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

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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

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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

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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

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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

19

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

Times Cited: 0  (from All Databases-Web of

Knowledge)

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Thanks a lot for your attention.