)" CUMPUTER

    X - SL

    s

    7.7 - 6.284

    0.494

    =

    =23.831

    S

    n

    =

    23.831

    100

    =

    0.23831

    = 0.488

    = 2.87

    6.284 - 4.7

    0.494

    =

    = 3.21

    SU - SL

    6s

    =

    7.7 - 4.7

    6 X 0.494

    3.0

    2.964

    =

    = 1.01

    " =AVERAGE (X1 : Xn)" CUMPUTER

    n

    fX

    n

    2

    2

    fX

    n

    = h

    ( s )

    =

    Xi

    n

    =STDEVP(Xi : Xn)

    X - SL

    s

    =

    SU - X

    s

    +

    SU - SL

    6s

    Cp=

    Cp .

    (Xi)

    n

    2

    &C

    &C

    ,()

    * () .

    ()

    ()

    * .

    * .

    * .

    * .

    * DATA .

    ()

    * .

    * DATA .

    1

    1

    Pr =

    u0.090.080.070.060.050.040.030.020.010.00

    -3.50.000170.000170.000180.000190.000190.000200.000210.000220.000220.00023

    -3.40.000240.000250.000260.000270.000280.000290.000300.000310.000330.00034

    -3.30.000350.000360.000380.000390.000400.000420.000430.000450.000470.00048

    -3.20.000500.000520.000540.000560.000580.000600.000620.000640.000660.00069

    -3.10.000710.000740.000760.000790.000820.000850.000870.000900.000940.00097

    -3.00.001000.001040.001070.001110.001140.001180.001220.001260.001310.00135

    -2.90.00140.00140.00150.00150.00160.00160.00170.00170.00180.0019

    -2.80.00190.00200.00210.00210.00220.00230.00230.00240.00250.0026

    -2.70.00260.00270.00280.00290.00300.00310.00320.00330.00340.0035

    -2.60.00360.00370.00380.00390.00400.00410.00430.00440.00450.0047

    -2.50.00480.00490.00510.00520.00540.00550.00570.00590.00600.0062

    -2.40.00640.00660.00680.00690.00710.00730.00750.00780.00800.0082

    -2.30.00840.00870.00890.00910.00940.00960.00990.01020.01040.0107

    -2.20.01100.01130.01160.01190.01220.01250.01290.01320.01360.0139

    -2.10.01430.01460.01500.01540.01580.01620.01660.01700.01740.0179

    -2.00.01830.01880.01920.01970.02020.02070.02120.02170.02220.0228

    -1.90.02330.02390.02440.02500.02560.02620.02680.02740.02810.0287

    -1.80.02940.03010.03070.03140.03220.03290.03360.03440.03510.0359

    -1.70.03670.03750.03840.03920.04010.04090.04180.04270.04360.0446

    -1.60.04550.04650.04750.04850.04950.05050.05160.05260.05370.0548

    -1.50.05590.05710.05820.05940.06060.06180.06300.06430.06550.0668

    -1.40.06810.06940.07080.07210.07350.07490.07640.07780.07930.0808

    -1.30.08230.08380.08530.08690.08850.09010.09180.09340.09510.0968

    -1.20.09850.10030.10200.10330.10570.10750.10930.11120.11310.1151

    -1.10.11700.11900.12100.12300.12510.12710.12920.13140.13350.1357

    -1.00.13790.14010.14230.14460.14690.14920.15150.15390.15620.1587

    -0.90.16110.16350.16600.16850.17110.17360.17620.17880.18140.1841

    -0.80.18670.18940.19220.19490.19770.20050.20330.20610.20900.2119

    -0.70.21480.21770.22070.22360.22660.22970.23270.23580.23890.2420

    -0.60.24510.24830.25140.25460.25780.26110.26430.26760.27090.2743

    -0.50.27760.28100.28430.28770.29120.29460.29810.30150.30500.3085

    -0.40.31210.31560.31920.32280.32640.33000.33360.33720.34090.3446

    -0.30.34830.35200.35570.35940.36320.36690.37070.37450.37830.3821

    -0.20.38590.38970.39360.39740.40130.40520.40900.41290.41680.4207

    -0.10.42470.42860.43250.43640.44040.44430.44830.45220.45620.4602

    0.00.46410.46810.47210.47610.48010.48400.48800.49200.49600.5000

    2

    U

    e

    x / 2d

    2

    Pr

    0

    2

    u0.000.010.020.030.040.050.060.070.080.09

    +0.00.50000.50400.50800.51200.51600.51990.52390.52790.53190.5359

    +0.10.53980.54380.54780.55170.55570.55960.56360.56750.57140.5753

    +0.20.57930.58320.58710.59100.59480.59870.60260.60640.61030.6141

    +0.30.61790.62170.62550.62930.63310.63680.64060.64430.64800.6517

    +0.40.65540.65910.66280.66640.67000.67360.67720.68080.68440.6879

    +0.50.69150.69500.69850.70190.70540.70880.71230.71570.71900.7224

    +0.60.72570.72910.73240.73570.73890.74220.74540.74860.75170.7549

    +0.70.75800.76110.76420.76730.77040.77340.77640.77940.78230.7852

    +0.80.78810.79100.79390.79670.79950.80230.80510.80790.81060.8133

    +0.90.81590.81860.82120.82380.82640.82890.83150.83400.83650.8389

    +1.00.84130.84380.84610.84850.85080.85310.85540.85770.85990.8621

    +1.10.86430.86650.86860.87080.87290.87490.87700.87900.88100.8830

    +1.20.88490.88690.88880.89070.89250.89440.89620.89800.89970.9015

    +1.30.90320.90490.90660.90820.90990.91150.91310.91470.91620.9177

    +1.40.91920.92070.92220.92360.92510.92650.92790.92920.93060.9319

    +1.50.93320.93450.93570.93700.93820.93940.94060.94180.94290.9441

    +1.60.94520.94630.94740.94840.94950.95050.95150.95250.95350.9545

    +1.70.95540.95640.95730.95820.95910.95990.96080.96160.96250.9633

    +1.80.96410.96490.96560.96640.96710.96780.96860.96930.96990.9706

    +1.90.97130.97190.97260.97320.97380.97440.97500.97560.97610.9767

    +2.00.97730.97780.97830.97880.97930.97980.98030.98080.98120.9817

    +2.10.98210.98260.98300.98340.98380.98420.98460.98500.98540.9857

    +2.20.98610.98640.98680.98710.98750.98780.98810.98840.98870.9890

    +2.30.98930.98960.98980.99010.99040.99060.99090.99110.99130.9916

    +2.40.99180.99200.99220.99250.99270.99290.99310.99320.99340.9936

    +2.50.99380.99400.99410.99430.99450.99460.99480.99490.99510.9952

    +2.60.99580.99550.99560.99570.99590.99600.99610.99620.99630.9964

    +2.70.99650.99660.99670.99680.99690.99700.99710.99720.99730.9974

    +2.80.99740.99750.99760.99770.99770.99780.99790.99790.99800.9981

    +2.90.99810.99820.99830.99830.99840.99840.99850.99850.99860.9986

    +3.00.998650.998690.998740.998780.998820.998860.998890.998930.998960.99900

    +3.10.999030.999060.999100.999130.999150.999180.999210.999240.999260.99929

    +3.20.999310.999340.999360.999380.999400.999420.999440.999460.999480.99950

    +3.30.999520.999530.999550.999570.999580.999600.999610.999620.999640.99965

    +3.40.999660.999670.999690.999700.999710.999720.999730.999740.999750.99976

    +3.50.999770.999780.999780.999790.999800.999810.999810.999820.999830.99983

    0

    * SPEC : 6.80.25

    5/65/75/85/95/115/125/135/145/155/165/185/195/20

    6.846.806.906.876.816.846.796.916.796.956.796.846.92

    6.976.996.926.866.796.896.796.946.886.916.886.896.95

    6.696.796.746.746.886.846.766.716.736.776.806.686.72

    20.5020.5820.5620.4720.4820.5720.3420.5620.4020.6320.4720.4120.59

    6.836.866.856.826.836.866.786.856.806.886.826.806.86

    (MAN, MACHINE, MATERIAL., METHOD)

    UCL

    LCLx

    n=40.3%2.3%15.9%50.0%84.1%97.7%99.1%

    R = (X max) - (X min)

    UCL = X + A RnA2D3D4

    21.883.27

    LCL = X - A R31.02"2.57

    40.73"2.28

    50.58"2.11

    60.48"2.00

    UCL = D R70.420.081.92

    80.370.141.86

    LCL = D R90.340.181.82

    100.310.221.78

    n2345678910

    1.1281.6932.0592.3262.5342.7042.8472.973.078

    0.8530.8880.8800.8640.8480.8330.8200.8080.797

    ex)R = 1.4

    &C

    &C

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    &A

    &P

    ()

    i

    = () 3 = 3

    n

    =

    2

    d

    R

    OC (Operating CharacteristicCurve)

    ,

    1.0

    0.0

    6.0

    3.0

    1.0

    2.0

    4.0

    5.0

    0.5

    ,

    1.0

    0.0

    6.0

    3.0

    1.0

    2.0

    4.0

    5.0

    0.5

    k

    X

    2

    2

    k

    R

    4

    3

    2

    2

    (Xi)

    n

    fX

    n

    2

    2

    fX

    n

    = h

    ( s )

    =

    Xi

    n

    X - SL

    s

    =

    SU - X

    s

    +

    SU - SL

    6s

    Cp(k)=

    Cpk Cpk .

