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l . ' e ~ s e ts en d ~ e m 2 8 0 9 8 8) ~ 5 - ~ 2 7N o a h - H o l e d 115

C A S E S T U D Y~ J Z Z Y I t U M A N ] ~ E L ~ I ~ I L I T Y A ~ ~ Y b ~ S O NC H ~ I ~ O B ~ . , A C C ~ E ~T a k e l ~ a O I ~ S A W A Deparanen~o f Bae~ Engineering gum am oto Un iverse 2-3~.I g u r o ~ , g u n m m . o t o , 860apanY a s u sh i N I S H I W A K I iDivision o f NuclearS a ~ y Intern~tiondAtomic Enem y Ag ency, A.1400, V~enna,Aus~iaReceived M ay 1987

~ ~fR ~ v ~ d A u s m t |.~8~A ~ a c I : Th is pa pe r c om par es th e result ~f ~u zzy reliability analysis using er~o~ po~ibi~i~ l, wi~htha t of p r o b a t e an~ys i~ , on the a ~ d e a t a~ ~he C~em obyl nuc lear pow er p lea t . T~ c.a~es tudy shows tha t fuzzy r~ |~b ~tv ane tys ls ~ ives ~fonn~f ion f rom mo re poin ts o f v iev~ thanproba b~sfi analysis.Keywords: Human reHab~ty ana lym; e r ror po~ib~i ty ; e r ror probab~ty; the Cheta tobylaccident. /

1 . b t ~ i ~ t o nThe wors t nuc lear - reac tor acc iden t to da te occur red a t the four th un i t o f theCh eraoby l nu c lear pow er s t a t ion in the Uk ra ine , Soviet UnioI l~ On Apr i l 26 in

1 9 8 6 . L a r g e a m o u n t s o f t h e r a d i o a c t i v e m a t e r i a l s i n t h e r e a c t o r ~ r e w e r e s p r e a don a g loba l sca le . The acc iden t happened dur ing a t es t be ing car r i ed ou t on aturbogenera tor a t the t ime of a normal scheduled shu tdown of the r eac tor . Thi swas in t~ded ~o t es t the aL2i ty of the tu rbog encra to r , dur ing the s t a tion b lackout ,to supply e lec t f i c~ energy for a shor t per iod un t~ the s t andby d iese l genera tor scould supply em ergency pow er . The m ain cause of the acc iden t was an imp roperw r i t t e n t e s t p r o c e d u r e f r o m s a f e t y p o i n t o f v i e w a n d s e r i o u s v i o | a t i o n s o f b a s i cope r a t i ng ~ e s by t he ope r a t o r s [2 , 5 ]. A p r e |~ n a r y anal ys is O f t he C he r noby la c c i d e n t h a s b e e n p e r f o r m e d [ I ] o n t h e b a s i s o f t h e. p r o b a b i l is t ic m e t h o d o fhum an re li ab il ity ana lysi s p ropo sed by Swa~a and Gu t tman n [4].Onisawa has proposed e r ror poss ib i l i ty ins tead of human er ror p robabi l i ty inhu m an rel iabi l ity analys is and shown th e val idity of the pro po sed ~alc ,~od [3] .This possib il ity i s expressed by a f ~ V se t on the in te rva l [0 , I ] .In this pa pe r an analys is o f t i~e Ch ernob yl a ccident i s performe l by us i~g er rorpossib il ity and the r esu l t o f the ~a lys i s i s com pared w i th the r esu l t o f p robabi l is t icana lys i s .0165-0114/88/$3.50 (~) 1988, E |s e~ er Science Publishers B.V . (N orth-Holland)

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116 F. Onisawa . Nis~i~e~2 . P m b a b l i h ~ ~ o f th e C h e ~ b y | ~ ~ e ~ t [1]

Out l ines of the probabi l i s t ic analysis by Hu and Zhang are f i r s t in t roduced inthis sect ion.2.1. T h r e e ~ u m p t i o n s

