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Lecture 4Lecture 4Control Chart for Control Chart for Variables Variables -- 11
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Review ►QUIZ ( 10 menit )
� Sebutkan pembagian penyebab variasipada proses manufaktur ? Berikancontoh ?contoh ?
� Kapan proses disebut in control dankapan out of control ? Berikan contoh?
JANGAN LUPA BERI NAMA DAN NIM
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Review
� Penyebab Variasi� Chance Cause ( Penyebab Umum )
Sesuatu yang melekat pada proses
25 October 2010 Materi ke-3
Sesuatu yang melekat pada proses( sesuatu yang alamiah ). Contoh : Suhu ruangan
� Assignable Cause ( PenyebabKhusus )Sesuatu yang dapat ditentukanContoh : salah alat, kesalahan operator
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Review
� Proses in control ketika proses yang berjalan hanya disebabkan oleh Chance Cause ( Penyebab Umum )Proses out of control ketika proses yang
25 October 2010 Materi ke-3
� Proses out of control ketika proses yang berjalan disebabkan oleh Assignable Cause ( PenyebabKhusus )
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Pengambilan Sampel
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Pemilihan subgroup
� Aturan : memilih subgrup sedemikiansehingga variasi yang terjadi dalam subgruphanya disebabkan oleh chance causes.
� Pengambilan subgrup berdasarkan waktu
25 October 2010 Materi ke-3
� Pengambilan subgrup berdasarkan waktu� Besarnya subgrup ( Subgroup Size ) adalah
jumlah produk yang diambil pada setiapsubgrup.
� Banyaknya sampling adalah jumlah subgrupdalam sampling.
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Pemilihan subgroup
subgroup size ( besarnya subgrup )
1 2 3 4 5 x s
subgrup ke-1 → 1
2
.
7
.
.
.
.
subgrup ke-35 → 35
↑
Jumlah sampel
( banyaknya
subgroup )
X
S
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Pendahuluan
• Variabel - karakteristik kualitas tunggal yang dapat diukur dalam skala numerik.
• Ketika bekerja dengan variabel, kita harusmemantau baik nilai rata-rata karakteristik dan
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memantau baik nilai rata-rata karakteristik danvariabilitas yang terkait dengan karakteristik.
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Pendahuluan
� Mean = kecenderungan pemusatandari proses.
� Variability = dispersi proses
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� Variability = dispersi proses
µ0 µ1LSL USL
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Pendahuluan
σ0
10
µ0LSL USL
σ1
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IntroductionIntroduction
� Monitor Mean Quality Level� x-bar control chart
Monitor Process Variability Quality
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� Monitor Process Variability Quality Level� Control chart for standard deviation, S
chart� Control chart for the range, R chart
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Selection Char. for Investigation
� There can be many possible quality characteristics
� The decision making process becomes
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� The decision making process becomes more complicated
� Selecting a few vital quality char. from the many candidate ( using Pareto analysis )
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Construction of Control Chart
� Selection of Rational Subgroups� Dif. among subgroups : maximized� Dif. within subgroups : minimized
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� Dif. within subgroups : minimized
� Subgroup Size� Normally between 4 – 10 ( 4 or 5 )
� Frequency of Subgroups Selection� Type of Measuring Instrument� Design of Recording Form for Data
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Construction of Control Chart
Notation for variables control charts� n - size of the sample (sometimes called a
subgroup) chosen at a point in time� m - number of samples selected
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� m - number of samples selected� = average of the observations in the ith
sample (where i = 1, 2, ..., m)� = grand average or “average of the
averages (this value is used as the center line of the control chart)
ix
x
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� Ri = range of the values in the ithsample
Ri = xmax - xmin
Construction of Control Chart