    R

    d

    2

    d

    2

    d

    3

    s =

    R

    d

    2

    =

    1.4

    2.059

    = 0.68

    =

    R

    d

    2

    SU - SL

    6s

    Cp(k) =

    Cpk Cpk .

    SU - SL

    6s

    Cp =

    {1/2(SU+ SL)-X }

    1/2(SU-SL)

    Cpk = (1 - k) Cp

    k() =

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    (RUN)

    7

    7 ,

    2( ) 3 27 310 4

    15 1( ) DATA (UCL, LCL )

    40% 1( ) DATA

    1. 2. 3.

    1. .2. .

    A, B, CD, E, F, G, H

    E, F, CI, J

    E, F, CI, J

    G

    D, EF, I

    A, B, G,H,I

    A, B, G

    A.

    B.

    C. (, )

    D.

    E. ( )

    F. ( )

    G. ( )

    H. . ( )

    I.

    J. .

    CPK

    D P MD P MD P MD P M

    0.30184,060368,1200.6525,58851,1761.001,3502,7001.352652

    0.31176,186352,3720.6623,85247,7041.011,2232,4461.362346

    0.32168,528337,0560.6722,21644,4321.021,1072,2141.372040

    0.33161,087322,1740.6820,67541,3501.031,0012,0021.381734

    0.34153,864307,7280.6919,22638,4521.049041,8081.391530

    0.35146,659293,3180.7017,86535,7301.058161,6321.401326

    0.36140,071280,1420.7116,58633,1721.067361,4721.411224

    0.37133,499266,9980.7215,38630,7721.076641,3281.421020

    0.38127,143254,2860.7314,26228,5241.085981,1961.43918

    0.39121,000242,0000.7413,20926,4181.095381,0761.44816

    0.40115,070230,1400.7512,22524,4501.104839661.45714

    0.41109,348218,6960.7611,30422,6081.114348681.46612

    0.42103,835207,6700.7710,44420,8881.123907801.47510

    0.4398,525197,0500.789,64219,2841.133507001.48510

    0.4493,417186,8340.798,89417,7881.143136261.4948

    0.4588,508177,0160.808,19816,3961.152805601.5036

    0.4683,793167,5860.817,54915,0981.162515021.5136

    0.4779,270158,5400.826,94713,8941.172404801.5236

    0.4874,934149,8680.836,38712,7741.182044081.5324

    0.4970,781141,5620.845,86811,7361.191793581.5424

    0.5066,807133,6140.855,38610,7721.201593181.5524

    0.5163,008126,0160.864,9409,8801.211422841.5612

    0.5259,380118,7600.874,5279,0541.221262521.5712

    0.5355,917111,8340.884,1458,2901.231122241.5812

    0.5452,616105,2320.893,7927,5841.241002001.5912

    0.5549,47198,9420.903,4676,9341.25891781.6012

    0.5646,47992,9580.913,1676,3341.26791581.6112

    0.5743,63387,2660.922,8905,7801.27701401.6212

    0.5840,93081,8600.932,6355,2701.28621241.6312

    0.5938,36476,7280.942,4014,8021.29551101.6400

    0.6035,93071,8600.952,1864,3721.3048961.6500

    0.6133,62567,2500.961,9883,9761.3143861.6600

    0.6231,44362,8860.971,8073,6141.3238761.6700

    0.6329,37858,7560.981,6413,2821.333366

    0.6427,42954,8580.991,4892,9781.342958

    0.750.75

    ex)

    #15.56.05.96.15.9#116.35.66.46.46.0-0.80-0.30-0.40-0.20-0.400.00-0.700.100.10-0.30-0.000.090.160.040.1600.490.010.010.09

    #25.86.06.66.06.1#126.06.56.27.66.7- SPEC-0.50-0.300.30-0.30-0.20-0.300.20-0.101.300.400.250.090.090.090.040.090.040.011.690.16

    #36.36.55.56.17.1#136.06.96.86.36.16.2 1.50.000.20-0.80-0.200.80-0.300.600.500.00-0.2000.040.640.040.640.090.360.2500.04

    #46.96.05.86.26.5#146.06.95.85.96.20.60-0.30-0.50-0.100.20-0.300.60-0.50-0.40-0.100.360.090.250.010.040.090.360.250.160.01

    #55.66.05.35.76.0#156.37.46.66.36.7- X max= 7.7-0.70-0.30-1.00-0.60-0.300.001.100.300.000.400.490.0910.360.0901.210.0900.16

    #67.16.86.37.06.3#166.06.26.07.66.3- X min = 5.30.800.500.000.700.00-0.30-0.10-0.301.300.000.640.2500.4900.090.010.091.690

    #76.06.06.66.46.1#176.36.77.75.66.0- k = 10-0.30-0.300.300.10-0.200.000.401.40-0.70-0.300.090.090.090.010.0400.161.960.490.09

    #86.46.66.26.47.0#187.65.66.76.06.20.100.30-0.100.100.701.30-0.700.40-0.30-0.100.010.090.010.010.491.690.490.160.090.010.23167

    #96.96.76.05.95.9#196.05.86.76.26.50.600.40-0.30-0.40-0.40-0.30-0.500.40-0.100.200.360.160.090.160.160.090.250.160.010.04

    #105.86.76.56.35.8#206.46.06.85.66.2-0.500.400.200.00-0.500.10-0.300.50-0.70-0.100.250.160.0400.250.010.090.250.490.01

    -0.70.3-2.3-0.9-0.3-0.10.62.70.5-0.1-0.3

    U =

    U = 0.0021 X 1,000,000 = 2,100 PPM

    U =

    U = 0.00066 X 1,000,000 = 660 PPM

    Cp =

    Cpk = (1-K)Cp = (1-0.084) X 1.01 = 0.925

    U =

    U = 0.0021 X 1,000,000 = 2,100 PPM

    U =

    U = 0.00054 X 1,000,000 = 540 PPM

    k === 0.0647

    Cp =

    Cpk = (1-K)Cp = (1-0.064) X 1.02 = 0.954

    #15.880.6#66.700.8#116.140.8#166.421.6

    #26.100.8#76.220.6#126.601.6#176.462.1

    #36.301.6#86.520.8#136.420.9#186.422.0

    #46.281.1#96.281.0#146.161.1#196.240.9

    #55.720.7#106.220.9#156.661.1#206.201.2

    22.2125.94

    U =

    U = 0.0016 X 1,000,000 = 1600 PPM

    U =

    U = 0.00040 X 1,000,000 = 400 PPM

    U = 1600 + 400 = 2000 PPM

    k === 0.0647

    0.97344

    Cp =

    Cpk = (1-K)Cp = (1-0.064) X 1.04 = 0.973

    6.2846.2976.297

    0.4940.4880.477

    210021001600

    660540400

    (PPM)276026402000

    0.0840.06470.0647

    Cp1.01 (2446 PPM)1.02 (2214 PPM)1.04 (1808 PPM)

    Cpk0.925 (5780 PPM)0.954 (4372 PPM)0.97 (3614 PPM)

    &C

    &C

    SU - X

    s

    fX

    n

    2

    *

    .

    * ( )

    .

    *

    . ( )

    *

    .

