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1 © 2005 Thomson/South-Western © 2005 Thomson/South-Western © 2004 Thomson/South-Western © 2004 Thomson/South-Western Peta Kendali Peta Kendali ATRIBUT ATRIBUT

Peta Kendali ATRIBUT

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Peta Kendali ATRIBUT. World Class. Control Chart Types. Continuous Numerical Data. Categorical or Discrete Numerical Data. Control. Charts. Variables. Attributes. Charts. Charts. R. P. C. X. Chart. Chart. Chart. Chart. Konsep. - PowerPoint PPT Presentation

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Page 1: Peta Kendali ATRIBUT

1 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Peta Kendali Peta Kendali ATRIBUTATRIBUT

Page 2: Peta Kendali ATRIBUT

2 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

ControlCharts

RChart

VariablesCharts

AttributesCharts

XChart

PChart

CChart

Continuous Numerical Data

Categorical or Discrete Numerical Data

Control Chart TypesControl Chart Types

Page 3: Peta Kendali ATRIBUT

3 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

KonsepKonsep

Atribut : karakteristik kualitas yg sesuai Atribut : karakteristik kualitas yg sesuai spesifikasi atau tidakspesifikasi atau tidak

Atribut dipakai jk ada pengukuran yg tidak Atribut dipakai jk ada pengukuran yg tidak mungkin dilakukan ( tidak dibuat) spt : mungkin dilakukan ( tidak dibuat) spt : goresan,apel yg busuk, kesalahan warna, ada goresan,apel yg busuk, kesalahan warna, ada bagian yg hilangbagian yg hilang

Page 4: Peta Kendali ATRIBUT

4 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

KelebihanKelebihan

Dapat diterapkan di semua tgkt organisasi , Dapat diterapkan di semua tgkt organisasi , separtemen, pusat kerja dan mesin separtemen, pusat kerja dan mesin operasional (tgk tertinggi – terendah)operasional (tgk tertinggi – terendah)

Membantu identifikasi permasalahan ( umum Membantu identifikasi permasalahan ( umum dan detil) dan detil)

Page 5: Peta Kendali ATRIBUT

5 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

KelemahanKelemahan

Tdk dapat diketahui sbrp jauh ketidaktepatan Tdk dapat diketahui sbrp jauh ketidaktepatan dg spesifikasi tsbdg spesifikasi tsb

Ukuran sampel yg besar akan bermasalah jk Ukuran sampel yg besar akan bermasalah jk pengukurannya mahal dan destruktifpengukurannya mahal dan destruktif

Page 6: Peta Kendali ATRIBUT

6 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Tipe Peta Kendali Tipe Peta Kendali ATRIBUTATRIBUT

1.1. Berdasar Distribusi BINOMIALBerdasar Distribusi BINOMIAL

• Kelompok pengendali unit ketidaksesuaianKelompok pengendali unit ketidaksesuaian

• Dinyatakan dalam proporsi (%)Dinyatakan dalam proporsi (%)

• Menunjukkan proporsi ketidaksesuaian Menunjukkan proporsi ketidaksesuaian dalam sampel / sub kelompokdalam sampel / sub kelompok

p dan npp dan np Chart Chart

Page 7: Peta Kendali ATRIBUT

7 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

2. Berdasar Distribusi POISSON2. Berdasar Distribusi POISSON

• bagian ketidaksesuaian dalam unit inspeksibagian ketidaksesuaian dalam unit inspeksi

• Berkaitan dg kombinasi ketidaksesuaian Berkaitan dg kombinasi ketidaksesuaian berdasar BOBOT yg dipengaruhi banyak berdasar BOBOT yg dipengaruhi banyak sedikitnya ketidaksesuaiansedikitnya ketidaksesuaian

c- Chart dan u-chartc- Chart dan u-chart

Page 8: Peta Kendali ATRIBUT

8 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Tahapan….Tahapan…. Menentukan sasaran Menentukan sasaran menentukan menentukan

karakteristik kualitasnya (ketidaksesuaian karakteristik kualitasnya (ketidaksesuaian dalam proporsi atau unit) dalam proporsi atau unit)

Memilih tipe peta kendali atributMemilih tipe peta kendali atribut Banyaknya sampel dan observasiBanyaknya sampel dan observasi Pengumpulan dataPengumpulan data Penentuan Penentuan BATAS KENDALI ( CL,UCL dan LCL)BATAS KENDALI ( CL,UCL dan LCL) Interpretasi hasil (pola in/out of control)Interpretasi hasil (pola in/out of control) Revisi jika perluRevisi jika perlu

Page 9: Peta Kendali ATRIBUT

9 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

p/np/cp/np/c Chart Structure Chart Structure

UCLUCL

LCLLCL

Process MeanProcess MeanWhen in ControlWhen in Control

Center LineCenter Line

TimeTime

p/np/c Upper Control Upper Control LimitLimit

Lower Control Lower Control LimitLimit

Page 10: Peta Kendali ATRIBUT

10 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Sampel SAMA…Sampel SAMA…pp chartchart

