Fuzzy Inference System Diagnose Assignable Cause Based on Hotelling’s Control Chart
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Transcript of Fuzzy Inference System Diagnose Assignable Cause Based on Hotelling’s Control Chart
Fuzzy Inference System
Diagnose Assignable Cause
Based on Hotelling’s Control Chart
Graduate:Syuan-Fong Jhong
Advisor: Jing-Er Chiu, Ph.D.
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1. Introduction
Variation in a process
Assignable causes
Common causes
Control chart
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point beyond control limits
Non-random pattern
s
Process out of control
Control chart
Interrelationship diagram
Reality tree
Cause-and-effect diagram
Need expertise of practitioners and time.
Root Cause Analysis (RCA)
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Montgomery(2005)、 Doty(1996)、 Smith(2004)
Assignable cause
Non-random patterns
Faster
Easier
diagnosis
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Author Year Method
Doggetti et al. 2005
Cause-and-effect diagram Interrelationship diagramReality tree
2. References review
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Author Year Method Results
Alaeddini 2011 Bayesian networks
Real time identification of single and multiple assignable causes
Alaeddini(2011)
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Author Year Method Results
Demirli et al. 2010 Fuzzy inference
system
Out of control: prioritize the assignable cause
In control: track and preventive action to prevent this process out of control
Demirliet al.(2010)
2.1 Assignable cause
1. Isolated causes› one particular point falling outside the
control limits
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possible causes
A mistake in measurement, recording or
plotting
Damage in
handling
Defect in raw-material used for that
unit alone
False alarm
2. Shift cause› produce a considerable shift in the process
mean
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possible causes
Tool brea
k
Change in raw-
material or
supplier
Change in inspection methods
or standards
Adjustments made in machine settings
Introduction of new
workers or inspectors
3.Gradual cause› change the process mean gradually over time
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possible causes
Gradual introduction of new
raw-material
Loosening
fixtures
Operator
fatigueMachine tool wear
Gauge
wear
Environmental changes
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2.2 Non-random patternsPattern
1 OCL One or more point falling beyond 3σ control limits
2 FR1 4 out of 5 consecutive points fall beyond 1σ control limit on the same side of center line
3 FR2 2 out of 3 consecutive points fall beyond 2σ control limit on the same side of center line
4 Run Seven consecutive points fall on the same side of centerline
5 Trend Seven consecutive points continuously increasing or decreasing
6 Cycle Repetitive forms of patterns observed on the control chart over a period of time
7 Instability Erratic zigzag patterns with points fluctuating up and down
2.3 Fuzzy inference system
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Fuzzification Inference
Defuzzificatio
n
Rule base
Crisp value Crisp value
Zadeh(1965)
Granulationcapabilities
Summarization
information compression
Zadeh(2008)
1. Quantifying the evidence from partially developed patterns
2. Combining evidence from different patterns to identify underlying causes
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2.4 Hotelling’s
(Montgomery,2004)
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Simulated data
Generatedcontrol limits
Monitored
OCL(R1)→Isolated cause(C1)OC(R1)L→Shift cause(C2)OCL(R1)→Gradual cause(C3)Freak(R2)→Shift cause(C2)Run(R3)→Shift cause(C2)Trend(R4)→Gradual cause(C3)
Aggregation
Fuzzy Inference System
RankedAssignable
cause
No Is the probability equal to
1?
Createdrun rules
3.Research method
Francisco Aparisi(2004)
Demirliet al.(2010)
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3.1 Simulated data
› :p quality characteristic measured at time t.
› ,› where is the magnitude of the process shifts in terms of , associated
with the quality characteristic
Chen et al. (2004)This research parameter setting
Quality characteristics(p) 2Correlation() 0.8
Covariance matrix()Magnitude of the process
shifts (0,1)、 (1,0)、 (1,1)
Sample number(m) 30Sample size (n) 5
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3.2 Generated control limits
› P(>CL|)=0.005› P(>ZA|)=0.03› P(>Median|)=0.5
Francisco Aparisi(2004)
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3.3 Created run rules
› Rule 1(R1): point above the control limit (CL)
› Rule 2(R2): two out of three consecutive points within the attention zone (zone A)
› Rule 3(R3): eight consecutive points over the median (zone B).
› Rule4 (R4): seven consecutive rising pointsFrancisco Aparisi(2004)
R1R2R3
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R2:two out of three consecutive points within the attention zone (zone A)
3.4 Monitored
Crisp value
R1 R2 R3 R4
0 2 3
R3:eight consecutive points over the median (zone B).R4:seven consecutive rising points
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3.5 Fuzzy Inference System
Ranked assignable causes
Aggregation
R1R2R3R4
R1
R2
R3
R4
C1
C2
C3
Inputvalue
Input membershi
pfunction
Output membershi
pfunction
Output value
Fuzzification Inference Defuzzificatio
n
Rule Based
Rulebase
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4. Expected results
𝑇❑2𝑖
R1
R2
R3
R4
C1
C2
C3
Rankcaus
e
Fuzzy inference system
Pattern Cause