    ( )

    2

    fX

    n

    * s = h

    2

    2

    = 0.2

    889

    100

    167

    100

    2

    = 0.2

    8.89 - 2.79

    = 0.2

    6.1

    = 0.494

    2

    - s =

    X - SL

    s

    7.7 - 6.284

    0.494

    =

    =23.831

    S

    n

    =

    23.831

    100

    =

    0.23831

    = 0.488

    = 2.87

    6.284 - 4.7

    0.494

    =

    = 3.21

    SU - SL

    6s

    =

    7.7 - 4.7

    6 X 0.488

    3.0

    2.928

    =

    = 1.02

    " =AVERAGE (X1 : Xn)" CUMPUTER

    (Xi)

    n

    2

    SU - X

    s

    X - SL

    s

    7.7 - 6.297

    0.488

    =

    = 2.875

    6.297 - 4.7

    0.488

    =

    = 3.272

    SU - SL

    6s

    =

    7.7 - 4.7

    6 X 0.494

    3.0

    2.964

    =

    = 1.01

    {1/2(SU+SL) - X}

    1/2(SU-SL)

    {1/2(7.7+4.7) - 6.297}

    1/2(7.7-4.7)

    " =AVERAGE (X1 : Xn)" CUMPUTER

    SU - X

    s

    X - SL

    s

    7.7 - 6.297

    0.477

    =

    = 2.94

    6.297 - 4.7

    0.477

    =

    = 3.35

    SU - SL

    6s

    =

    7.7 - 4.7

    6 X 0.477

    3.0

    2.862

    =

    = 1.04

    {1/2(SU+SL) - X}

    1/2(SU-SL)

    {1/2(7.7+4.7) - 6.297}

    1/2(7.7-4.7)

  • 1. /Histogram53 . = 50

  • 2. 54-. . 1) . 2) 50 .-. (X max) (X min) . -. R(Range) . R = Xmax - Xmin. -. (k) (h) . k = h = R() / k( ) * h .

  • 3. 55-. . -. . 1) = data / 2 . = X min . 2) .

    1. ()

    . (QUALITY) ?

    () .

    , .

    * :

    (Quality characteristics) .

    * /(Specification) .

    . ()

    - (Quality of design)

    ,

    ,

    .

    - // (Quality of conformance)

    .

    - (Quality of market)

    .

    . (Management/Control)?

    (plan), (do),

    (check), (action) (cycle) .( )

    . (Quality Control)?

    ,

    (SQC : Statistical

    Quality Control) . (KS A 3001)

    - (SQC) : .

    - (TQC/TQM) : ,,,,

    , .

    2. () ()

    * (Specification)

    (Standard) .

    * (Tolerance)

    .

    ==> .

    * ex)502mm

    .

    *

    .

    3. DATA

    - .

    - DATA DATA .

    - DATA DATA .

    . (Stratification)

    / , , , ,

    .

    * (4M) ,

    .

    ex) SAMPLING

    50 .

    ex) . 4 .

    4F4F-

    3F- 3F-

    2F- 2F-

    1F .1F-

    . (SAMPLING) ()

    1)

    * (Population)

    ,

    DATA

    .

    - (Infinite population)

    - (Finite population)

    * /(Sample)

    DATA.

    * (Sampling)

    .

    ==> :

    .

    2) (Error)

    * (Error)

    DATA .

    * (Reliability)

    DATA ,

    .

    * (Precision)

    DATA .()

    * (Accurancy)

    DATA (Bias) .

    3)

    ) (Random sampling)

    .

    (1) :

    , ,, .

    (2) : .( )

    (3) :

    .

    ( )

    ) 2 (Two stage sampling)

    2

    .

    ) (Stratified sampling)

    .

    ) (Cluster sampling)

    .

    &C

    &C

    ()

    (/)

    50mm

    52mm

    48mm

    LOT

    DATA

    LOT

    DATA

    Sampling

    Sampling

    ()

    ()

    1

    2

    4. ()

    . (Frequency distribution)?

    .

    .

    1) DATA .

    2) .

    3) DATA .

    * DATA 100, 50 .

    .

    1) DATA (n) .

    2) DATA X max X min .

    3) (R: Range) .

    R = X max - X min

    4) (Iterval) h (k) .

    DATA 50 ~ 100100 ~ 250250

    6 ~ 10 7 ~1210 ~ 20

    5) .

    6) .

    , "DATA / 2" .

    * = X min - .

    ex)X min = 5.3- : 0.1 / 2 = 0.05

    X max = 7.7- : 5.3 - 0.05 = 5.25

    R = 7.7 - 5.3 = 2.4- 1 : 5.25 ~ 5.45

    k = 10, h = 2.4/10 = 0.2- 2 : 5.45 ~ 5.65

    7) .

    1 = 1 / 2

    2 = 2 / 2

    8) DATA .

    5 . ( "" )

    9) .

    .

    0.750.75

    ex) 100 .

    5.56.05.96.15.96.35.66.46.46.0-0.80-0.30-0.40-0.20-0.400.00-0.700.100.10-0.30-0.000.090.160.040.1600.490.010.010.09

    5.86.06.66.06.16.06.56.27.66.7- SPEC-0.50-0.300.30-0.30-0.20-0.300.20-0.101.300.400.250.090.090.090.040.090.040.011.690.16

    6.36.55.56.17.16.06.96.86.36.16.2 1.50.000.20-0.80-0.200.80-0.300.600.500.00-0.2000.040.640.040.640.090.360.2500.04

    6.96.05.86.26.56.06.95.85.96.2- n = 1000.60-0.30-0.50-0.100.20-0.300.60-0.50-0.40-0.100.360.090.250.010.040.090.360.250.160.01

    5.66.05.35.76.06.37.46.66.36.7- X max= 7.7-0.70-0.30-1.00-0.60-0.300.001.100.300.000.400.490.0910.360.0901.210.0900.16

    7.16.86.37.06.36.06.26.07.66.3- X min = 5.30.800.500.000.700.00-0.30-0.10-0.301.300.000.640.2500.4900.090.010.091.690

    6.06.06.66.46.16.36.77.75.66.0- k = 10-0.30-0.300.300.10-0.200.000.401.40-0.70-0.300.090.090.090.010.0400.161.960.490.09

    6.46.66.26.47.07.65.66.76.06.20.100.30-0.100.100.701.30-0.700.40-0.30-0.100.010.090.010.010.491.690.490.160.090.010.231922

    6.96.76.05.95.96.05.86.76.26.50.600.40-0.30-0.40-0.40-0.30-0.500.40-0.100.200.360.160.090.160.160.090.250.160.010.04

    5.86.76.56.35.86.46.06.85.66.2-0.500.430.200.00-0.500.10-0.300.50-0.70-0.100.250.18490.0400.250.010.090.250.490.01

    1) (R) : 7.7 - 5.3 =2.4-0.70.3-2.3-0.9-0.3-0.10.62.70.5-0.1-0.3

    2) (h) : 2.4/10 = 0.24 0.2* .

    3) : 0.1 / 2 = 0.05

    4)

    - : 5.3 - 0.05 = 5.25

    No (f)f X (U)fXfX

    15.25 ~ 5.455.3611

    25.45 ~ 5.655.5578

    35.65 ~ 5.855.75715

    45.85 ~ 6.055.952439

    56.05 ~ 6.256.151453

    66.25 ~ 6.456.351669

    76.45 ~ 6.656.55877

    86.65 ~ 6.856.751188

    96.85 ~ 7.056.95593

    107.05 ~ 7.257.15295

    117.25 ~ 7.457.35196

    127.45 ~ 7.657.55399

    137.65 ~ 7.857.751100

    100

    .

    .

    .

    * .

    .

    .

    * "1"

    * .

    . .

    1) X ( U) .

    - "0" 1,2,3, ...., -1,-2,-3..... .

    - (Xo) .

    2) "fX" .

    - fX = X

    3) "fX " .

    - fX = X

    4) .- Xo : .- n :

    - X = Xo + (fX / n) X h- fX : fX - h :

    * (= Xi / n) .

    No (f)f X (U)fXfX

    15.25 ~ 5.455.3611-3-39- :

    25.45 ~ 5.655.5578-2-14285.95 + ((167/100) X 0.2)

    35.65 ~ 5.855.75715-1-77= 6.284

    45.85 ~ 6.055.952439000

    56.05 ~ 6.256.15145311414* (Xi / n) :

    66.25 ~ 6.456.35166923264629.7 /100 = 6.297

    76.45 ~ 6.656.5587732472

    86.65 ~ 6.856.751188444176

    96.85 ~ 7.056.95593525125

    107.05 ~ 7.257.1529561272

    117.25 ~ 7.457.351967749

    127.45 ~ 7.657.55399824192

    137.65 ~ 7.857.7511009981

    10010039167889

    5) (S) .

    *

    - S = ( Xi - X )= Xi -

    .

    1)

    U =U = 2.87 .

    U = 0.0021 X 1,000,000 = 2,100 PPM

    2)

    U =U = 3.21 .

    U = 0.00066 X 1,000,000 = 660 PPM

    3) , .

    U = 2,100 + 660 = 2,760PPM

    . .

    d = X - = 6.284 - 6.2 = 0.084mm .

    .

    Cp =

    * Cp(k)

    Cp = 1.01 2,446 PPM

    COMPUTER

    ( X )= Xo + (fX / n) X h= Xi / n= AVERAGE(Xi : Xn)

    * Cp

    (U)

    U

    .

