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Journal of Electrostatics 67 (2009) 297–300

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Journal of Electrostatics

journal homepage: www.elsevier .com/locate/e lstat

Increasing the reliability of risk assessment for systems endangered byelectrostatic discharges

Istvan Kiss*

Budapest University of Technology and Economics, Dept. of Electric Power Engineering, 18. Egry J. u., 1111 Budapest, Hungary

a r t i c l e i n f o

Article history:Received 16 September 2008Received in revised form21 November 2008Accepted 31 December 2008Available online 20 January 2009

Keywords:Risk assessmentReliabilityFault tree analysisFuzzy logicProbability values

* Tel.: þ36 1 463 2784; fax: þ36 1 463 3231.E-mail address: kiss.istvan@vet.bme.hu

0304-3886/$ – see front matter � 2009 Elsevier B.V.doi:10.1016/j.elstat.2008.12.009

a b s t r a c t

Risk assessment for systems endangered by electrostatic discharges is especially important in industrialelectrostatics. Different methods are widely used for the approximation of the risk. One of them is thefuzzy logic based fault tree analysis. The reliability of the calculated probability of the top event in thefault tree (in our case fire or explosion) strongly depends on the accuracy of the probability valuesconnected to the basic events. This paper deals with that problem, how the reliability of risk assessmentcan be increased by the application of a complex model for the determination of initial probabilities forthe basic events. A case study is analysed to overview reliability problems for risk assessment in such anindustrial process where risk of fire or explosion is present due to the electrostatic discharges.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Several papers were published before about the application offuzzy logic based fault tree analysis (FFTA) as a useful tool in theevaluation of risk arising from electrostatic discharge [1–4]. Inthese papers it was pointed out, how the uncertainties can behandled using this method and why it is advantageous in thecomparison of different solutions to increase safety. Most ofthe analysed examples were taken from the industry and themethod was applied for real, existing processes as well.

However in the analysed cases the probability values connectingto the basic events of the fault tree were often estimated ones,because of the lack of information or the nature of a certain event.In this paper we focus on that problem, how the probability valuesof the basic events can be determined more accurately increasingthe reliability of the FFTA. In general it can be said, that forimproving the accuracy of initial probability estimation the qualityof the knowledge base is necessary to be improved e.g. by collectingsignificant data of operation.

Our goal is to produce such a complex system for the riskanalysis that provides an interface for a user to give measuredresults of different parameters and different properties of theexamined process as the input of the system and calculates a risk

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value for fire or explosion. The structure of this model can be seenin Fig. 1. The model has three main parts, namely the pre-processorgenerating initial probability values for the basic events of fuzzyfault tree, the fault tree analyser and a risk calculator unit. Now thepaper is focused on the pre-processor.

2. Case study

There are several processes that are hazardous in the processindustry because of electrostatic discharge [5,6]. Experimentalstudies of these processes (e.g. [7]) are very important to obtaininformation for the knowledge base of a risk analysing system.However general information is necessary to apply for the certainspecific process to be analysed to obtain adequate data for theinitial values for the calculation of risk. For the illustration of theproblem such an industrial process was selected, where a workerwearing charge dissipating cloths, gloves and shoes pours powderfrom a metal can into a mixer. The mixer contains a given solvent –and its vapour of course – which has known ignition energy vs.concentration diagram, so its minimal ignition energy (MIE) isknown. The enclosure of the mixer is grounded metal; the metalcan is connected to the mixer by a wire. The simplified event tree ofthe process is represented in Fig. 2.

Assigning probability values to the event the fault tree is con-structed, while replacing simple probability values by triangularfuzzy membership functions (as it is illustrated in Fig. 3) and usingfuzzy logical operators for AND and OR relations the fuzzy fault tree

Fig. 3. Fuzzy membership function for the probability of an event.

Fig. 1. Structure of complex risk analyser model.

I. Kiss / Journal of Electrostatics 67 (2009) 297–300298

can be constructed. Table 1 shows the calculated values for differentevents.

3. Analysis of basic events

To determine the initial probability values (and their member-ship functions) it is necessary to analyse the basic events todetermine what kind of data can be used as a basis of calculationsand which parameters are influencing the reliability of these data.In the following analysis such data sets are taken into considerationthat can be typical in case of the examined process. The determi-nation of probability values for the basic events is detailed below.

3.1. Inflammable atmosphere

In the analysed case the flammable material is the vapour of thesolvent that can be mixed with the air when the mixer is opened.For the fault tree analysis the following simplification is made: we

Fig. 2. Simplified fault tree o

do not take into consideration the change of ignition energy asa function of solvent vapour concentration, we try to determine theprobability that the concentration is between the minimal andmaximal critical limit. Thus the probability of event ‘‘electrostaticdischarge’’ is p(Wdischarge>MIE). Therefore only those dischargesare interesting for us that have higher energy than the MIE of thevapour. In our simplified process this is practically the sparkbetween the worker or his tool and the mixer.

