Download - 9 10 kendali variabel xr
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Peta KendaliVariabel
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• Menggambarkan variasi atau penyimpangan yg terjadi pd kecenderungan data variabel
• Kondisi in-out of control tapi tdk identik dg kepuasan pelanggan
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Manfaat…
• Perbaikan kualitas
• Menentukan kemampuan proses
• Membuat keputusan berkaitan dg proses produksi dan produk yg dihasilkan
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Tahapan…
1. Pemilihan karakteristik kualitas– panjang, berat, volume, waktu– Mempengaruhi kinerja produk– Pemilihan karakteristik dg Diagram Pareto
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2. Pemilihan Sub Kelompok
Ukuran Sampel menurut Inspeksi Normal ANSI/ASQC Z1.9-1993
Byknya produk yg dihasilkan Ukuran Sampel
91 – 150
151 – 280
281 – 400
401 – 500
501 – 1200
1201 – 3200
3201 – 10000
10001 – 35000
35001 - 150000
10
15
20
25
35
50
75
100
150
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3. Pengumpulan Data
4. Penentuan Batas Kendali untuk pet X-R dan Nilai Faktor Guna
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X Chart
Range for sample i
# Samples
Mean for sample i
From Table Nilai Guna
RAxxLCL
RAxxUCL
n
R R
i
n
1i
n
xi
n
ix
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Nilai Faktor Guna
Sample Size, n
Mean Factor, A2
Upper Range, D4
Lower Range, D3
2 1.880 3.268 0
3 1.023 2.574 0
4 0.729 2.282 0
5 0.577 2.115 0
6 0.483 2.004 0
7 0.419 1.924 0.076
8 0.373 1.864 0.136
9 0.337 1.816 0.184
10 0.308 1.777 0.223
12 0.266 1.716 0.284 0.184
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R Chart
Range for Sample i
# Samples
From Table Nilai Guna
n
R R
R D LCL
R D UCL
i
n
1i
3R
4R
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Process Capability Ratio, Cp
process the of deviation standard
6σionSpecificat LowerionSpecificat Upper
pC
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Process Capability Cpk
population process the of deviation standard mean process x where
LimitionSpecificatLower x
or , x Limit ionSpecificatUpper
of minimum
3
3pkC
Assumes that the process is:• under control• normally distributed
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Warning Conditions…..
Western Electric :1. 1 titik diluar batas kendali ( 3σ)2. 2 dr 3 titik berurutan diluar batas
kendali (2σ)3. 4 dr 5 titik berurutan jauh dari GT
(1σ)4. 8 titik berurutan di satu sisi GT5. Giliran panjang 7-8 titik6. 1/beberapa titik dekat satu batas
kendali7. Pola data TAK RANDOM
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Examples: Compute the 3 control charts for X and R from 15 samples of size n=3. Plot the control limits and the X and R values and comment about the underlying process. Sample OBSERVED DIMENSIONS (cm)
1 4.843 4.863 4.859 2 4.925 4.882 4.891 3 4.866 4.914 4.873 4 4.852 4.883 4.88 5 4.92 4.884 4.821 6 4.915 4.902 4.898 7 4.887 4.892 4.858 8 4.868 4.888 4.842 9 4.904 4.863 4.866 10 4.921 4.92 4.894 11 4.914 4.884 4.899 12 4.892 4.896 4.887 13 4.866 4.829 4.88 14 4.85 4.875 4.872 15 4.867 4.9 4.885
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Sample OBSERVED DIMENSIONS (cm) mean range1 4.843 4.863 4.859 4.855 0.0202 4.925 4.882 4.891 4.899 0.0433 4.866 4.914 4.873 4.884 0.0484 4.852 4.883 4.88 4.872 0.0315 4.92 4.884 4.821 4.875 0.0996 4.915 4.902 4.898 4.905 0.0177 4.887 4.892 4.858 4.879 0.0348 4.868 4.888 4.842 4.866 0.0469 4.904 4.863 4.866 4.878 0.041
10 4.921 4.92 4.894 4.912 0.02711 4.914 4.884 4.899 4.899 0.03012 4.892 4.896 4.887 4.892 0.00913 4.866 4.829 4.88 4.858 0.05114 4.85 4.875 4.872 4.866 0.02515 4.867 4.9 4.885 4.884 0.033
4.882 0.037
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844.4)037(.023.1882.4
920.4)037(.023.1882.4
x
x
LCL
UCL
x Chart
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Six Sigma Control Chart (x-bar)
4.840
4.850
4.860
4.870
4.880
4.890
4.900
4.910
4.920
4.930
0 2 4 6 8 10 12 14 16
Observation
cm
Sample Mean
Upper Control Limit
Lower Control Limit
Center Line
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R- Chart
0951.037.57.24 RD
0037.03 RD
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Range Example
0
0.02
0.04
0.06
0.08
0.1
0.12
0 2 4 6 8 10 12 14 16
Sample Number
ran
ge
(cm
) Upper Control Limit
Center Line
Lower Control Limit
Sample Range
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Contoh
No Hasil Pengukuran Xֿ R
1
2
3
4
5
6
7
8
9
10
20,22,21,23,22
19,18,22,20,20
25,18,20,17,22
20,21,22,21,21
19,24,23,22,20
22,20,18,18,19
18,20,19,18,20
20,18,23,20,21
21,20,24,23,22
21,19,20,20,20
Jumlah/Rata-rata
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n =
A2 =
D4 =
D3 =
• GT =
• BKA =
• BKB =
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n = 5
A2 = 0,577
D4 = 2,115
D3 = 0
• GT =
• BKA =
• BKB =
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No X1 X2 X3 X4 X5 X6 X7 X¯ R
1
2
3
4
5
6
7
8
9
10
6
11
9
12
16
10
15
12
16
7
9
7
6
11
10
4
16
14
9
13
10
8
13
10
8
9
10
16
13
10
15
10
9
10
9
7
13
6
15
12
10
5
10
7
8
8
13
11
4
8
7
5
12
9
7
6
13
11
10
Jumlah/Rata-rata
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• X¯(rata-rata) = ni (Xi)/ni
= n1X1 +n2X2 +……niXi
ni
• R¯ = ni (Ri)/ni
= n1R1 +n2R2 +……niRi
ni
• BP-X¯ = X¯rata-rata ± A2.R¯
• BPA-R = R¯D4
• BPB-R = R¯D3
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No X¯ BPA BPB R BPA BPB
1
2
3
4
5
6
7
8
9
10
8,57
8,17
13,25
10,00
13,25
13,74
15,65
13,25
6,75
6,26
4,35
6,75
11
6
7
6
14,91
15,53
17,69
14,91
0,59
0
0
0.59
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• Xֿ(rata-rata) = GT peta kendali X = 7(8,57) +6(8,17)+…+4(13,25)+7(10) 7+6+7+……+4+7 = • Rֿ = GT peta kendali R =7(11)+6(6)+7(7)…+4(7)+7(6) 7+6+7+…+4+7 = Ada 10 macam BATAS KENDALI