    &C

    &C

    SU - X

    s

    fX

    n

    R

    (k)

    * h =

    ...

    ...

    2

    *

    .

    * ( )

    .

    *

    . ( )

    *

    .

    ( )

    2

    2

    2

    2

    * k =

    n

    fX

    n

    * s = h

    2

    2

    = 0.2

    889

    100

    167

    100

    2

    = 0.2

    8.89 - 2.79

    = 0.2

    6.1

    = 0.494

    2

    2

    2

    (Xi)

    - s =

    "=STDEVP (X1 : Xn)" CUMPUTER

    X - SL

    s

    7.7 - 6.284

    0.494

    =

    =23.831

    S

    n

    =

    23.831

    100

    =

    0.23831

    = 0.488

    = 2.87

    6.284 - 4.7

    0.494

    =

    = 3.21

    SU - SL

    6s

    =

    7.7 - 4.7

    6 X 0.494

    3.0

    2.964

    =

    = 1.01

    " =AVERAGE (X1 : Xn)" CUMPUTER

    n

    fX

    n

    2

    2

    fX

    n

    = h

    ( s )

    =

    Xi

    n

    =STDEVP(Xi : Xn)

    X - SL

    s

    =

    SU - X

    s

    +

    SU - SL

    6s

    Cp=

    Cp .

    (Xi)

    n

    2

    &C

    &C

    ,()

    * () .

    ()

    ()

    * .

    * .

    * .

    * .

    * DATA .

    ()

    * .

    * DATA .

    1

    ()

    U

    1

    Pr =

    u0.090.080.070.060.050.040.030.020.010.00

    -3.50.000170.000170.000180.000190.000190.000200.000210.000220.000220.00023

    -3.40.000240.000250.000260.000270.000280.000290.000300.000310.000330.00034

    -3.30.000350.000360.000380.000390.000400.000420.000430.000450.000470.00048

    -3.20.000500.000520.000540.000560.000580.000600.000620.000640.000660.00069

    -3.10.000710.000740.000760.000790.000820.000850.000870.000900.000940.00097

    -3.00.001000.001040.001070.001110.001140.001180.001220.001260.001310.00135

    -2.90.00140.00140.00150.00150.00160.00160.00170.00170.00180.0019

    -2.80.00190.00200.00210.00210.00220.00230.00230.00240.00250.0026

    -2.70.00260.00270.00280.00290.00300.00310.00320.00330.00340.0035

    -2.60.00360.00370.00380.00390.00400.00410.00430.00440.00450.0047

    -2.50.00480.00490.00510.00520.00540.00550.00570.00590.00600.0062

    -2.40.00640.00660.00680.00690.00710.00730.00750.00780.00800.0082

    -2.30.00840.00870.00890.00910.00940.00960.00990.01020.01040.0107

    -2.20.01100.01130.01160.01190.01220.01250.01290.01320.01360.0139

    -2.10.01430.01460.01500.01540.01580.01620.01660.01700.01740.0179

    -2.00.01830.01880.01920.01970.02020.02070.02120.02170.02220.0228

    -1.90.02330.02390.02440.02500.02560.02620.02680.02740.02810.0287

    -1.80.02940.03010.03070.03140.03220.03290.03360.03440.03510.0359

    -1.70.03670.03750.03840.03920.04010.04090.04180.04270.04360.0446

    -1.60.04550.04650.04750.04850.04950.05050.05160.05260.05370.0548

    -1.50.05590.05710.05820.05940.06060.06180.06300.06430.06550.0668

    -1.40.06810.06940.07080.07210.07350.07490.07640.07780.07930.0808

    -1.30.08230.08380.08530.08690.08850.09010.09180.09340.09510.0968

    -1.20.09850.10030.10200.10330.10570.10750.10930.11120.11310.1151

    -1.10.11700.11900.12100.12300.12510.12710.12920.13140.13350.1357

    -1.00.13790.14010.14230.14460.14690.14920.15150.15390.15620.1587

    -0.90.16110.16350.16600.16850.17110.17360.17620.17880.18140.1841

    -0.80.18670.18940.19220.19490.19770.20050.20330.20610.20900.2119

    -0.70.21480.21770.22070.22360.22660.22970.23270.23580.23890.2420

    -0.60.24510.24830.25140.25460.25780.26110.26430.26760.27090.2743

    -0.50.27760.28100.28430.28770.29120.29460.29810.30150.30500.3085

    -0.40.31210.31560.31920.32280.32640.33000.33360.33720.34090.3446

    -0.30.34830.35200.35570.35940.36320.36690.37070.37450.37830.3821

    -0.20.38590.38970.39360.39740.40130.40520.40900.41290.41680.4207

    -0.10.42470.42860.43250.43640.44040.44430.44830.45220.45620.4602

    0.00.46410.46810.47210.47610.48010.48400.48800.49200.49600.5000

    2

    U

    e

    x / 2d

    2

    Pr

    0

    2

    ()

    U

    , U

    "+", "-" .

    "1 - Pr".

    u0.000.010.020.030.040.050.060.070.080.09

    +0.00.50000.50400.50800.51200.51600.51990.52390.52790.53190.5359

    +0.10.53980.54380.54780.55170.55570.55960.56360.56750.57140.5753

    +0.20.57930.58320.58710.59100.59480.59870.60260.60640.61030.6141

    +0.30.61790.62170.62550.62930.63310.63680.64060.64430.64800.6517

    +0.40.65540.65910.66280.66640.67000.67360.67720.68080.68440.6879

    +0.50.69150.69500.69850.70190.70540.70880.71230.71570.71900.7224

    +0.60.72570.72910.73240.73570.73890.74220.74540.74860.75170.7549

    +0.70.75800.76110.76420.76730.77040.77340.77640.77940.78230.7852

    +0.80.78810.79100.79390.79670.79950.80230.80510.80790.81060.8133

    +0.90.81590.81860.82120.82380.82640.82890.83150.83400.83650.8389

    +1.00.84130.84380.84610.84850.85080.85310.85540.85770.85990.8621

    +1.10.86430.86650.86860.87080.87290.87490.87700.87900.88100.8830

    +1.20.88490.88690.88880.89070.89250.89440.89620.89800.89970.9015

    +1.30.90320.90490.90660.90820.90990.91150.91310.91470.91620.9177

    +1.40.91920.92070.92220.92360.92510.92650.92790.92920.93060.9319

    +1.50.93320.93450.93570.93700.93820.93940.94060.94180.94290.9441

    +1.60.94520.94630.94740.94840.94950.95050.95150.95250.95350.9545

    +1.70.95540.95640.95730.95820.95910.95990.96080.96160.96250.9633

    +1.80.96410.96490.96560.96640.96710.96780.96860.96930.96990.9706

    +1.90.97130.97190.97260.97320.97380.97440.97500.97560.97610.9767

    +2.00.97730.97780.97830.97880.97930.97980.98030.98080.98120.9817

    +2.10.98210.98260.98300.98340.98380.98420.98460.98500.98540.9857

    +2.20.98610.98640.98680.98710.98750.98780.98810.98840.98870.9890

    +2.30.98930.98960.98980.99010.99040.99060.99090.99110.99130.9916

    +2.40.99180.99200.99220.99250.99270.99290.99310.99320.99340.9936

    +2.50.99380.99400.99410.99430.99450.99460.99480.99490.99510.9952

    +2.60.99580.99550.99560.99570.99590.99600.99610.99620.99630.9964

    +2.70.99650.99660.99670.99680.99690.99700.99710.99720.99730.9974

    +2.80.99740.99750.99760.99770.99770.99780.99790.99790.99800.9981

    +2.90.99810.99820.99830.99830.99840.99840.99850.99850.99860.9986

    +3.00.998650.998690.998740.998780.998820.998860.998890.998930.998960.99900

    +3.10.999030.999060.999100.999130.999150.999180.999210.999240.999260.99929

    +3.20.999310.999340.999360.999380.999400.999420.999440.999460.999480.99950

    +3.30.999520.999530.999550.999570.999580.999600.999610.999620.999640.99965

    +3.40.999660.999670.999690.999700.999710.999720.999730.999740.999750.99976

    +3.50.999770.999780.999780.999790.999800.999810.999810.999820.999830.99983

    0

    6. (CONTROL CHART)

    . (Control Chart)?

    AVANTE CLUTCH COVER ASS'Y PRESSURE PLATE RIVET'G DATA

    .* SPEC : 6.80.25

    5/65/75/85/95/115/125/135/145/155/165/185/195/20

    6.846.806.906.876.816.846.796.916.796.956.796.846.92

    6.976.996.926.866.796.896.796.946.886.916.886.896.95

    6.696.796.746.746.886.846.766.716.736.776.806.686.72

    20.5020.5820.5620.4720.4820.5720.3420.5620.4020.6320.4720.4120.59

    6.836.866.856.826.836.866.786.856.806.886.826.806.86

    1) 2) () ?