To determine, how often can be the actual solvent vapourconcentration in the critical zone, two main cases have to beseparated. First one is, when no inert gas is used, thus when theworker opens the inlet of the mixer, the solvent vapour can exitthe mixer. In this case measurement of the concentration as afunction of the time can give answer for the probability of thepresence of inflammable atmosphere during the operation. A set ofmeasurement makes it possible to estimate minimal and maximalvalues for the membership function. Without such information theinitial probability can be supposed to be 1 (worst case; that isapplied in our case study). Remark: in the fault tree the basic eventsare independent ones, presence of inflammable atmosphere isstochastical.

f the examined process.

Table 1Calculated results of the fuzzy fault tree.

No. of event Name of event Relation No. of event1 No. of event2 pmin pe pmax

1 Fire, explosion and 2 3 1.774E�05 7.684E�05 0.0003372 Electrostatic discharge and 4 5 1.774E�05 7.684E�05 0.0003373 Inflammable atmosphere basic event 1 1 14 Charging process and 6 7 0.54 0.665 0.95 High grounding resistance and 8 9 3.284E�05 0.0001156 0.0003746 Insulating dust basic event 0.6 0.7 0.97 Fast filling basic event 0.9 0.95 18 Ungrounded metal can basic event 0.0005 0.001 0.0029 No secondary grounding path or 10 11 0.0656863 0.11555 0.1871810 Insulating floor basic event 0.03 0.05 0.0811 No grounding path through the worker or 12 13 0.03679 0.069 0.116512 Insulating contact between the metal can and the worker and 14 15 0.007 0.02 0.0513 Insulating shoes basic event 0.03 0.05 0.0714 Insulating gloves basic event 0.1 0.2 0.2515 Insulating clothes basic event 0.07 0.1 0.2

I. Kiss / Journal of Electrostatics 67 (2009) 297–300 299

Significantly lower probability will be the initial value, whena certain safety measure like leading nitrogen into the mixer isapplied. In this case the initial probability will depend on thefrequency of malfunction of the safety system.

3.2. Shoes, gloves, cloths

In case of danger because of fire or explosion safety regulationsrequire to wear charge dissipating clothes, shoes and gloves. Inpractice the manufacturers guarantee, that their product fulfils thisrequirement, but it is useful to check some samples from time totime, because the quality of these products can be changed asa function of time (number of usage). According to our experience,unfortunately some ‘‘dedicated products’’ do not fulfil therequirements, in such case these products have to be replaced.

Theoretically for the calculation of probability that an object isinsulating, a simple selection problem that has to be solved.Assuming that the objects are divided into two groups, (first:Robject� Rcritical; second: Robject> Rcritical), that probability has to becalculated, that the object will be selected from the second group.

Assuming that the total number of objects (pair of shoes, pair ofgloves, set of clothes) is N and the number of object in the secondgroup is n, the probability value is obviously p¼ n/N.

Unfortunately the situation is not so simple. Usually the resis-tance values for all of the objects are not known, the member of thetwo groups has to be estimated according to the measurements ofa limited number of samples. Determination of Rcritical is alsointeresting. Fig. 4 shows the well-known simplified model fora charging process. According to that Rcrit¼Ubr/Ich depends on thebreakdown voltage of the spark gap Sg (Ubr) and the chargingcurrent (Ich). For a given process these parameters can be changingfrom time to time, so the information about that is uncertain. Mostof the standards supposes, that limits the voltage of the capacitor at100 V and the charging current supposed to has a maximum of10�4 A, thus Rcrit is assumed to be 106 U. Without further infor-mation, this limit can be used for the critical value.

In the case study pe was calculated at Rcrit¼ 106 U. Number ofpossible sets used by workers is supposed N¼ 20. Test result was

Fig. 4. Simplified model of charging.

assumed resulting in n¼ 4 for gloves, n¼ 1 for shoes and n¼ 2 forclothes. The pmin and pmax values of the fuzzy membership func-tions in the case study were determined by taking into consider-ation how many measurement results were nearly below or nearlyabove the critical limit.

3.3. Floor

Determination of probability of insulating floor has similarproblems, like it was found in the previous chapter. The onlydifference is, that in this case the possible areas where the workercan stay are the elements that has to be divided into the ‘‘abovecritical’’ and ‘‘not above critical’’ groups. For this purpose standardmeasurement of grounding resistance of floor is necessary to obtaindata for statistical evaluation.

In the case study critical limit was 106 U. Assumed inputparameters consist of grounding resistance values measured in 20points at 5 different times. 92% of measured values was below thelimit, 3% was significantly above, 2% was very near to the criticallimit.

3.4. Insulating dust and filling velocity

The two main parameters influencing the charging level.Determination of critical limit for the two parameters is not inde-pendent, however events that the first or second one exceeds thelimit are independent ones. To obtain critical values a set ofmeasurement has to be made. For the specific resistance a set ofsamples is necessary to obtain information about the possiblelimits. Pouring velocity usually situated in certain limits, dependingon dust property (e.g. are the particles stick together or not.)

