an alternative evaluation of fmea: fuzzy art

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AN ALTERNATIVE AN ALTERNATIVE EVALUATION OF FMEA: EVALUATION OF FMEA: FUZZY ART ALGORITHMFUZZY ART ALGORITHM

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OutlineOutline

IntroductionIntroductionFailure Mode and Effects Analysis (FMEA)Failure Mode and Effects Analysis (FMEA)Adaptive Resonance Theory (ART)Adaptive Resonance Theory (ART)Fuzzy Adaptive Resonance Theory (Fuzzy Fuzzy Adaptive Resonance Theory (Fuzzy

ART) ART) Computational ExperimentComputational ExperimentResults Results Conclusion and DiscussionConclusion and Discussion

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IntroductionIntroduction

TThe he traditional FMEAtraditional FMEA has many has many shortcomingsshortcomings..

This study describes an alternative This study describes an alternative algorithm for evaluating Risk Priority algorithm for evaluating Risk Priority Number of Failure Mode and Effect Number of Failure Mode and Effect Analysis.Analysis.

Introduction Failure Mode and Effects Analysis (FMEA) Adaptive Resonance Theory (ART) Fuzzy Adaptive Resonance Theory (Fuzzy

ART)

Computational Experiment Results Conclusion and Discussion

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Failure Mode and EffectFailure Mode and Effectss Analysis Analysis

The FMEA method is based on brainstorming for The FMEA method is based on brainstorming for the failures that might occur the failures that might occur

TThree indices have been used: hree indices have been used: OOccurence (O) , ccurence (O) , SSeverity (S) and everity (S) and DDetection (D) etection (D)

The product of the three indices gives a risk The product of the three indices gives a risk degree, known as risk priority number (RPN). degree, known as risk priority number (RPN).

Introduction Failure Mode and Effects Analysis

(FMEA) Adaptive Resonance Theory (ART) Fuzzy Adaptive Resonance Theory (Fuzzy

ART)


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ShortcomingsShortcomings of FMEA of FMEAAt the classical FMEA method;At the classical FMEA method; One of the shortcomings of FMEA method is about grading One of the shortcomings of FMEA method is about grading The failure modes over the threshold value are improved. This situation increases The failure modes over the threshold value are improved. This situation increases

the cost. the cost. RPN = 5 X 5 X 5 RPN = 5 X 5 X 5 isis improved but RPN = 8 X 1 X 10 improved but RPN = 8 X 1 X 10 is notis not considered. considered. The condition assigning to (S, O, D) indexes the values (8, 1, 1) are considered at the The condition assigning to (S, O, D) indexes the values (8, 1, 1) are considered at the

same level as (2, 2, 2). same level as (2, 2, 2). Both situations determine an RPN= 8. Both situations determine an RPN= 8. S, O and D values are evaluated by multiplying each other. So three risk factor’s S, O and D values are evaluated by multiplying each other. So three risk factor’s

importance importance isis disappeared. disappeared. The traditional FMEA is that various sets of S, O and D may produce an identical The traditional FMEA is that various sets of S, O and D may produce an identical

value of RPNvalue of RPN For example, a RPN equal to 64 may be obtained from 10 different combinations of For example, a RPN equal to 64 may be obtained from 10 different combinations of

the S, O, and D indices. the S, O, and D indices. Some numbers between 1 and 1000 cannot be obtained from the product of three Some numbers between 1 and 1000 cannot be obtained from the product of three

numbers, for example, 11, 22, 33 . . . . . 990numbers, for example, 11, 22, 33 . . . . . 990

Introduction Failure Mode and Effects Analysis

(FMEA) Adaptive Resonance Theory (ART) Fuzzy Adaptive Resonance Theory (Fuzzy

ART)


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Adaptive Resonance TheoryAdaptive Resonance Theory

Adaptive Resonance Theory (ART) was developed Adaptive Resonance Theory (ART) was developed by Grossberg (1976)by Grossberg (1976)

Input vectors which are close to each other according Input vectors which are close to each other according to a specific similarity measure should be mapped to to a specific similarity measure should be mapped to the same clusterthe same cluster

ART adapts itself by storing input patterns, and tries ART adapts itself by storing input patterns, and tries to match best the input pattern to match best the input pattern


ART)


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ART clustering algorithmsART clustering algorithms ART1ART1 ART2ART2 ART3ART3 ARTMAP ARTMAP Fuzzy ARTFuzzy ART


ART)


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Fuzzy ART ModelingFuzzy ART Modeling


ART)


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Fuzzy ARTFuzzy ART

LayerLayer 1 1 consists of neurons that are consists of neurons that are connected to the neurons in connected to the neurons in LLayerayer 2 2 through through weight vectors.weight vectors.

TheThe number of neurons in number of neurons in Layer 1Layer 1 depends depends on the characteristics of the input data.on the characteristics of the input data.

The Layer 2 represent clusters.The Layer 2 represent clusters.


ART)


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Fuzzy ART Architecture Fuzzy ART Architecture


ART)


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Fuzzy ART FMEAFuzzy ART FMEA

FMEA values are evaluated separately with FMEA values are evaluated separately with severity, detection and occurrence valuesseverity, detection and occurrence values

TThe aim is to apply Fuzzy ART algorithm to he aim is to apply Fuzzy ART algorithm to FMEA method and by performing FMEA on FMEA method and by performing FMEA on test problems, most favorable parameter test problems, most favorable parameter combinations (α , β and ρ) are investigated.combinations (α , β and ρ) are investigated.