    - ,

    .

    - .

    - , .

    - .

    - .

    - .

    ===> 4M

    * .(MAN, MACHINE, MATERIAL., METHOD)

    3)

    - (Chance cause)

    , () .

    - (Assignable cause)

    .

    .

    * : .

    * : .

    4) ?

    1 ,

    .

    * ()

    - 1 ()( )

    . ( )

    - 2 ()( )

    .( )

    , 3 .

    1 0.27%

    5) ?

    ,

    .

    , !

    *

    (CENTER LINE : CL) : .

    (UPPER CONTROL LIMIT : UCL)

    (LOWER CONTROL LIMIT : LCL)

    * 3

    1 .

    3 3

    .

    UCL

    LCLx

    6) ?

    " " . .

    1)

    , .

    UCL, LCL .( )

    2)

    . ( )

    . .

    - 1924 (W.A. Shewhart) .

    - 1933(E.S. Pearson) BS 600 .

    - 19412 .

    - 1942 .

    - 1945 JIS Z 9021 .

    - 1950 JIS .

    - 1963 KS A 3201 .

    .

    - X - R ( () )

    1) - X ( )

    - X - R ( )

    - : , , , , .

    - X - R X .

    - X .

    , ,

    .

    - X - R .

    - Pn ( )

    2) - P ( )

    - C ( )

    - U ( )

    - : , , .

    - Pn : , (n)

    .

    ( ,

    )

    - P : .

    .(, )

    - C : ( ) .

    ( )

    - U : .

    .

    1) .

    ( , , , )

    2) .

    - .

    - .

    - .

    - , .

    - .

    - .

    - .

    - .

    - .

    3) .

    - data .

    4) () .

    5)

    6) , .

    7) data (PLOT).

    8) .

    9) .

    . ()

    * (), ( 2 ) .

    * X

    0.00.51.01.52.02.53.0

    n=40.3%2.3%15.9%50.0%84.1%97.7%99.1%

    -

    - .

    - 5

    .

    * 2 = 1 -

    2.

    . X - R

    1) X - R

    () X

    .

    2) X - R

    ) DATA .

    - : 20 ~ 25(k) . ( , )

    - (n) : 4 ~ 5 DATA .( )

    6 .

    - DATA : .

    - : .

    ) ( X ), ( R )

    X = X / n

    R = (X max) - (X min)

    * .

    )

    ) : ( X ) ( R ) .

    )

    1) X

    CL() = X =X = ( X ) k =

    2) R

    CL() = R =R = ( R ) k =

    3) X X R

    UCL = X + A RnA2D3D4

    21.88 3.27

    LCL = X - A R31.02"2.57

    40.73"2.28

    50.58"2.11

    3) R 60.48"2.00

    UCL = D R70.420.081.92

    80.370.141.86

    LCL = D R90.340.181.82

    100.310.221.78

    )

    1)

    2) , ()

    () .

    )

    DATA

    .

    * : .

    3) X - R

    n2345678910

    ) (s) =1.1281.6932.0592.3262.5342.7042.8472.973.078

    0.8530.8880.8800.8640.8480.8330.8200.8080.797

    ex)R = 1.4

    n = 4 (s) ?

    4)

    ( X )= Xo + (fX / n) X h= Xi / nX = X / k

    * Cp(k) * Cp(k)

    (U)

    U

    .

    &C

    &C

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    &A

    &P

    ()

    : .

    .

    i

    = () 3 = 3

    n

    =

    2

    d

    R

    OC (Operating CharacteristicCurve)

    ,

    1.0

    0.0

    6.0

    3.0

    1.0

    2.0

    4.0

    5.0

    0.5

    ,

    1.0

    0.0

    6.0

    3.0

    1.0

    2.0

    4.0

    5.0

    0.5

    k

    X

    2

    2

    k

    R

    4

    3

    2

    2

    (Xi)

    n

    fX

    n

    2

    2

    fX

    n

    = h

    ( s )

    =

    Xi

    n

    X - SL

    s

    =

    SU - X

    s

    +

    SU - SL

    6s

    Cp(k)=

    Cpk Cpk .

    R

    d

    2

    d

    2

    d

    3

    s =

    R

    d

    2

    =

    1.4

    2.059

    = 0.68

    =

    R

    d

    2

    SU - SL

    6s

    Cp(k) =

    Cpk Cpk .

    SU - SL

    6s

    Cp =

    {1/2(SU+ SL)-X }

    1/2(SU-SL)

    Cpk = (1 - k) Cp

    k() =

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    1

    2

    3

    3

    2

    1

    UCL

    LCL

    CL

    (RUN)

    7

    7 ,

    2( ) 3 27 310 4

    15 1( ) DATA (UCL, LCL )

    40% 1( ) DATA

    1. 2. 3.

    1. .2. .

    A, B, CD, E, F, G, H

    E, F, CI, J

    E, F, CI, J

    G

    D, EF, I

    A, B, G,H,I

    A, B, G

    A.

    B.

    C. (, )

    D.

    E. ( )

    F. ( )

    G. ( )

    H. . ( )

    I.

    J. .

    CPK

    Cpk

    D P MD P MD P MD P M

    ()() ()() ()() ()()

    0.30184,060368,1200.6525,58851,1761.001,3502,7001.352652

    0.31176,186352,3720.6623,85247,7041.011,2232,4461.362346

    0.32168,528337,0560.6722,21644,4321.021,1072,2141.372040

    0.33161,087322,1740.6820,67541,3501.031,0012,0021.381734

    0.34153,864307,7280.6919,22638,4521.049041,8081.391530

    0.35146,659293,3180.7017,86535,7301.058161,6321.401326

    0.36140,071280,1420.7116,58633,1721.067361,4721.411224

    0.37133,499266,9980.7215,38630,7721.076641,3281.421020

    0.38127,143254,2860.7314,26228,5241.085981,1961.43918

    0.39121,000242,0000.7413,20926,4181.095381,0761.44816

    0.40115,070230,1400.7512,22524,4501.104839661.45714

    0.41109,348218,6960.7611,30422,6081.114348681.46612

    0.42103,835207,6700.7710,44420,8881.123907801.47510

    0.4398,525197,0500.789,64219,2841.133507001.48510

    0.4493,417186,8340.798,89417,7881.143136261.4948

    0.4588,508177,0160.808,19816,3961.152805601.5036

    0.4683,793167,5860.817,54915,0981.162515021.5136

    0.4779,270158,5400.826,94713,8941.172404801.5236

    0.4874,934149,8680.836,38712,7741.182044081.5324

    0.4970,781141,5620.845,86811,7361.191793581.5424

    0.5066,807133,6140.855,38610,7721.201593181.5524

    0.5163,008126,0160.864,9409,8801.211422841.5612

    0.5259,380118,7600.874,5279,0541.221262521.5712

    0.5355,917111,8340.884,1458,2901.231122241.5812

    0.5452,616105,2320.893,7927,5841.241002001.5912

    0.5549,47198,9420.903,4676,9341.25891781.6012

    0.5646,47992,9580.913,1676,3341.26791581.6112

    0.5743,63387,2660.922,8905,7801.27701401.6212

    0.5840,93081,8600.932,6355,2701.28621241.6312

    0.5938,36476,7280.942,4014,8021.29551101.6400

    0.6035,93071,8600.952,1864,3721.3048961.6500

    0.6133,62567,2500.961,9883,9761.3143861.6600

    0.6231,44362,8860.971,8073,6141.3238761.6700

    0.6329,37858,7560.981,6413,2821.333366

    0.6427,42954,8580.991,4892,9781.342958

    DPM : Defective per million. PPM : Part per million(DPM PPM )

    0.750.75

    ex) 100 .

