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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. 1. Introduction. Common causes. Variation in a process. Control chart . Assignable causes. Control chart . Root Cause Analysis (RCA).

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Fuzzy Inference System Diagnose Assignable Cause Based on Hotelling’s Control Chart

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  1. Fuzzy Inference System Diagnose Assignable CauseBased on Hotelling’s Control Chart Graduate:Syuan-FongJhong Advisor: Jing-Er Chiu, Ph.D.

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

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

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

  5. 2. References review

  6. Alaeddini(2011)

  7. Demirlietal.(2010)

  8. 2.1 Assignable cause 1. Isolated causes one particular point falling outside the control limits

  9. 2. Shift cause produce a considerable shift in the process mean

  10. 3.Gradual cause change the process mean gradually over time

  11. 2.2 Non-random patterns

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

  13. 2.4 Hotelling’s (Montgomery,2004)

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

  15. 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)

  16. 3.2 Generated control limits • P(>CL|)=0.005 • P(>ZA|)=0.03 • P(>Median|)=0.5 Francisco Aparisi(2004)

  17. 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 points Francisco Aparisi(2004) R1 R2 R3

  18. 3.4 Monitored R4:seven consecutive rising points R3:eight consecutive points over the median (zone B). R2:two out of three consecutive points within the attention zone (zone A)

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

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

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