ART)


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Computational ExperimentComputational Experiment

AA non-binarynon-binarydataset of FMEA isdataset of FMEA isused to evaluate theused to evaluate theperformance of theperformance of theFuzzy ART neuralFuzzy ART neural network on differentnetwork on different test problemstest problems

Introduction Failure Mode and Effects Analysis (FMEA) Adaptive Resonance Theory (ART) Fuzzy Adaptive Resonance Theory (Fuzzy ART)


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For aFor a comprehensivecomprehensiveanalysis of the effectsanalysis of the effects of parameters on theof parameters on the performance of Fuzzyperformance of Fuzzy ART in FMEA case, aART in FMEA case, anumber of levels ofnumber of levels of parameters areparameters are considered.considered.



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The Fuzzy ART neural network method is applied The Fuzzy ART neural network method is applied to determine the most favorable parameter (α, β to determine the most favorable parameter (α, β and ρ) combinations during application of FMEA and ρ) combinations during application of FMEA on test problemson test problems



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ResultsResults

For any test problem 900 solutions are obtained. For any test problem 900 solutions are obtained. The β-ρ interactions for parameter combinations The β-ρ interactions for parameter combinations

are considered where solutions are obtained. are considered where solutions are obtained. For each test problem, all the combinations are For each test problem, all the combinations are evaluated and frequency distribution of clusters evaluated and frequency distribution of clusters are constitutedare constituted



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ResultsResults

For example, for testFor example, for test problem 1, four groupsproblem 1, four groups which consist the 70% ofwhich consist the 70% of combinations arecombinations are s selected,elected, cluster numbers thatcluster numbers that contains minimum 80% ofcontains minimum 80% of the all combinations arethe all combinations are determined according todetermined according to the results of paretothe results of pareto analysis. These are groupsanalysis. These are groups 2-3 and 42-3 and 4



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ResultsResults

Parameter combinations, Parameter combinations, β-ρ interactions and the β-ρ interactions and the number of α parameters number of α parameters in any combination of β in any combination of β and ρ, is shown at the and ρ, is shown at the sideside.. Favorable solutions Favorable solutions are marked as bold and are marked as bold and italicitalic



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ResultsResults Number of cluster increases with the increase in ρ.Number of cluster increases with the increase in ρ. Number of cluster increases with the increase in β.Number of cluster increases with the increase in β. Clustering of the data in most problems depends on Clustering of the data in most problems depends on

the interaction between the β and ρ parameters. α the interaction between the β and ρ parameters. α parameter has no effect on solution in small scaled parameter has no effect on solution in small scaled problems, but in large scale problems, effect of α turns problems, but in large scale problems, effect of α turns to an irregular state to an irregular state

Also with the increase in problem scale, the change in Also with the increase in problem scale, the change in number of clusters is defined. number of clusters is defined.



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ResultsResults

In FMEA test problems, In FMEA test problems, which determine most which determine most favorable parameter favorable parameter combinations, βcombinations, β -- ρ ρ interactions providing interactions providing appropriate cluster numbers appropriate cluster numbers are noted on the summary are noted on the summary table that evaluates each table that evaluates each test problem separately. The test problem separately. The values involve favorable βvalues involve favorable β -- ρ combinations are marked ρ combinations are marked with the blue areawith the blue area.. This is a This is a suitable solution area for suitable solution area for FMEA problem. FMEA problem.



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Conclusion and DiscussionConclusion and Discussion Fuzzy ART neural network is applied to FMEA Fuzzy ART neural network is applied to FMEA Appropriate parameter intervals are investigated for giving Appropriate parameter intervals are investigated for giving

successful results of Fuzzy ART in FMEA problems. successful results of Fuzzy ART in FMEA problems. The investigations show us, if input number is smaller than or The investigations show us, if input number is smaller than or

equal to 30, FMEA problem is defined as small scale, equal to 30, FMEA problem is defined as small scale, otherwise it is large scale. otherwise it is large scale.

We suggest that cluster numbers should be determined We suggest that cluster numbers should be determined between 2 and 6 at small scale problems for practical studies.between 2 and 6 at small scale problems for practical studies.

Cluster numbers of large scale problems should be maximum Cluster numbers of large scale problems should be maximum 1212 for practical studies. for practical studies.



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Conclusion and DiscussionConclusion and Discussion

Determinations about α:Determinations about α: In small scale problems, alfa increases cluster number only if β is In small scale problems, alfa increases cluster number only if β is

greater than or equal to 0.8. In other conditions, it is observed that α greater than or equal to 0.8. In other conditions, it is observed that α values have no effect on solution. values have no effect on solution.

In large scale problems, appropriate interval cannot be determined In large scale problems, appropriate interval cannot be determined because the effect of α becomes irregularbecause the effect of α becomes irregular

Determinations about β:Determinations about β: For both small and large scale problems, number of cluster For both small and large scale problems, number of cluster

increases with the increase in β. increases with the increase in β. Determinations about ρ:Determinations about ρ: For both small and large scale problems, number of cluster For both small and large scale problems, number of cluster

increases with the increase in ρ. increases with the increase in ρ.



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Conclusion and DiscussionConclusion and Discussion

For small and large scale problems in FMEA, Fuzzy ART For small and large scale problems in FMEA, Fuzzy ART algorithm is fast, effective and easy to implement. algorithm is fast, effective and easy to implement. Parameter combinations are acquired where the best Parameter combinations are acquired where the best solution is obtained for non-binary problems. solution is obtained for non-binary problems.



an alternative evaluation of fmea: fuzzy art

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