    #15.56.05.96.15.9#116.35.66.46.46.0-0.80-0.30-0.40-0.20-0.400.00-0.700.100.10-0.30-0.000.090.160.040.1600.490.010.010.09

    #25.86.06.66.06.1#126.06.56.27.66.7- SPEC-0.50-0.300.30-0.30-0.20-0.300.20-0.101.300.400.250.090.090.090.040.090.040.011.690.16

    #36.36.55.56.17.1#136.06.96.86.36.16.2 1.50.000.20-0.80-0.200.80-0.300.600.500.00-0.2000.040.640.040.640.090.360.2500.04

    #46.96.05.86.26.5#146.06.95.85.96.2- n = 1000.60-0.30-0.50-0.100.20-0.300.60-0.50-0.40-0.100.360.090.250.010.040.090.360.250.160.01

    #55.66.05.35.76.0#156.37.46.66.36.7- X max= 7.7-0.70-0.30-1.00-0.60-0.300.001.100.300.000.400.490.0910.360.0901.210.0900.16

    #67.16.86.37.06.3#166.06.26.07.66.3- X min = 5.30.800.500.000.700.00-0.30-0.10-0.301.300.000.640.2500.4900.090.010.091.690

    #76.06.06.66.46.1#176.36.77.75.66.0- k = 10-0.30-0.300.300.10-0.200.000.401.40-0.70-0.300.090.090.090.010.0400.161.960.490.09

    #86.46.66.26.47.0#187.65.66.76.06.20.100.30-0.100.100.701.30-0.700.40-0.30-0.100.010.090.010.010.491.690.490.160.090.010.23167

    #96.96.76.05.95.9#196.05.86.76.26.50.600.40-0.30-0.40-0.40-0.30-0.500.40-0.100.200.360.160.090.160.160.090.250.160.010.04

    #105.86.76.56.35.8#206.46.06.85.66.2-0.500.400.200.00-0.500.10-0.300.50-0.70-0.100.250.160.0400.250.010.090.250.490.01

    1.

    1) (R) : 7.7 - 5.3 =2.4-0.70.3-2.3-0.9-0.3-0.10.62.70.5-0.1-0.3

    2) (h) : 2.4/10 = 0.24 0.2* .

    3) : 0.1 / 2 = 0.05

    4)

    - : 5.3 - 0.05 = 5.25

    5) .- Xo : .- n :

    - X = Xo + (fX / n) X h- fX : fX - h :

    = 5.95 + ((167/100) X 0.2) = 6.284

    6) (S) .

    7)

    )

    U =U = 2.87 .

    U = 0.0021 X 1,000,000 = 2,100 PPM

    )

    U =U = 3.21 .

    U = 0.00066 X 1,000,000 = 660 PPM

    ) (, .)

    U = 2,100 + 660 = 2,760PPM

    7)

    d = X - = 6.284 - 6.2 = 0.084mm .

    8)

    Cp = = 2446 PPM

    Cpk = (1-K)Cp = (1-0.084) X 1.01 = 0.925

    = 5780 PPM

    2.

    1)

    X = Xi / n = 629.7/100 = 6.297

    2)

    - S = ( Xi - X )= Xi -

    3)

    )

    U =U = 2.87 .

    U = 0.0021 X 1,000,000 = 2,100 PPM

    )

    U =U = 3.27 .

    U = 0.00054 X 1,000,000 = 540 PPM

    ) (, .)

    U = 2,100 + 540 = 2,640PPM

    4)

    k === 0.0647

    5)

    Cp = = 2214 PPM

    Cpk = (1-K)Cp = (1-0.064) X 1.02 = 0.954 = 4372 PPM

    3. (X-R)

    1)

    #15.880.6#66.700.8#116.140.8#166.421.6

    #26.100.8#76.220.6#126.601.6#176.462.1

    #36.301.6#86.520.8#136.420.9#186.422.0

    #46.281.1#96.281.0#146.161.1#196.240.9

    #55.720.7#106.220.9#156.661.1#206.201.2

    - R =22.2- X =125.94k = 20 ( )

    -

    X = X / k = 125.94 / 20 = 6.297

    R = R / k = 22.2/20 = 1.11

    2) n=5

    s = R / d2 = 1.11/2.326 = 0.477

    3)

    )

    U =U = 2.94 .

    U = 0.0016 X 1,000,000 = 1600 PPM

    )

    U =U = 3.35 .

    U = 0.00040 X 1,000,000 = 400 PPM

    ) (, .)

    U = 1600 + 400 = 2000 PPM

    4)

    k === 0.0647

    5) 0.97344

    Cp = = 1808 PPM

    Cpk = (1-K)Cp = (1-0.064) X 1.04 = 0.973 = 3614 PPM

    ( X )6.2846.2976.297

    ( s )0.4940.4880.477

    210021001600

    (U)660540400

    (PPM)276026402000

    (k)0.0840.06470.0647

    Cp1.01 (2446 PPM)1.02 (2214 PPM)1.04 (1808 PPM)

    Cpk0.925 (5780 PPM)0.954 (4372 PPM)0.97 (3614 PPM)

    * ,

    .

    &C

    &C

    SU - X

    s

    fX

    n

    2

    *

    .

    * ( )

    .

    *

    . ( )

    *

    .

    ( )

    2

    fX

    n

    * s = h

    2

    2

    = 0.2

    889

    100

    167

    100

    2

    = 0.2

    8.89 - 2.79

    = 0.2

    6.1

    = 0.494

    2

    - s =

    X - SL

    s

    7.7 - 6.284

    0.494

    =

    =23.831

    S

    n

    =

    23.831

    100

    =

    0.23831

    = 0.488

    = 2.87

    6.284 - 4.7

    0.494

    =

    = 3.21

    SU - SL

    6s

    =

    7.7 - 4.7

    6 X 0.488

    3.0

    2.928

    =

    = 1.02

    " =AVERAGE (X1 : Xn)" CUMPUTER

    (Xi)

    n

    2

    SU - X

    s

    X - SL

    s

    7.7 - 6.297

    0.488

    =

    = 2.875

    6.297 - 4.7

    0.488

    =

    = 3.272

    SU - SL

    6s

    =

    7.7 - 4.7

    6 X 0.494

    3.0

    2.964

    =

    = 1.01

    {1/2(SU+SL) - X}

    1/2(SU-SL)

    {1/2(7.7+4.7) - 6.297}

    1/2(7.7-4.7)

    " =AVERAGE (X1 : Xn)" CUMPUTER

    SU - X

    s

    X - SL

    s

    7.7 - 6.297

    0.477

    =

    = 2.94

    6.297 - 4.7

    0.477

    =

    = 3.35

    SU - SL

    6s

    =

    7.7 - 4.7

    6 X 0.477

    3.0

    2.862

    =

    = 1.04

    {1/2(SU+SL) - X}

    1/2(SU-SL)

    {1/2(7.7+4.7) - 6.297}

    1/2(7.7-4.7)

  • 4. 56-. . = / 2-. 1) () (f) , . 2) X, fX fX2 . - 0 1, 2, 3,. 1, -2, -3, ..

    VXXXXXXXXXXXXXXXXXXXXXXXX

    &A

    &P

    VXXXXXXXXXXXXXXXXXXXXXXXX

    &A

    &P

    1

    2/12/22/32/42/52/62/72/82/92/102/112/122/132/142/152/162/172/182/19

    63

    F/C 59

    S/PIN49

    24

    17131091613912126984951313107195

    CU/RIVET'G .

    100 ~ 250

    7 ~1210 ~ 20

    R = X max - X min

    ex)X min = 10.02

    X max = 10.08

    ex)

    5.56.05.96.15.96.35.66.46.46.0

    5.86.06.66.06.16.06.56.27.66.7- SPEC

    6.36.55.56.17.16.06.96.86.36.16.2 1.5

    6.96.05.86.26.56.06.95.85.96.2

    5.66.05.35.76.06.37.46.66.36.7- X max= 7.7

    7.16.86.37.06.36.06.26.07.66.3- X min = 5.3

    6.06.06.66.46.16.36.77.75.66.0- k = 10

    6.46.66.26.47.07.65.66.76.06.2

    6.96.76.05.95.96.05.86.76.26.5

    5.86.76.56.35.86.46.06.85.66.2

    NoX (U)fXfX

    15.25 ~ 5.455.3611-3-39

    25.45 ~ 5.655.5578-2-1428

    35.65 ~ 5.855.75715-1-77

    45.85 ~ 6.055.952439000

    56.05 ~ 6.256.15145311414

    66.25 ~ 6.456.35166923264

    76.45 ~ 6.656.5587732472

    86.65 ~ 6.856.751188444176

    96.85 ~ 7.056.95593525125

    107.05 ~ 7.257.1529561272

    117.25 ~ 7.457.351967749

    127.45 ~ 7.657.55399824192

    137.65 ~ 7.857.7511009981

    10010039167889

    NoX (U)fXfX

    15.25 ~ 5.455.3611-3-39

    25.45 ~ 5.655.5578-2-14285.95 + ((167/100) X 0.2)

    35.65 ~ 5.855.75715-1-77= 6.284

    45.85 ~ 6.055.952439000

    56.05 ~ 6.256.15145311414

    66.25 ~ 6.456.35166923264

    76.45 ~ 6.656.5587732472

    86.65 ~ 6.856.751188444176

    96.85 ~ 7.056.95593525125

    107.05 ~ 7.257.1529561272

    117.25 ~ 7.457.351967749

    127.45 ~ 7.657.55399824192

    137.65 ~ 7.857.7511009981

    10010039167889

    = Xi -

    U =

    U = 0.0021 X 1,000,000 = 2,100 PPM

    U =

    U = 0.00066 X 1,000,000 = 660 PPM

    U = 2,100 + 660 = 2,760PPM

    Cp =

    = Xo + (fX / n) X h= Xi / n= AVERAGE(Xi : Xn)

