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

3

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)

4

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