FUZZY METHOD FOR FAILURE CRITICALITY ANALYSIS

Journal of Shanghai Jiaotong Univcrsity , Vol. E-5,No. 2,2000,38~11Article ID: 1007- 1172(2000)02 0038-04FUZZY METHOD FOR FAILURE CRITICALITY ANALYSIS ,HUANG Hong-zhong (黄洪钟), XU Lei (须雷)，HU Zhong wu (胡宗武)(School of Mechanical Eng. , Shanghai Jiaotong Univ. . Shanghai 200030，China)Abstract: The greatest benefit is realized from failure mode，efect and criticality analysis (FMECA) when itis donc carly in the design phase and tracks product changes as they evolve; design changes can then be mademore economically than if the problems are discovered after the design has been completed. However, whenthe discovered design flaws must be prioritized for corrective actions. precise information ou their probabilityof occurrence. the effect of the failure ，and their detectability often are not availabe. To solve this problem.this paper described a new method, based on fuzzy sets, for prioritizing failures for corrective actions in aFMCEA. Its successful application to the container crane shows that the proposed method is both reasonableand practical.Key words; failure ; safety; criticality analysis ; container crane ; fuzzy se1sDocument code:AFMECA is an analysis method which classifiesIntroductioneach item failure according to the severity of itsFailure mode， effect and criticality analysisconsequence and the probability of its occur-(FMECA) is a design methodology which putsrence. It has the following objcctives: ①toforward preventive and corrective methods thateliminate those failure modes with high criticali-may be taken to improve the reliability of prod-ty as far as possible;②to reducc as far as possi-ucts through the analysis of the various potentialble probability of occurrence of failure modesfailure modes of the different components of thewith high criticality in design， manufacture,system，their influence on the system and themaintenance, etc. when it is impossible to elimi-severity of their consequences in system design.nate those failure modes; 3 10 add protectiveFMECA is suitable for the study of the influencedevices，monitoring warning devices to the com-of the failure of system components on the sys-ponents or products according to their differenttem and can be used in different technologicalcriticality.process. What's more, as it does not requireprofound knowledge of mathematics, it is easyThere are many ways 10 calculate failure critical-to master and hence very practical. With allty. We can use, for example, the risk prioritythese advantages, now FMECA is not onlynumber (RPN) and criticality number (CN). Aswidely used in the aerospace but also applied tofor mechanical products, because of the lack ofautomotive, mechanical. nuclear, and medicalthe basic data for reliability analysis, the RPN isoften used. Its calculation formula is as follows :technologies industries.The failure criticality analysis (FCA) o[ the中国煤化工: failure mode (PReceived date: 1999-05-06:MYHCNMHGsisthesveriyFoundation item: National Natural Science Foundation ofof the failure mode, D is the detectability of theChina under the Contract Number:59475043.failure mode.FU2ZY METHOD FOR FAILURE CRITICALITY ANALYSIS39It is quite difficult to get a definite value consid- have a corresponding value co, then C= {c,Cz,ering the fact that there is much fuzziness in the...,c}.assessment of P. S and D, for cxample, to as-Tab. 1 Frequency of ocurrence of failure modesess S, the consequence or severity of failure(Factor 4n)must involve factors such as the casualties of theElement of gradeGradeMembership degreeworking personnel or the public ，the equipmentset础.losses and its consequent economic losses bothRemotc1~20. 7.20.9dircct and indirect. In view of this, we applyModerate5~60.50.7l 0.5fuxy sets to the FCA and present a new methodHigh7~80..7 0.8for FCA.Very high9~ 101 Fuzzy Comprehensive EvaluationTab.2 Severily of failure mode (Factor u2)Model of FCA[1~4]Membership degree 咄set喝2341.1 To Form Factor Set U and Factor Grade0.1~1.1 0.5Set 4;1.1~3 0.2 0.7 0.6 IThe set of three factors u,(i= 1,2,3) which3.1~6affect failure criticality is denoted by6.1~100.7_ 0.8 0.1U = {U,Uz,Uz}Tab.3 Detectability of failure mode (Factor uz)where u1 is the frequency of failure mode, u2 theseverity of failure mode, us the detectability ofMembership degree喝set 嘴failure mode.2~30.2 0.4 0.1 0.2The conditions of the factors in the factor set can0.4 0.7be defined as“high, relatively high, medium,7~g0.8 0.6 0.8 1relatively low, low". This set is called factorNon detection1grade set and the factor grade set of lth failureTab.4 The criticality levelmode can be expressed asu,”= (u,”,u" ,.u".Elernent of evaluation set动Value oVery lowDue to the fuzziness of each factor and its corre-Lowsponding grade, it is difficult to determine whichRelatively lowgrade a certain factor belongs to. Thus the fac-tor should be regarded as a fuzzy set of the gradeRelatively highuniverse of discourse u, namely_1u,"= {"," ,...“where 0≤J°≤1 is the membership degree of 1. 