    X

    kkkk

    8029850177126

    9130951187227

    10131952187327

    11132953187428

    122331054197528

    132341055197628

    142351156207729

    153361157207829

    163371258217930

    174381259218030

    184391260218131

    194401361228231

    205411362228332

    215421463238432

    225431464238532

    236441565248633

    246451566248733

    257461567258834

    267471668258934

    277481669259035

    28849177026

    * SPEC : 6.80.25

    5/65/75/85/95/115/125/135/145/155/165/185/195/20

    6.846.806.906.876.816.846.796.916.796.956.796.846.92

    6.976.996.926.866.796.896.796.946.886.916.886.896.95

    6.696.796.746.746.886.846.766.716.736.776.806.686.72

    20.5020.5820.5620.4720.4820.5720.3420.5620.4020.6320.4720.4120.59

    6.836.866.856.826.836.866.786.856.806.886.826.806.86

    (MAN, MACHINE, MATERIAL., METHOD)

    UCL

    LCLx

    n=40.3%2.3%15.9%50.0%84.1%97.7%99.1%

    X = X / n

    R = (X max) - (X min)

    UCL = X + A RnA2D3D4

    21.883.27

    LCL = X - A R31.02"2.57

    40.73"2.28

    50.58"2.11

    60.48"2.00

    UCL = D R70.420.081.92

    80.370.141.86

    LCL = D R90.340.181.82

    100.310.221.78

    n2345678910

    1.1281.6932.0592.3262.5342.7042.8472.973.078

    0.8530.8880.8800.8640.8480.8330.8200.8080.797

    ex)R = 1.4

    = Xo + (fX / n) X h= Xi / nX = X / k

    &C

    &C

    1

    1

    1

    1

    1

    2

    3

    R

    (k)

    * h =

    * k =

    n

    ...

    ...

    2

    *

    .

    * ( )

    .

    *

    . ( )

    *

    .

    ( )

    fX

    n

    2

    2

    2

    2

    fX

    n

    * s = h

    2

    2

    = 0.2

    889

    100

    167

    100

    2

    = 0.2

    8.89 - 2.79

    = 0.2

    6.1

    = 0.494

    2

    - s =

    "=STDEVP (X1 : Xn)" CUMPUTER

    =23.831

    S

    n

    =

    23.831

    100

    =

    0.23831

    = 0.488

    " =AVERAGE (X1 : Xn)" CUMPUTER

    (Xi)

    n

    2

    SU - X

    s

    X - SL

    s

    7.7 - 6.284

    0.494

    =

    = 2.87

    6.284 - 4.7

    0.494

    =

    = 3.21

    SU - SL

    6s

    =

    7.7 - 4.7

    6 X 0.494

    3.0

    2.964

    =

    = 1.01

    2

    2

    (Xi)

    n

    fX

    n

    2

    2

    fX

    n

    = h

    ( s )

    =

    Xi

    n

    =STDEVP(Xi : Xn)

    X - SL

    s

    =

    SU - X

    s

    +

    SU - SL

    6s

    Cp=

    Cp .

    Y

    n(1)=15

    n(4)=3

    n(2)=3

    n(3)=15

    1

    6.8333333333

    6.86

    6.8533333333

    6.8233333333

    6.8266666667

    6.8566666667

    6.78

    6.8533333333

    6.8

    6.8766666667

    6.8233333333

    6.8033333333

    6.8633333333

    &A

    &P

    ()

    i

    = () 3 = 3

    n

    =

    2

    d

    R

    OC (Operating CharacteristicCurve)

    ,

    1.0

    0.0

    6.0

    3.0

    1.0

    2.0

    4.0

    5.0

    0.5

    ,

    1.0

    0.0

    6.0

    3.0

    1.0

    2.0

    4.0

    5.0

    0.5

    k

    X

    2

    2

    k

    R

    4

    3

    2

    2

    (Xi)

    n

    fX

    n

    2

    2

    fX

    n

    = h

    ( s )

    =

    Xi

    n

    X - SL

    s

    =

    SU - X

    s

    +

    SU - SL

    6s

    Cp(k)=

    Cpk Cpk .

    R

    d

    2

    d

    2

    d

    3

    s =

    R

    d

    2

    =

    1.4

    2.059

    = 0.68

    =

    R

    d

    2

    SU - SL

    6s

    Cp(k) =

    Cpk Cpk .

    SU - SL

    6s

    Cp =

    {1/2(SU+ SL)-X }

    1/2(SU-SL)

    Cpk = (1 - k) Cp

    k() =

  • 5. 57-. . 1) () . 2) .

    -. . 6.156.35

  • 6. 58 * . * () .SLSU

  • 7. 59

  • 8. 60-. . 1) . (XO) XO = . 2) X = XO + ( fX / n) x h ex) X = (5.95 + (167/100) x 0.2) = 6.284 3) s. s = h

    = 0.2 * .

  • 9. 61-. . 1) U = (SU X )/ s * SU : 2) U = ( X - SL)/ s * SU : 3) U .Ex) . 1) U = (7.7 6.284 )/ 0.494 = 2.87 2.87 0.0021 => 0.0021 x 1,000,000 = 2,100 ppm 2) U = (6.284 4.7)/ 0.494 = 3.21 3.21 0.00066 => 0.00066 x 1,000,000 = 660 ppm 3) U = 2,100 + 660 = 2760 ppm

  • 10. 62 s =-. (Cp/ Cpk) Cpk . -. - = AVERAGE (Xi : Xn) - = STDEVP (Xi : Xn)

  • 11. 63 () . .(, ), 2

  • 12. 64 . data ()

  • 13. 65Data CpkCp = (SU SL) / 6 * Cpk = (1 k ) Cp * Cpk .

  • 4.2.5 -. (scatter diagram) X,Y -. ,

  • 1. -. , -. () () , .-.

    -.

    1 .: (: , 30 )2 : 3 : . 2 (x), 4 : . No.1 .5 : . , , .

  • 2. (X Y )

  • 36

  • /Scatter Diagram372 x y (Plotting) .=> . ? ? . , . , , .

  • 38 . 30 . , . 1) , . 2) , . 3) , ... . .

  • 39()()

  • 40 1) . 2) . . 1) n1 + n3 . (n+) 2) n2 + n4 . (n-) 3) . (k) n+ = 30n- = 10 k = 40

  • 41 1) k . 2) . 3) n+ n- . 4) 3) . 5) : > 3) . - : n+ > n- - : n+ < n- 6) : < 3) .

  • 42 r .

  • 43 r -1 r 1

  • 44 ? / . , . ? . ? .

  • 4.2.6 Pareto -. , .

    -. Pareto .

    -. 1906 Milan . 20% 80% , -. 80/20 . -. 80% 20% .-. . pareto

    -. Pareto

  • 1.-.

    -. Alfred Pareto , . 20 : 80

    -. .

  • 2. ( )

    1 : . , , , , , ,

    2 :

  • 3 : 4:

  • 5 : 6 : , .A:B:C: D:E:F:G:

  • 4.2.7 Graph -.

    -. , . -. -. -. -.

  • 1. /Graph20Data . . . . . . .

  • 2. 21 (,) . . ( S/Ware ) . : . : .()

  • 3. 22 . , .2 : . . - .

  • 4. 23 . (,) .

  • 5. 24 . .

    Chart1

    11

    11

    10.977

    10.933

    11

    10.983

    11

    11

    (PD-APM 01.03.1A)

    COVERCOVER1COVER2COVER3CNC1

    1. 1010.0010.0010.0010.0010.0010.00COVER

    Involvement1010.0010.0010.0010.0010.0010.00

    of Personnel109.779.569.749.819.929.82

    (35S)109.339.159.509.459.359.20

    1010.0010.0010.0010.0010.0010.00

    2. 85%

    Production2019.6619.8520.0020.0018.6819.76 "ZERO"

    System

    3. PPM2020.0020.0020.0020.0015.0015.00

    Total Quality PPM1010.0010.0010.0010.0010.0010.00

    10098.7698.5699.2499.2692.9593.78

    32154

    *GALLOPER TCI*P/P *HAC-08P/P UN*FDC-03,05

    BALANCE DIA/SP

    REMARKS ASS'YASS'Y C/LOAD

    OVER

    &L&","&10PD/APM 01.03.1A&C&","&10 &R&","&10A4(297X210)

    ( 02 )

    35S(PD-APM 01.03.2A)

    (LINE):

    :

    : 20

    NO.

