Graduate:Syuan-Fong Jhong Advisor: Jing-Er Chiu, Ph.D.

1.Introduction Variation in a process Assignable causes Common causes Control chart 2

point beyond control limits Non- random patterns Process out of control Control chart Interrelationship diagram Reality tree Cause-and-effect diagram 3 Need expertise of practitioners and time. Root Cause Analysis (RCA)

Montgomery(2005) 、 Doty(1996) 、 Smith(2004) Assignable cause Non-random patterns 4 Faster Easier diagnosis

5 AuthorYearMethod Doggetti et al.2005 Cause-and-effect diagram Interrelationship diagram Reality tree 2.References review

6 AuthorYearMethodResults Alaeddini2011Bayesian networks Real time identification of single and multiple assignable causes Alaeddini(2011)

7 AuthorYearMethodResults Demirli et al. 2010Fuzzy 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 8 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 9 possible causes Tool break 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 10 possible causes Gradual introduction of new raw- material Loosening fixtures Operator fatigue Machine tool wear Gauge wear Environmental changes

2.2 Non-random patterns Pattern 1OCLOne or more point falling beyond 3σ control limits 2FR1 4 out of 5 consecutive points fall beyond 1σ control limit on the same side of center line 3FR2 2 out of 3 consecutive points fall beyond 2σ control limit on the same side of center line 4Run Seven consecutive points fall on the same side of centerline 5Trend Seven consecutive points continuously increasing or decreasing 6Cycle Repetitive forms of patterns observed on the control chart over a period of time 7Instability Erratic zigzag patterns with points fluctuating up and down 11

2.3 Fuzzy inference system 12 Fuzzifi cation Inference Defuzzi fication Rule base Crisp value Zadeh(1965) Granulation capabilities Summarization information compression Zadeh(2008) 1. Quantifying the evidence from partially developed patterns 2. Combining evidence from different patterns to identify underlying causes

13 (Montgomery,2004)

Simulated data Generated control limits 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 Ranked Assignable cause Confirmed assinable cause Yes No Is the probability equal to 1? Created run rules 14 3.Research method Francisco Aparisi(2004) Demirliet al.(2010)

3.1Simulated data 15 This research parameter setting Quality characteristics(p)2 0.8 Magnitude of the process shifts (0,1) 、 (1,0) 、 (1,1) Sample number(m)30 Sample size (n)5

3.2Generated control limits 16 Francisco Aparisi(2004)

3.3Created 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 points Francisco Aparisi(2004) 17 R1 R2 R3

R2:two out of three consecutive points within the attention zone (zone A) 18 Crisp value R1R2R3R4 023 R3:eight consecutive points over the median (zone B). R4:seven consecutive rising points

3.5Fuzzy Inference System Ranked assignable causes Aggregation R1 R2 R3 R4 R1 R2 R3 R4 C1 C2 C3 Input value Input membership function Output membership function Output value FuzzificationInferenceDefuzzification Rule Based Rule base 19

4. Expected results 20 R1 R2 R3 R4 C1 C2 C3 Rank cause Fuzzy inference system Pattern Cause