3 First Stage Fuzzy Comprehensive Evaluajth grade of ith factor.tionThe three factors which influence failure critical-Suppose we need to evaluate a certain conditionity and their corresponding grade sets are shownby the jth grade of the ith factor, and the mem-bership degree of kth element in the evaluationin Tabs. 1,2 and 3 respectively.1.2 To Form the Evaluation Set Vset isa中国煤化工the variousThe evaluation set V= wv1+1e.",7z} isa set ofgrades:YTHCNMH Gthe various possible evaluation results vxobatinedby ssessing the criticality level of failure mode,and forms a matrix with the elements of all thewhose factors are shown in Tab. 4. Let each Uk grade evaluation sets as follows :40.. HUANG Hong xhong (黄洪钟)，XU Lei (须雷)et al .follows :B()= w●A=A,"=2 a2..a,::...:(w1,Wz,w3).b唱b磁...唱=A."”is called the grade evaluation matrix of the(b"b2.础」ith factor.(b" ,6”,.")Normalization of the membership degree , bywhere:b"= 2 w,bl;"; W is the factor weightthe jth grade of the ith factor can be done byset, the element w, indicates the importance ofw"="/乙哨the role played by the factor u, in the evaluation.The elements satisfyAssume w," as the weight of this grade, thenthe grade weight set of the ith factors is之w=1W!" = (w;" ,w{? , ,w[)b, is the membership degree of the condition ofSo，by fuzzy transformation， the first stagethe kth element in the evaluation set when allfuzzy comprehensive evaluation set can be ob-factors are taken into account.tained from1.5 Criticality AssessmentB"=W!".A,"=Let b;") be weight, and make the weighted mean[al2..a]of co, then the criticality of lth failure mode is asu(l2au12... al2follows:(wv," ,w:" ,... ,w(")::.:C“=之”叫它b.”u, a... a:2」(b;"? ,bw".-,b")2 Examplewhere: b2 = 2 wu,"ui}2; which forms a matrixThe container crane model CHT12 is shown in .with b; as follows:Fig.1 and taken as an example to describe its[b"? b昭criticality assessment. The typical failure modes|b吆b唱.b唱of the container crane are listed in Tab. 5. Themembership degree of grades of factors affecting(B"」criticality of failure mode is shown in Tabs. 1, 2A“is called the first stage fuzzy comprehensiveand 3 respectively.evaluation matrix.1.4 Second Stage Fuzzy Comprehensive Evalua-The first stage fuzzy comprehensive evaluationset B"” includes the contributions of variousgrades and reflects the influence of one factor,so matrix A“may be regarded as a single-factorevaluation set for the second stage fuzzy compre-hensive evaluation.中国煤化工e ]To carry out the second stage fuzzy comprehen-YHCNMHsive evaluation by all the influencing factors, thesecond stage comprehensive evaluation set B“Fig.1 Container crane model CHT12can be obtained through fuzzy transformation asFUZZY METHOD FOR FAILURE CRITICALITY ANALYSIS10.6 0.3 0.100Tab.5 Typical failure modes of container craneA%=0.610.60.30.100Number: F ailure modeiote0.30.610.60.30.10OverlurningBesides overload front over-l0.1 0.3 0.6 1 0.6 0.3 0.1turning,From the statistics, the weight allocation of thefront-overturning and side-factors isoverturning. It is a serious fail -W = (0.3.0.4,0. 3)2 Fracture of the main This is usually prevented byTake C={1,2,3,5,7,9,10}，thenstructural component defectocopy and 25% or 10%C.(1) = 8.2,C*(2)= 5.4,C*(2) = 7.6,C*<>= 4.6overload tests. It is a seriourfailure.3 Conclusion3 Falling down of the The container crane takes holdcontainers becauseof the container automaticallyIt is known from the calculated results aboveof misoperationby its spreader and this opera-that C'>C*4)>C*8>>C*4 it is the over-tion is dfficult and complcat-turning of container crane and falling down ofed. This failure is serous.container due to misoperation that are the mostOi- leakage due to the This is the most common fail-important failure modes of the container crane.damage of the seal of ure mode for construction ma-the hydraulic system chinery and equipment,They require special attention and must beamounting to over 70% of allavoided. In view of this, the following measureskinds of failures.are taken in the design of the container cranemodel CHT12:①Raise steadiness margin. ②The grade evaluation matrixes for the factors areProvide the container crane with a safety deviceas follows :to avoid overturning. ③Adopt an interlockingA=A9= AI"=A"=A49?=A]"=device to remove the hidden danger of unlocking「1).8 0.6 0.3 0.1 0 07and hence the falling down of containers due to0.810.80.60.30.1(misoperation.0.3 0.6 0.8 1 0.8 0.6 0.3).1 0.3 0.7 0.9 1 0.9References :0) 0.1 0.3 0.6 0.8 1」[I] Huang H Z. Reliability evaluation of a hydraulicA"=A= AS=ruck crane using field data with fuzziness [J]「10.80.60.30.100Microeletronics and Reliability, 1996， 36 (10);1531~1536.0.1 0.4 0.8 1 0.8 0.4 0.12] Bowles J B, Bonnell R D. Failure mode and effect00.10.30.60.810.9analysis [A]. Ann Reliab & Maint Symp 1995 Tu-0.10.30.50.70.91Jtorial Notes [C]. Washington DC, USA. 1995.A{=A$°=[3] Zadeh L. A. Fuzzy sets []. Information and Con-).6 0.3 0.1 00 0]trol, 1965. 8:338~ 353.0.7 0.4 0.1 000I[4] Zadeh I. A. The concept of a linguistic variable0.810.60.30.100|and application to approxinate reasoning-Part I0.80.910.60.30.10[J]. Inf Sci, 1975, 8:199~249;Part 1 , Inf Sci,8:301~357; Part 1. Inf Sci, 1975. 9:43~80. .l0.5 0.6 0.8 1 0.6 0.1 0]中国煤化工MHCNMH G .