B ef ~ the anelysis the fo l lowing gs assum ed.( I ) On ly hum an e r ro r s a r e cons ide red fo r d i scuss ion . ~11 nuc lea r power p l an tperson nel ac t in a m ann er they bel ieve to b e in the be~t in terests of the p iant .( 2) Th e d i s f u n ~ o n o f t h e sy s te m r e s~d t s f ro m h u m a n e r ro r s . A n i n h e r e n tdefect o f the system is not co nsidered in ~zis analysis .(3 ) T he opera t ion c r ew a re depen den t on each o th e r comple te ly .2.2. Task analys is

According to the above-ment ioned assumpt ions and a repor t p~ 'esented byUSSR exper t s [5 ] , s ix l i nks o f human e r ro r s a r e d r awn ou t . They con t r ibu ted tothe accident as fol lows:A: Dur inig the r educ t ion o f r eac to r power , t he o pera to r d id no t en te r a ' ho ldpower ' r eques t a t t he r equ i r ed l eve l i n t r ans fe r r ing un i t power con t ro l f rom thel o ~ to the g loba l au to -r egu la t ing sys t em, so tha t t he r eac to r pow er r an d ownr ap i dl y t o 3 0 M W i n s te a d o f t h e h o p e d - fo r t ar g e t l ev e l o f 7 0 0 - 1 ~ MW .B : Af te r the r ea c to r f el l i n to the ' i od ine we l l' , the o pera to r wi thdrew ma ny o fthe con t ro l r ods , wi th the mot ive o f conduc ting the t e s t p rogram , to r e t r i eve the

pow er to 200 M W , desp i t e it be ing fo rb idden to op era t e the r eac to r a t such lowlevel by normal safe ty procedure .C : U n d e r t h e l o w p o w e r o p e r a ti o n a l c o n ~ t i o n , in m e e t i n g th e r e q u i r e m e n t s o fth e p l a n n e d t e s t tw o s ta n d b y m a i n cir c~ fla tio n p u m p s w e r e c o n n e c te d to th e c o r ewhich resul ted in v io la t ing the tLienno-hydraul ic balance in the core ~oolantsystem a ud som e indiv idual pu m p discharges exce eding the permi~.sib l ~ levelsspe~f i ed in the r egu la t ion . Th i s opera t iona l mode was a v io la t io l o f no rmals ta t ion procedures .D: L1 o rder to co n t inue the t e s t wi thou t in te r rup t ion , t he opera to r o lock~d tLe

trip signals ggso ciated with steamdrun~ w ate r ~v el an d pre ssu re re:::~ardi~ss th eens t~b]~ r eac to r con ~t io n . Hen ce the r eac to r p ro tec t ion sys tem t r iggered by he a tt ransfer param eters w as complete ly cut off .E : Th e o p e r a t o r r e g u la t e d t h e s t e ~ n - ~ l ev e l w i t h d iffic ulty b y m e a n s o fra is ing the feedwater f low ( there i s no such funct ion in the design of thes t e a n l ~ ) f or s t a b ' ~ n g t he p r u s s i c a n d w a t er le v el in t h e d ru m a n d c re a ti ngthe adeq ua te cond i t ion to beg in the t e s t . M eanwhi l e , more con t ro l rods had to bew/ thdrawn to com pensa te the nega t ive r eac tiv ity in t roduced by the above ac t ion .A t tha t t ime , th e num ber o f the c on t rd rods r emain ing in the co re was f a r le sst h a n t h e m i n ~ a | n u m b e r a c c o rd in g t o t h e s a f et y p r in c ip le .F : lIn o rde r to be ab le to r epea t t he t e s t ff necessa ry , t he op era to r b locked thereac to r p ro tec t ion sys t em re ly ing on shu t -down s igna ls f rom bo th tu rbo-genera to r s . Consequen t ly , t he l a s t poss ib i l i t y o f au tomat i c shu tdown o f thereacto r was lost .

