### Document

```Peta Kendali
Variabel
• Menggambarkan variasi atau
data variabel
• Kondisi in-out of control tapi tdk identik dg
kepuasan pelanggan
Manfaat…
• Perbaikan kualitas
• Menentukan kemampuan proses
• Membuat keputusan berkaitan dg proses
produksi dan produk yg dihasilkan
Tahapan…
1.
Pemilihan karakteristik kualitas
– panjang, berat, volume, waktu
– Mempengaruhi kinerja produk
– Pemilihan karakteristik dg Diagram Pareto
2. Pemilihan Sub Kelompok
Ukuran Sampel menurut Inspeksi Normal ANSI/ASQC Z1.9-1993
Byknya produk yg dihasilkan
91 – 150
151 – 280
281 – 400
401 – 500
501 – 1200
1201 – 3200
3201 – 10000
10001 – 35000
35001 - 150000
Ukuran Sampel
10
15
20
25
35
50
75
100
150
3. Pengumpulan Data
4. Penentuan Batas Kendali untuk peta X-R
dan Nilai Faktor Guna
X Chart
UCL x  x  A  R
From
Table Nilai
Guna
Range for
sample i
LCL x  x  A  R
n
x 
Mean for
sample i
 xi
i 
n
n
R 
# Samples
 Ri
i 1
n
Nilai Faktor Guna
Sample
Size, n
2
Mean
Factor, A2
1.880
Upper
Range, D4
3.268
Lower
Range, D3
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
R Chart
UCL R  D4 R
LCLR  D3 R
n
R 
 Ri
From Table Nilai
Guna
Range for Sample i
i 1
n
# Samples
Process Capability Ratio, Cp
Upper Specification  Low erSpecification
Cp 
6σ
  standard dev iationof the process
Process Capability Cpk
 Upper Specification Limit  x
C pk  minimum of 
, or
3

x  Low er Specification Limit 

3

w here x  process mean
  standard dev iation of the process population
Assumes that the process is:
• under control
• normally distributed
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
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
OBSERVED DIMENSIONS (cm)
4.843
4.863
4.859
4.925
4.882
4.891
4.866
4.914
4.873
4.852
4.883
4.88
4.92
4.884
4.821
4.915
4.902
4.898
4.887
4.892
4.858
4.868
4.888
4.842
4.904
4.863
4.866
4.921
4.92
4.894
4.914
4.884
4.899
4.892
4.896
4.887
4.866
4.829
4.88
4.85
4.875
4.872
4.867
4.9
4.885
S a m p le
O B S E R V E D D IM E N S IO N S (c m )
m ean
ra n g e
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
x Chart
UCLx  4.882  1.023(.037)  4.920
LCLx  4.882  1.023(.037)  4.844
S ix S i g m a C o n tro l C ha rt ( x -b a r)
4 .9 3 0
4 .9 2 0
4 .9 1 0
4 .9 0 0
S a m p le M e a n
4 .8 9 0
cm
U p p e r C o n tro l L im it
L o w e r C o n tro l L im it
C e n te r L i n e
4 .8 8 0
4 .8 7 0
4 .8 6 0
4 .8 5 0
4 .8 4 0
0
2
4
6
8
O b s e r v a tio n
10
12
14
16
R- Chart
D4 R  2.57  .037  .0951
D3 R  0  .037  0
Range Example
0.12
0.1
0.08
Upper Control Lim
Center Line
0.06
Lower Control Lim
Sample Range
0.04
0.02
0
0
2
4
6
8
10
12
14
16
Contoh
No Hasil Pengukuran
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
Xֿ
R
n =
A2 =
D4 =
D3 =
• CL =
• UCL =
• LCL =
n =5
A2 = 0,577
D4 = 2,115
D3 = 0
• CL =
• UCL =
• LCL =
Terima Kasih
```