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Ri = xmax - xmin
� = average range for all m samples� µ is the true process mean� σ is the true process standard
deviation
R
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Contoh : Control Chart for the Mean and Range
Month Week 1 Week 2 Week 3 Week 41 6,60 7,16 3,12 6,032 8,81 4,98 6,38 5,763 0,51 4,56 4,68 7,744 5,05 5,82 5,47 3,455 9,64 8,57 6,31 6,356 0,85 10,00 1,95 4,037 5,68 8,34 5,69 9,60
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7 5,68 8,34 5,69 9,608 5,47 4,11 1,72 7,239 2,46 4,46 2,22 6,9710 6,05 2,04 5,44 7,8111 4,72 4,84 4,22 10,5312 7,12 6,35 6,44 0,5013 6,60 0,88 8,99 7,0714 7,86 5,93 3,09 6,8215 11,32 8,57 5,62 4,2116 4,38 2,50 8,43 7,2117 7,51 6,13 2,14 9,8418 6,60 7,16 3,12 6,0319 8,83 4,99 4,77 1,5420 4,42 7,34 5,11 6,77
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Contoh : Control Chart for the Mean and Range
� Development of the Chart
Rn
X
gg
n
i i
R
XXX
∑∑
∑ = −==minmax
1 ,
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gR
gX
g
i i
g
i i RX ∑∑ == == 11 ,
( ) RAXLCLUCLXX 2, ±=
RDLCLRDUCL RR 34 , ==
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Contoh : Control Chart for the Mean and Range
Month Week 1 Week 2 Week 3 Week 4 X (Avg) Range
1 6,60 7,16 3,12 6,03 → 5,73 4,04
2 8,81 4,98 6,38 5,76 → 6,48 3,83
19 8,83 4,99 4,77 1,54 → 5,03 7,29
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19 8,83 4,99 4,77 1,54 → 5,03 7,29
20 4,42 7,34 5,11 6,77 → 5,91 2,92
Sum(X)= 113,9025 Sum(R)= 110,7
X= 5,695125 R= 5,535
A2= 0,729 D4= 2,282
UCL(X)= 9,73014 D3= 0
LCL(X)= 1,66011 UCL= 12,63087
LCL= 0
A2,D4 dan D3 dari tabel
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Contoh : Control Chart for the Mean and Range
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Contoh : Control Chart for the Mean and Range
8,00
10,00
12,00
0,00
2,00
4,00
6,00
8,00
0 5 10 15 20 25Month
X(Avg) X UCL LCL
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Contoh : Control Chart for the Mean and Range
10,00
12,00
14,00
0,00
2,00
4,00
6,00
8,00
0 5 10 15 20 25Month
Range R UCL LCL
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Example
The thickness of magnetic coating on audio tape is an important
Samplenumber
Sample mean
sample stdv
1 36,4 4,6
2 35,8 3,7
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important characteristics. Table shows the mean and standard dev for 20 samples. The spec are 38 ± 4.5 . ( Note n = 4 )
2 35,8 3,7
3 37,3 5,2
18 39,2 4,8
19 36,8 4,7
20 37,7 5,4
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Example� Find the trial control limit for an X and s Chart
79.420
8.95
20
20
1 ==== ∑ =s
sCL i i
s
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0)79.4)(0(
854.10)79.4)(266.2(
79.42020
3
4
===
===
====
sBLCL
sBUCL
sCL
s
s
s
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Example� Find the trial control limit for an X and s Chart
075.3720
5.741
20
20
1 ==== ∑ =X
XCL ii
X
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277.29)79.4)(628.1(075.37
873.44)79.4)(628.1(075.37
2020
3
3
=−=−=
=+=+=
sAXLCL
sAXUCL
X
X
X
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Example : S chart
4
5
6
7
CL
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0
1
2
3
4
1 3 5 7 9 11 13 15 17 19 LCL
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Example : X Chart
37383940
CL
27
313233343536
1 3 5 7 9 11 13 15 17 19
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Example� Assuming the thickness to be normally dist. what
proportion of the product will not meet spec ?
199.59213.0
79.4ˆ ===
c
sσ
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1492.004.1199.5
075.375.42
2451.069.0199.5
075.375.33
199.59213.0
1
1
4
⇒=−=
⇒−=−=
===
z
z
cσ
proportion of the product not meet spec = 0.2451 + 0.1492 = 0.3943
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Kata Inspirasi Hari Ini
Semakin luas Anda mengait-ngaitkan berbagai hal , semakin
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ngaitkan berbagai hal , semakin banyak anda belajar
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QuizQuiz
1. Definisikan variabel menurut anda dan contohnya ?Apa yang dapat dimonitor oleh
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2. Apa yang dapat dimonitor oleh peta kendali variabel ?
3. Apa perbedaan fungsi X-chart dan R-chart ?