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uzz y hum an reliability analysis 117In the v iew of hum an re li ab il ity ana lysi s, am ong these hum an er ror s , A

b e l o n g s t o a n e r r o r o f o m i t t in g a s t e p in a t a s k ; w h i le t h e o t h e r s b e l o n g t o e r r o r sof adm ini st r a tive cont ro l due to the ope ra tor s neg lec t ing and v io la t ing the safe typ r i nc i p l e s and ope r a t i ng p r ocedu r es . T he human pe r f o r mance mode l s and t hehuman er ror p robabi l i t i es on average indus t r i a l condi t ions a re shown in Table1 1 4 12.3. D evelopm ent o f hur~mn reliability a n a l y s i s vent t r e e

A b r a n c h o f t h e e v e n t t r e e i s d e v e l o p e d i n t h e o r d er o f t h e a c c i d e n t p r o c e s s a sshown in F igu re 1 . Her e ca p i ta l le t t e r s r eprese n t f a ilu re and smal l ones r epre sen ts u c c e s s .2 4 f f e c t f the perfomum ce shapingf a c t o r

Accord ing to [4] and the i r judgement , the dependence be tween the ac t ions i sassum ed as shown in Figu re 2(b) . Howeve~ in accord~nce wi th the ba ckgro und ofthe Ch em oby l acc ident , the fo llowing s i tua t ions a re cons idered .(1) Chem ob yl Uni t Fou r used to be a f lag- sh ip un i t in the na t iona l r eac torl ine because of i ts p rev ious good o pera t ing record . T he un i t s ta f f took par t in theinnovat ion t es t M th grea t en thus iasm; a s imi la r t es t had a l r eady bee n car r i ed ou tbut f a i l ed to meet the r equi red t a rge t and , what i s more , i t was no t easy toa r r a n g e s u c h a t e s t o n th e o p e r a t i n g p l a n t ; s o th a t i t b e c a m e th e i n t e n s i v em o t i v a t i o n s o f t h e s ta f f t o c o m p l e t e t h e t e s t w i th a l l e f fo r ts b e f o r e M a y D a y ' .

T a b l e 1 . H u m a n p e r fo r m a n c e m o d e l sI t em Hu ma n er ror s and hum an er ro r p robab i l it i es1 Om it t ing a s tep or an imp or tant ~ns truct ion f rom a forma l or adhoc procedure :

[ 6 1 0 - 4 , : - 3 , 1 . 5 10 -2]Fa i lu re o f admin i s t ra t ive con t ro l in car ry ing ou t a p lan t po l icy

or s ch eduled t asks :[2 x 10 -3, 1 x 10 -2, 5 x 1 0 2 ]

Modi f i ca t ion o f es t imated hum an e r ro r s p robab i l it i es fo r theeffects Of very low s t ress level :

x 2Equ at ions fo r condi t iona l p robab il i ti es o f f a ilu re on t ask Ngiven f a ilu re on p rev ious t ask N - 1 fo r d i ff e ren t l eve l o f

d e p e n d e n c eP F N I N - I I Z D -- E r~ H ,N - 11LD)= (1 + 19 x Er)/20P ~ N IN - I I M D) = 1 + 6 Er ) /7P ~ N I N - lJ H D ) = 1 + E r ) / 2P~N I N - ~l cm) = 1

wh ere E l ~ epresen t s the hum an er ro r p robab i l i ty o f t ask N

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118 7 . O ~ a w a , . N ~ I d m d dA - - - o m i t e n t e r i n g h o l d p o w e r

b ~ _ _ _ k e e p t h e r e s c t o r o p e r a t i n g a t~ t h e p ow e r o f 2 0 0 1 ~c ~ C - - - c o n n e c t tw o s ta n d b y c i r c u l a t i o n~ p um p s t o t h e c o r e

~ - - - b l o c k t h e d rum w a t e r l e v e l an d~ p r e s s u r e t r i p- - - r e g u l a t e t h e f e e d w a t e r fl ow

~ F - - - b l oc k t h e t r i p o f l o s so f b o t h t u r b o g e n e r a t o r sF i g 1 B r a n c h o f C h e r n o b y l a c c id e n t e v e n t ~ e e