In the case study we assumed that measurement results madeon 50 samples are known. Specific resistance of 30 samples weresignificantly above 106 U m, 5 samples had significantly lowerresult than this value and 15 samples had a specific resistance ofnearly 106 U m. During the filling electric field intensity near thedust exceeded 100 V/m in 9 cases out of 10. In the remaining casethe measured value was near the limit.

3.5. Grounding of metal can

Usually the problem is that workers forget the grounding, seechapter ‘‘Human factor’’ for details. Other possible problems can bethe corrosion of contacts, damage of connection points or con-necting wire. Regarding, that this is the primary grounding path, itsinitial probability has a significant influence on the top event.During the estimation of the initial probability of this event several

I. Kiss / Journal of Electrostatics 67 (2009) 297–300300

factors has to be taken into consideration, like material of can,contacts, wire, humidity or other materials causing corrosion, etc.In the case study 0.0005, 0.001 and 0.002 was assumed for pmin, pe

and pmax respectively.

3.6. Relative humidity

Comparing the FFTA in Fig. 2 to FFTAs published previously,a very important difference can be seen: the effect of relativehumidity is not declared as a basic event. However its effect is takeninto consideration, it modifies practically all the probability valuesdecreasing the resistance values for gloves, floors, etc. For thismodification the dependence of the previous quantities on therelative humidity has to be known or estimated. Taking intoaccount the effect of humidity there is a significant differencebetween air conditioned and not air conditioned rooms. In the firstcase change of humidity is mainly connected to the malfunction ofair conditioner, while in the other case it can change stochastically.Practically in the latter case ‘‘wider’’ membership functions will beassigned to the basic events, meaning that the reliability of initialprobability value is decreased.

To illustrate the effect of relative humidity on the results, itsvalue has been increased from 30% to 50%. If the humidity had nosignificant effect on event 8 (main reason of grounding failure washuman error), the calculation result for the top event in this case ispmin¼ 1.27�10�5, pe¼ 5.8� 10�5 and pmax¼ 2�10�4, thus theprobability of the top event decreased. If the increase of humidityincreases the initial probability of event 8 (assumption, justto illustrate its effect), probability of top event can be slightlyincreased: pmin¼ 1.8� 10�5, pe¼ 8.2�10�5 and pmax¼ 2.7�10�4.

3.7. The human factor

In the previous calculations membership function for theprobabilities of the basic events was calculated based onmeasurement result, statistical data etc. But there is one importantfactor which can modify practically all initial probability of thebasic events and that is the human factor. Sometimes it occurs, thatthe worker does not wear charge dissipating cloth, shoes, gloves,does not connects the metal can to the ground, etc. According toour experience behaviour of the worker strongly depends on theeducation: when the worker knows the danger caused by theelectrostatic discharge, he/she is more careful during a certainprocess and does not take safety regulations easy.

(Remark that in some cases the handbook of the operation – theworker must follow the steps involved in it – did not contain thesafety requirements!)

Estimation of the effect of human factor on the initial probabilityvalues (or membership functions) is a very difficult task. It is usefulto evaluate the educational program, management of humanresources and safety regulations of a given company to predict howoften it can occur that a worker will be against the safety rules.

4. Calculation of risk

Fault tree analysis provides probability value for the top event,so its average frequency can be estimated. To calculate risk, this

probability value has to be multiplied by a weighting factor c, the socalled relative cost, that is a ratio of the damage caused by the fireor explosion and a reference cost (usually the total possible cost ofa damage), similarly to the method presented in [8].

Although in the paper we focused on the input part of the riskassessment, it has to be underlined, that cost estimation itself isa complex task. The actual cost of damage is influenced by severalfactors, the presence of the worker, the extend of the flame, theeffectiveness of protective clothes, the amount of vapour ignited,the diameter of the loading manhole, the volume of the mixer, thefree space inside the mixer, etc. Cost of destroyed material,economical loss because the stop of production, social and legalconsequences also has to be taken into consideration.

It is possible that in a certain process different type of dischargeswith different energy can appear, causing different consequences.In this case separate fault trees can be constructed for each type ofdischarges. Assigning the probabilities of top events by pe1, pe2, .,pen and the relative costs by c1, c2, ., cn the weighted probabilitiesare w1¼ pe1c1, ., wn¼ pencn. Regarding, that a certain number ofbasic event can be the same in the different fault trees, the weightedprobabilities are not independent from each other, thereforea resultant weighting factor can be determined by subtracting theproduct of their complements from 1, thus w¼ 1�P(1�wi),i¼ 1.n. This value can be used to determine the resultantfrequency of damage and calculate risk for a given period [8].

5. Conclusion

Reliability of the probability values connected to the basicevents strongly influences the reliability of probability assigned tothe top event predicting its relative frequency. In a complex riskassessment process it is necessary to create such a module thatdetermines the initial probability values for basic events. To takeinto consideration the reliability of input data, use of fuzzymembership functions is important.

Acknowledgements

Author thanks for the financial support of National Office forResearch and Technology in the program of Hungarian ScientificResearch Found (OTKA, project 68756 F).

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