• Proporsi diketahui

• Garis Tengah = p¯

pp p

n

( )1

UCL p

LCL p

p p

p p

3

3

Page 11: Peta Kendali ATRIBUT

11 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Sampel SAMA…Sampel SAMA…pp chart chart

• Proporsi TIDAK diketahuim nomer sampel (vertikal) n ukuran sampel (horisontal) D bagian tidak sesuai

p¯ = ∑Di/(mn)

Garis Tengah = p¯

pp p

n

( )1UCL p

LCL p

p p

p p

3

3

Page 12: Peta Kendali ATRIBUT

12 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Sampel BEDA …Sampel BEDA …a.a. Metode Metode INDIVIDUINDIVIDU Batas Kendali Batas Kendali

tergantung ukuran sample tertentu shg tergantung ukuran sample tertentu shg BKA/BKB tidak berupa garis LURUSBKA/BKB tidak berupa garis LURUS

b.b. Metode Metode RATA_RATARATA_RATA Ukuran sampel RATA - Ukuran sampel RATA -RATA dg perbedaan tidak terlalu besarRATA dg perbedaan tidak terlalu besar

( n¯ = ∑n/observasi)( n¯ = ∑n/observasi)

c.c. Peta Kendali TERSTANDAR dg GT=0 dan BK Peta Kendali TERSTANDAR dg GT=0 dan BK ± 3± 3

Page 13: Peta Kendali ATRIBUT

13 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

npnp Chart Chart

UCL = np np p 3 1( )

LCL = np np p 3 1( )

Note: If computed LCL is negative, set LCL = 0Note: If computed LCL is negative, set LCL = 0

assuming:assuming: npnp >> 5 5

nn(1-(1-pp) ) >> 5 5

Page 14: Peta Kendali ATRIBUT

14 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

c-chart dan u-chartc-chart dan u-chart

Mengetahui banyaknya kesalahan unit produk Mengetahui banyaknya kesalahan unit produk sbg sampelsbg sampel

Sampel konstan Sampel konstan c-chart c-chart

Sampel bervariasi Sampel bervariasi u-chart u-chart

Aplikasi : bercak pd tembok, gelembung udara Aplikasi : bercak pd tembok, gelembung udara pd gelas, kesalahan pemasangan sekrup pd pd gelas, kesalahan pemasangan sekrup pd mobilmobil

Page 15: Peta Kendali ATRIBUT

15 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Number of defects per unit:Number of defects per unit:

c¯ = ∑ ci / nc¯ = ∑ ci / n

UCL cc c 3

LCL cc c 3

c c

C - chartC - chart

Page 16: Peta Kendali ATRIBUT

16 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

U-chartU-chart

u¯ = ∑ ci/nu¯ = ∑ ci/n n ¯ = ∑ ni/gn ¯ = ∑ ni/g

g = banyaknya observasig = banyaknya observasi

Model IndividuModel Individu BPA-u = u¯ + 3 √ (u¯ /ni)BPA-u = u¯ + 3 √ (u¯ /ni) BPB-u = u¯ - 3 √ (u¯ /ni)BPB-u = u¯ - 3 √ (u¯ /ni)

Model Rata-rataModel Rata-rata BPA-u = u¯ + 3 √ (u¯ /n¯)BPA-u = u¯ + 3 √ (u¯ /n¯) BPB-u = u¯ - 3 √ (u¯ /n¯)BPB-u = u¯ - 3 √ (u¯ /n¯)

Page 17: Peta Kendali ATRIBUT

17 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Warning Conditions…..Warning Conditions…..

Western Electric :Western Electric :1. 1 titik diluar batas kendali 1. 1 titik diluar batas kendali

( 3( 3σ)σ)2. 2 dr 3 titik berurutan diluar 2. 2 dr 3 titik berurutan diluar

batas kendbatas kend1717li (li (22σ)σ)3. 4 dr 5 titik berurutan jauh 3. 4 dr 5 titik berurutan jauh

dari GT (dari GT (11σ)σ)4. 8 titik berurutan di satu sisi 4. 8 titik berurutan di satu sisi

GTGT5. Giliran panjang 7-8 titik5. Giliran panjang 7-8 titik6. 1/beberapa titik dekat satu 6. 1/beberapa titik dekat satu

batas kendalibatas kendali7. Pola data TAK RANDOM7. Pola data TAK RANDOM

Page 18: Peta Kendali ATRIBUT

18 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Patterns to Look for in Control ChartsPatterns to Look for in Control Charts

Page 19: Peta Kendali ATRIBUT

19 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

TwTwenty samples, each consisting of enty samples, each consisting of

250 checks, The number of 250 checks, The number of defective defective

checks found in the 20 samples are checks found in the 20 samples are

listed below.listed below.

