Upload
zoe
View
284
Download
25
Embed Size (px)
DESCRIPTION
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
Citation preview
1 Slide
© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western
Peta Kendali Peta Kendali ATRIBUTATRIBUT
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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¯)
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
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
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
$$
115006529 25447581 1445
26552655
Simon Says
Simon SaysAugusta, ME 01227
Augusta, ME 01227
20 Slide
© 2005 Thomson/South-Western© 2005 Thomson/South-Western© 2004 Thomson/South-Western© 2004 Thomson/South-Western
LCL = 3 .016 3(.007936) -.007808 0pp
(1 ) .016(1 .016) .015744.007936
250 250p
p pn
UCL = 3 .016 3(.007936) .039808pp
Note that theNote that thecomputed computed
LCLLCLis negative.is negative.
Estimated Estimated pp = 80/((20)(250)) = 80/5000 = .016 = 80/((20)(250)) = 80/5000 = .016
Control Limits For a Control Limits For a pp Chart Chart$$
115006529 25447581 1445
26552655
Simon Says
Simon SaysAugusta, ME 01227
Augusta, ME 01227
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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