1 Antonio F. B. Costa Marcela A. G. Machado São Paulo State University Production Department Brazil BRAZILIAN ADVICE OF SCIENTIFIC AND TECHNOLOGICAL DEVELOPMENT CNPq A Side-Sensitive Synthetic chart to Control the Process Mean Tuesday, July 9, 2013 Session 2: Special Topics of Process Control 12:05 - 12:30
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1 Antonio F. B. Costa Marcela A. G. Machado São Paulo State University Production Department Brazil BRAZILIAN ADVICE OF SCIENTIFIC AND TECHNOLOGICAL DEVELOPMENT.
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1
Antonio F. B. Costa
Marcela A. G. Machado
São Paulo State University
Production Department
Brazil
BRAZILIAN ADVICE OF SCIENTIFIC AND TECHNOLOGICAL DEVELOPMENT
CNPq
A Side-Sensitive Synthetic chart to Control the Process Mean
Tuesday, July 9, 2013Session 2: Special Topics of Process Control
12:05 - 12:30
2
A run sum Hotelling's chi(2) control chart COMPUTERS & INDUSTRIAL ENGINEERING 2013 A multivariate synthetic double sampling T-2 control chart Source: COMPUTERS & INDUSTRIAL ENGINEERING 2013 Economically Optimum Design of a Synthetic (X)over-bar Chart QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2012 Optimal design of the synthetic chart for the process mean based on median run length IIE TRANSACTIONS 2012 Optimal Designs of the Multivariate Synthetic Chart for Monitoring the Process Mean Vector Based on Median Run Length QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2011 A synthetic double sampling control chart for the process mean IIE TRANSACTIONS 2011
The synthetic (X)over-bar chart with estimated parameters IIE TRANSACTIONS 2011 A combined synthetic & X chart for monitoring the process mean INTERNATIONAL JOURNAL OF PRODUCTION 2010 A Synthetic Scaled Weighted Variance Control Chart for Monitoring the Process Mean of Skewed Populations COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2009
Synthetic Charts
3
0 1 2 3 4 5 6 7 8 9 10
Sample number
UCL
LCL
UCL
L=5
LCL
CL
The synthetic X chart Alarm
CRL L=5
CRL=3
4
0 1 2 3 4 5 6 7 8 9 10
Sample number
UCL
LCL
UCL
L = 5
LCL
CL
CRL=3
Alarm
CRL L=5
The synthetic X chart
Alarm ?
5
Controling the Process
Walter Andrew Shewhart
0Shift
)N(0,~e e,X 00
Shewhart model
X
f(X)
Time
3T
4T
1T X
X
X
2T
f(X)
f(X)
f(X)
0
6
Controling the Process
0Shift
)N(0,~e e,X 00
Shewhart model
0 1 2 3 4 5 6 7 8 9 10
UCL
LCL
L = 5
LCL0 1 2 3 4 5 6 7 8 9 10
Sample number
UCL
LCL
UCL
L =5
LCL
X
f(X)
Time
3T
4T
1T X
X
X
2T
f(X)
f(X)
f(X)
0
7
Controling the Process
0Shift
)N(0,~e e,X 00
Shewhart model
X
f(X)
Time
3T
4T
1T
X
X
X 2T
f(X)
f(X)
f(X)
0
15 30 45 60 75 90 105 Time (min)
X
LCL
CL
UCL
0 1 2 3 4 5 6 7 8 9 10
UCL
LCL
L = 5
LCL
8
0 1 2 3 4 5 6 7 8 9 10
UCL
LCL
L = 5
LCLCRL=3
The Side Sensitive Synthetic Chart X
No alarm
CL
60
80
100
120
140
160
180
1 6 11 16L
SSARL
S ide s ens itive S ynthetic
Figure 4: SSARLs for the Side Sensitive and Synthetic charts (d=0.5)
20
24
28
32
36
40
1 6 11 16L
SSARL
S ide s ens itive S ynthetic
Figure 5: SSARLs for the Side Sensitive and Synthetic charts ( d =1.0)
8
9
10
11
12
13
1 3 5 7L
SSARL
S ide s ens itive S ynthetic
Figure 6: SSARLs for the Side Sensitive and Synthetic charts ( d =1.5)
4
4,4
4,8
5,2
5,6
1 3 5 7
L
SSARL
S ide s ens itive S ynthetic
Figure 7: SSARLs for the Side Sensitive and Synthetic charts ( d =2.0)
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The side sensitive synthetic median chart
If doesn’t go we draw a point below the LCL
If goes we draw a point above the UCL
14
CL
UCL
LCL
The side sensitive synthetic median chart
1 2 3 4 5 6 7 8 9 105
CRL=2L=5
Alarm
SSARLs for the SSSyn Median chart and the Xbar chart (L=3, n=3)
In-control ARL=1000
SSARLs for the SSSyn Median chart and the Xbar chart (L=3, n=3)
In-control ARL=370.4
SSARLs for the SSSyn Median chart and the Xbar chart (L=3, n=2)
In-control ARL=1000
SSARLs for the SSSyn Median chart and the Xbar chart (L=3, n=2)
In-control ARL=370.4
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Controling the Process
Walter Andrew Shewhart
Title: Quality Control ChartsAuthor(s): Shewhart, W. A.
Source: BELL SYSTEM TECHNICAL JOURNAL Volume: 5 Issue: 4 Pages: 72-82
Published: OCT 1926
Times Cited: 0 (from All Databases-Web of
Knowledge)
Title: Quality ControlAuthor(s): Shewhart, W. A.Source: BELL SYSTEM TECHNICAL JOURNAL Volume: 6 Issue: 4 Pages: 175-192 Published: OCT 1927