    1 ,

    2 , , ,

    3 ,

    4, , ,

    5,

    6 ,

    7 ,

    8 ,

    9, OIL,

    10 ,

    V.M11,AUTO MATRIX ,

    12TPM ,

    13 ,

    14

    15 SPC

    16

    17LOT

    18 ,

    19 ,

    20 ,

    TOTAL

    PD/APM 01.03.2A A4(210X297)

    :(0.5):(0.3):( 0 )

    3 5S -

    TOTAL

    (02)

    TOTAL35S

    100%100%100%100%100%100%100%100%

    100.0%100.0%97.7%93.3%100.0%98.3%100.0%100.0%

    1010101010202010

    10109.779.331019.66201098.76

    :98.76

    PD/APM 01.03.3A A4(210X297)

    TOTAL

    (12)

    35S

    100%100%100%100%100%100%100%100%

    100.0%94.0%91.1%94.3%200.0%57.8%75.0%100.0%

    10510105302010

    104.79.119.431017.34151085.58

    :85.58

    :0.00

    :85.58

    PD/APM 01.03.3A A4(210X297)

    COVER1

    (02)

    COVER 135S

    100%100%100%100%100%100%100%100%

    100.0%100.0%95.6%91.5%100.0%99.3%100.0%100.0%

    1010101010202010

    10109.569.151019.85201098.56

    :98.56

    PD/APM 01.03.3A A4(210X297)

    COVER1

    COVER2

    (02)

    COVER 235S

    100%100%100%100%100%100%100%100%

    100.0%100.0%97.4%95.0%100.0%100.0%100.0%100.0%

    1010101010202010

    10109.749.51020201099.24

    :99.24

    PD/APM 01.03.3A A4(210X297)

    COVER2

    COVER3

    (02)

    COVER 335S

    100%100%100%100%100%100%100%100%

    100.0%100.0%98.1%94.5%100.0%100.0%100.0%100.0%

    1010101010202010

    10109.819.451020201099.26

    :99.26

    PD/APM 01.03.3A A4(210X297)

    COVER3

    CNC

    (02)

    CNC 35S

    100%100%100%100%100%100%100%100%

    100.0%100.0%99.2%93.5%100.0%93.4%75.0%100.0%

    1010101010202010

    10109.929.351018.68151092.95

    1)HAC-08P/P UN BALANCE

    :92.95ASS'Y OVER

    PD/APM 01.03.3A A4(210X297)

    CNC

    (02)

    135S

    100%100%100%100%100%100%100%100%

    100.0%100.0%98.2%92.0%100.0%98.8%75.0%100.0%

    1010101010202010

    10109.829.21019.76151093.78

    1)FDC-03,05 DIA/SP

    :93.78ASS'Y C/LOAD

    PD/APM 01.03.3A A4(210X297)

    1. /Involvement of Personnel1. /Involvement of Personnel1. /Involvement of Personnel1. /Involvement of Personnel1. /Involvement of Personnel

    9595959595959595

    7893/4 1234 7893/4 7893/4

    11111

    (35S)(35S)(35S)(35S)(35S)

    22222

    (35S)(35S)(35S)(35S)(35S)

    33333

    (35S)(35S)(35S)(35S)(35S)

    (35S)(35S)(35S)(35S)(35S)

    R / B R / B R / B R / B R / B

    (35S)(35S)(35S)(35S)(35S)

    DISCDISCDISCDISCDISC

    TOTALTOTALTOTALTOTALTOTAL

    (35S)(35S)(35S)(35S)(35S)

    1. /Involvement of Personnel1. /Involvement of Personnel1. /Involvement of Personnel1. /Involvement of Personnel1. /Involvement of Personnel

    95959595959595959595

    1/42/43/44/4 7893/4 1234 7893/4 7893/4

    11111

    (35S)(35S)(35S)(35S)(35S)

    22222

    (35S)(35S)(35S)(35S)(35S)

    33333

    (35S)(35S)(35S)(35S)(35S)

    (35S)(35S)(35S)(35S)(35S)

    COVERCOVERCOVERCOVERCOVER

    TOTALTOTALTOTALTOTALTOTAL

    (35S)(35S)(35S)(35S)(35S)

    1. /Involvement of Personnel1. /Involvement of Personnel1. /Involvement of Personnel1. /Involvement of Personnel1. /Involvement of Personnel

    95959595959595959595

    1/42/43/44/4 7893/4 1234 7893/4 7893/4

    HUBHUBHUBHUBHUB

    (35S)(35S)(35S)(35S)(35S)

    CNCCNCCNCCNCCNC

    (35S)(35S)(35S)(35S)(35S)

    11111

    (35S)(35S)(35S)(35S)(35S)

    22222

    (35S)(35S)(35S)(35S)(35S)

    TOTALTOTALTOTALTOTALTOTAL

    (35S)(35S)(35S)(35S)(35S)

    2./Production System2./Production System2./Production System2./Production System

    9595959595959595

    1/42/43/44/4 7893/4 1234 1234

    1111

    2222

    3333

    R / BR / BR / BR / B

    DISCDISCDISCDISC

    TOTALTOTALTOTALTOTAL

    2./Production System2./Production System2./Production System2./Production System

    9595959595959595

    1/42/43/44/4 7893/4 1234 1234

    1 1 1 1

    2 2 2 2

    3 3 3 3

    COVERCOVERCOVERCOVER

    TOTALTOTALTOTALTOTAL

    2./Production System2./Production System2./Production System2./Production System

    9595959595959595

    1/42/43/44/4 7893/4 1234 1234

    HUBHUBHUBHUB

    CNCCNCCNCCNC

    1 1 1 1

    2 2 2 2

    TOTALTOTALTOTALTOTAL

    3. /Total Quality3. /Total Quality3. /Total Quality3. /Total Quality

    9595959595959595

    1/42/43/44/4 7893/4 1234 1234

    1 PPM1 PPM1 PPM1 PPM

    PPM PPM PPM PPM

    2 PPM2 PPM2 PPM2 PPM

    PPM PPM PPM PPM

    3 PPM3 PPM3 PPM3 PPM

    PPM PPM PPM PPM

    PPM PPM PPM PPM

    PPM PPM PPM PPM

    R/B PPMR/B PPMR/B PPMR/B PPM

    PPM PPM PPM PPM

    HUB PPMHUB PPMHUB PPMHUB PPM

    PPM PPM PPM PPM

    PPM PPM PPM PPM

    2 PPM2 PPM2 PPM2 PPM

    DISC PPMDISC PPMDISC PPMDISC PPM

    TOTAL PPMTOTAL PPMTOTAL PPMTOTAL PPM

    3. /Total Quality3. /Total Quality3. /Total Quality3. /Total Quality

    9595959595959595

    1/42/43/44/4 7893/4 1234 1234

    1 PPM1 PPM1 PPM1 PPM

    PPM PPM PPM PPM

    2 PPM2 PPM2 PPM2 PPM

    PPM PPM PPM PPM

    3 PPM3 PPM3 PPM3 PPM

    PPM PPM PPM PPM

    PPM PPM PPM PPM

    CNC PPMCNC PPMCNC PPMCNC PPM

    PPM PPM PPM PPM

    PPM PPM PPM PPM

    1 1 1 1

    COVER PPMCOVER PPMCOVER PPMCOVER PPM

    TOTAL TOTAL TOTAL TOTAL

    3. /Total Quality3. /Total Quality

    95959595

    1/42/43/44/4 7893/4

    1 PPM1 PPM

    PPM PPM

    2 PPM2 PPM

    PPM PPM

    3 PPM3 PPM

    PPM PPM

    PPM PPM

    PPM PPM

    R/B PPMR/B PPM

    PPM PPM

    HUB PPMHUB PPM

    PPM PPM

    PPM PPM

    2 PPM2 PPM

    DISC PPMDISC PPM

    TOTAL PPMTOTAL PPM

    3. /Total Quality3. /Total Quality

    95959595

    1/42/43/44/4 7893/4

    1 PPM1 PPM

    PPM PPM

    2 PPM2 PPM

    PPM PPM

    3 PPM3 PPM

    PPM PPM

    PPM PPM

    CNC PPMCNC PPM

    PPM PPM

    PPM PPM

    1 1

    COVER PPMCOVER PPM

    TOTAL TOTAL

  • 6. 25108131091211

  • 7. 1. : . 2. : , , 3. : 4. : , . 5. : ,,, , 6. : . 7.: , ,,

  • 8.

    . , .

  • 9 . . , , , , .

  • ()100 5 , 5 (Control Chart) .

    **. , , 6 .