This document discusses control charts, which describe variation in data variables. It outlines the benefits of control charts like quality improvement and process capability assessment. The steps involve selecting quality characteristics, determining sample sizes, collecting data, and establishing control limits for X-bar and R charts. An example is provided to calculate 3-sigma control limits from 15 samples of size 3 and comment on the underlying process.

1. Peta Kendali
Variabel

2. • Menggambarkan variasi atau penyimpangan
yg terjadi pd kecenderungan data variabel
• Kondisi in-out of control tapi tdk identik dg
kepuasan pelanggan

3. Manfaat…
• Perbaikan kualitas
• Menentukan kemampuan proses
• Membuat keputusan berkaitan dg proses
produksi dan produk yg dihasilkan

4. Tahapan…
1. Pemilihan karakteristik kualitas
– panjang, berat, volume, waktu
– Mempengaruhi kinerja produk
– Pemilihan karakteristik dg Diagram Pareto

5. 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

6. 3. Pengumpulan Data
4. Penentuan Batas Kendali untuk pet X-R
dan Nilai Faktor Guna

7. 
X Chart
Range for
sample i
# Samples
Mean for
sample i
From
Table Nilai Guna
RAxxLCL
RAxxUCL
2−=
2+=
n
R
R
i
n
1i=
∑
=
n
x
i
n
i
x
1=
∑
=

8. 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

9. R Chart
Range for Sample i
# Samples
From Table Nilai Guna
n
R
R
RDLCL
RDUCL
i
n
1i
3R
4R
=
∑
=
=
=

10. Process Capability Ratio, Cp
processtheofdeviationstandard
6σ
ionSpecificatLowerionSpecificatUpper
=
−
=
σ
pC

11. Process Capability Cpk
populationprocesstheofdeviationstandard
meanprocessxwhere
LimitionSpecificatLowerx
or,
xLimitionSpecificatUpper
ofminimum
=
=


−


 −
=
σ
σ
σ
3
3
pkC
Assumes that the process is:
• under control
• normally distributed

12. 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 GT
5. Giliran panjang 7-8 titik
6. 1/beberapa titik dekat satu batas
kendali
7. Pola data TAK RANDOM

13. Examples: Compute the 3σ control charts for and R from 15 samples of size n=3. Plot the
control limits and the 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

14. Sample OBSERVED DIMENSIONS (cm) mean range
1 4.843 4.863 4.859 4.855 0.020
2 4.925 4.882 4.891 4.899 0.043
3 4.866 4.914 4.873 4.884 0.048
4 4.852 4.883 4.88 4.872 0.031
5 4.92 4.884 4.821 4.875 0.099
6 4.915 4.902 4.898 4.905 0.017
7 4.887 4.892 4.858 4.879 0.034
8 4.868 4.888 4.842 4.866 0.046
9 4.904 4.863 4.866 4.878 0.041
10 4.921 4.92 4.894 4.912 0.027
11 4.914 4.884 4.899 4.899 0.030
12 4.892 4.896 4.887 4.892 0.009
13 4.866 4.829 4.88 4.858 0.051
14 4.85 4.875 4.872 4.866 0.025
15 4.867 4.9 4.885 4.884 0.033
4.882 0.037

15. 844.4)037(.023.1882.4
920.4)037(.023.1882.4
=−=
=+=
x
x
LCL
UCL
x Chart

16. 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

17. R- Chart
0951.037.57.24 =×=RD
0037.03 =×=RD

18. 0
0.02
0.04
0.06
0.08
0.1
0.12
0 2 4 6 8 10 12 14 16
range(cm)
Upp
Cen
Low
Sam

19. 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

20. n =
A2 =
D4 =
D3 =
• GT =
• BKA =
• BKB =

21. n = 5
A2 = 0,577
D4 = 2,115
D3 = 0
• GT =
• BKA =
• BKB =

22. 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

23. • 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

24. 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

25. • 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