(proporsi tidak diketahui)(proporsi tidak diketahui)

4 1 5 3 2 7 4 5 2 3

2 8 5 3 6 4 2 5 3 6

Example………Example………p-np chartp-np chart

$$

115006529 25447581 1445

26552655

Simon Says

Simon SaysAugusta, ME 01227

Augusta, ME 01227

Page 20: Peta Kendali ATRIBUT

20 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

LCL = 3 .016 3(.007936) -.007808 0pp

(1 ) .016(1 .016) .015744.007936

250 250p

p pn

UCL = 3 .016 3(.007936) .039808pp

Note that theNote that thecomputed computed

LCLLCLis negative.is negative.

Estimated Estimated pp = 80/((20)(250)) = 80/5000 = .016 = 80/((20)(250)) = 80/5000 = .016

Control Limits For a Control Limits For a pp Chart Chart$$

115006529 25447581 1445

26552655

Simon Says

Simon SaysAugusta, ME 01227

Augusta, ME 01227

Page 21: Peta Kendali ATRIBUT

21 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Tdk sesuai Proporsi Tdk sesuai Proporsi

4

1

5

3

2

7

4

5

2

3

(4/250) = 0,016

(1/250) =0,004

2

8

5

3

6

4

2

5

3

6

(2/250) = 0,008

(8/250) = 0,032

Page 22: Peta Kendali ATRIBUT

22 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

p Chart for Norwest Bank

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0 5 10 15 20

Sample Number

Sa

mp

le P

rop

ort

ion

p

UCL

LCL

Control Limits For a Control Limits For a pp Chart Chart$$

115006529 25447581 1445

26552655

Simon Says

Simon SaysAugusta, ME 01227

Augusta, ME 01227

Page 23: Peta Kendali ATRIBUT

23 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Ukuran sampel sama = 50 (Ukuran sampel sama = 50 ( p p-chart)-chart)

no Banyak produk cacat

no Banyak produk cacat

1

2

3

4

5

6

7

8

9

10

4

2

5

3

2

1

3

2

5

4

11

12

13

14

15

16

17

18

19

20

3

5

5

2

3

2

4

10

4

3

Page 24: Peta Kendali ATRIBUT

24 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

n n == m m == D D == p¯p¯ == BKABKA == BKB BKB == Tabel proporsi untuk plot ke grafikTabel proporsi untuk plot ke grafik

Page 25: Peta Kendali ATRIBUT

25 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

n n = 50= 50 m m = 20= 20 D D = 72= 72 p¯p¯ = 72 / (20.50) = .072= 72 / (20.50) = .072 pp = √ (0,072)(0,928)/50 = .037= √ (0,072)(0,928)/50 = .037 BKABKA = 0,072 + 3(0,037)= 0,072 + 3(0,037) = 0,183= 0,183 BKB BKB = 0,072 - 3(0,037) = -0,039 = 0= 0,072 - 3(0,037) = -0,039 = 0 Tabel proporsi untuk plot ke grafikTabel proporsi untuk plot ke grafik

Page 26: Peta Kendali ATRIBUT

26 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Ukuran sampel sama = 50 (Ukuran sampel sama = 50 ( p p-chart)-chart)

cacat

proporsi cacat proporsi

4

2

5

3

2

1

3

2

5

4

(4/50 ) = 0,08

(2/50) = 0,04

3

5

5

2

3

2

4

10

4

3

(5/50) = 0,01

(10/50) = 0,20 (out) revisi

(4/50) = 0,08

(3/50) = 0,06

Page 27: Peta Kendali ATRIBUT

27 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

RevisiRevisi

p¯ = (72-10) / (1000-50) = 62/950 = 0,065p¯ = (72-10) / (1000-50) = 62/950 = 0,065

p = √ (0,065)(0,935)/50 = 0,035p = √ (0,065)(0,935)/50 = 0,035

BKA = 0,065 + 3 (0,035) = 0.17BKA = 0,065 + 3 (0,035) = 0.17

BKB = 0,065 - 3 (0,035) = -0,04 = 0BKB = 0,065 - 3 (0,035) = -0,04 = 0

Grafiknya juga berubahGrafiknya juga berubah

Page 28: Peta Kendali ATRIBUT

28 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Ukuran sampel beda (Ukuran sampel beda (p p chart)chart)

no sampel

Produk cacat

no sampel

Produk cacat

1

2

3

4

5

6

7

8

9

10

200

180

200

120

300

250

400

180

210

380

14

10

17

8

20

18

25

20

30

15

11

12

13

14

15

16

17

18

19

20

190

380

200

210

390

120

190

380

200

180

15

26

10

14

24

15

18

19

11

12

Jml

sampel

4860 Jml

Cacat

341

Page 29: Peta Kendali ATRIBUT

29 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Metode Rata-rataMetode Rata-rata

Sampel rata-rataSampel rata-rata

n¯ n¯ = total sampel /observasi= total sampel /observasi

= 4860/20 = = 4860/20 = 243243

p¯p¯ = D/(n¯m)= D/(n¯m)

= 341 / (243.20) = = 341 / (243.20) = 0,07 (CL)0,07 (CL)

p p = √ (0,07(0,93))/243 = 0,0164= √ (0,07(0,93))/243 = 0,0164

BPAp = 0,07 + 3 (0,0164) = 0,119BPAp = 0,07 + 3 (0,0164) = 0,119

BPBp = 0,07 - 3 (0,0164) = 0,021BPBp = 0,07 - 3 (0,0164) = 0,021

Page 30: Peta Kendali ATRIBUT

30 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Metode IndividuMetode Individu

Sampel rata-rataSampel rata-rata

n¯ n¯ = total sampel /observasi= total sampel /observasi

= 4860/20 = = 4860/20 = 243243

pp ¯ ¯ = D/(n¯m)= D/(n¯m)

= 341 / (243.20) = = 341 / (243.20) = 0,07 (CL) semua titik 0,07 (CL) semua titik samasama

BP (obs-1)BP (obs-1)

p p = √ (0,07(0,93))/200 = 0,018= √ (0,07(0,93))/200 = 0,018

BPA = 0,07 + 3 (0,018) = 0,124BPA = 0,07 + 3 (0,018) = 0,124

BPB = 0,07 - 3 (0,018) = 0,016……………….dstBPB = 0,07 - 3 (0,018) = 0,016……………….dst

Page 31: Peta Kendali ATRIBUT

31 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Tabel Proporsi untuk GrafikTabel Proporsi untuk Grafik

No observasi sampel cacat proporsi

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

200

180

200

120

300

250

400

180

210

380

190

380

200

210

390

120

190

380

200

180

14

10

17

8

20

18

25

20

30

15

15

26

10

14

24

15

18

19

11

12

0,070

0,055

0,085

0,067

0,095

0,050

0,055

0,067

Page 32: Peta Kendali ATRIBUT

32 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Example…c-chartExample…c-chart

no

Byknya kesalahan

no Byknya kesalahan

1

2

3

4

5

6

7

8

9

10

5

4

7

6

8

5

6

5

16

10

11

12

13

14

15

16

17

18

19

20

9

7

8

11

9

5

7

6

10

8

Page 33: Peta Kendali ATRIBUT

33 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

c¯ = ∑c/n = 152/20 = 7,6c¯ = ∑c/n = 152/20 = 7,6

BPA c = (7, 6) + 3 (√7,6) = 15,87BPA c = (7, 6) + 3 (√7,6) = 15,87 BPB c = (7, 6) - 3 (√7,6) = -0,67 = 0BPB c = (7, 6) - 3 (√7,6) = -0,67 = 0

Page 34: Peta Kendali ATRIBUT

34 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Example…u-chartExample…u-chart

no

Sampel cacat no

sampel cacat

1

2

3

4

5

6

7

8

9

10

20

30

25

15

25

10

20

15

15

25

5

14

8

8

12

6

20

10

6

10

11

12

13

14

15

16

17

18

19

20

30

25

25

25

10

20

20

10

30

20

9

16

12

10

6

8

5

5

14

8

Page 35: Peta Kendali ATRIBUT

35 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Metode Rata-rataMetode Rata-rata

Sampel Rata-rataSampel Rata-rata

u¯ = 192/415 = 0,462 (CL)u¯ = 192/415 = 0,462 (CL)

n¯ = 415/20 = 20,75n¯ = 415/20 = 20,75

BPAu = (0,462) + 3 √ (0,462/20,75) = 0,906 BPAu = (0,462) + 3 √ (0,462/20,75) = 0,906

BPBu = (0,462) - 3 √ (0,462/20,75) = 0,018BPBu = (0,462) - 3 √ (0,462/20,75) = 0,018

Page 36: Peta Kendali ATRIBUT

36 Slide

© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western

Metode IndividuMetode Individu

Sampel Rata-rataSampel Rata-rata

u¯ = 192/415 = 0,462 (CL)u¯ = 192/415 = 0,462 (CL)

n¯ = 415/20 = 20,75n¯ = 415/20 = 20,75

Batas KendaliBatas Kendali Observasi -1Observasi -1

BPA-1 = (0,462) + 3 √ (0,462/20) = 0,916 BPA-1 = (0,462) + 3 √ (0,462/20) = 0,916

BPB-1 = (0,462) - 3 √ (0,462/20) = BPB-1 = (0,462) - 3 √ (0,462/20) = 0,008…….dst0,008…….dst