(2) The m anag em ent of the test was not serious and the adm inist rative cont rolwas poor. Without necessary safety review of the test program, the test wasconsidered merely as an electrical-technical test with no danger in reactor s a f e t y(3) The operators were overconfident . Th ey gave the test priori ty whileneglect ing the safety princip |e and operat ing procedures. At the event of theabnormal condi tion , even though the moni toring computer p r in to ut had shownthat there was not enough react ivi ty reserve to meet the shutdown requi rement ,they were st i l l in a very low stress level , and not aware of the potential danger.Tha t br ou gh t abou t successive violat ions of operat ing procedures and eventual lycaused the catastrophe.(4) Some important actions were card ed ou t aroun d midnight (e .g . , the act ionA was per formed on Apri l 26, 0 : 2 8 :~ ) . Because of the fa tigue of theop erato rs, the reliability of their- pe;~formance wo uld b e red uce d.Considering the above si tuat io~:s the relat ionship betw een th e act ions ischanged, that i s, the dep endence tends to the higher level . The depe nden ce in theChernobyl accident is assumed as shown in Figure 2(a).

2.5. Joint h l o n n e r r o r p r o b b i l it yBased on the previous analysi~ and Table 1, the joint hu m an err or probabi li ty

is obt~ned as fol lows.A is an omission error . The upper uncertainty bound of the human errorprobab~ ity is mod ified by th e stress factor:PF(A) = 0 0 1 5 x 2 = 0 0 3

A . . . . . B . . . . . . C . . . . . D . . . . . m . . . . . VZD CD HD HD lid

a )

A . . . . B . . . . C . . . . D . . . . E . . . . FZ D H D L D L D L D(b)Fig. 2. Dependencebetween actions under different assumptions.

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u z zy h u n u m m~ q~y a n d y s i 119B i s a n e r r o r o f a d m i n is t r a ti v e c on e z ~ l. T h e h u m a n e r r o r p r o b a b ~ t y o f B

e s t i m a t e d a s t h e u p p e r u n c e r ta i n t y b o u n d o f t h e h u m ~ l e r r o r p r o b a b i li ty a n d g e r od e p e n d e n c e w i t h A :

P B IAI X V )--0.05.T ~ b | e 2 . T h e e s t i m a t e d h m n a n e r r o r p r o b a b if i fi e s

Error Typeof error D e p e n d e n c e H u m a n e r r o r p r o ba b il it yF i g . 2 a ) A O m i s s i o n -

B F a i l u r e o fa d m i n i s t r a t i v e Z Dc o n t r o l

C F ~ l u r e o fa d m i n i s t r a t i v e C Dc o n t r o l

D F a i l m e o fa d m i n i s t r a t i v e H i )c o n t r o l

E F a i l u r e o fa d m i n i s t r a t i v e H Dc e n t r e |

F , F a i l u r e o ~a d ~ i s t . r a t i v e H Dc o m r o l

J o i m h u m a n e r r o r p r o b a b i f i t y

3 i 0 - 2 a

5 1 0 - 2 a

1

5.05 X 10-1

5.05 X 10 -1

5.05 x 10 -1

1 . 9 x 1 0 - *

F i g . 2 ( b ) A O m i s s i o nB F ~ i i m e o f

a d m i n i s t r a t i v e Z Dc~mtrol

C l~ailure ofa d m i n i s t r a t i v e H Dc o n t r o l

D F a i lu r e o fa d m i n i s t r a t i v e L Dc o n t r o |

E F a i l u r e o fa d m i n i s t r a t i v e L Dc o n t r o |

F F a i l u r e o fa d m i n i s t r a t i v e L Dc o n t r o l

J o i n t h u m a n e r r o r p r o b a b i l i t y

3 10 -3

1 x 10 -2

5.05 x 10 -1

5.95 10 2

5.95 X 10 2

5.95 X 10 2

3.19 x 10- 9

a Th e me dian of t he hu m an emi~r i :~robabili ty is used.

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122 T. Onisawa . b~wak~Tab le 5 Parameter m

C lass m k ~ 3 3 < k ~ 5 5 < k ~ 1 0 | 0 < kC 2 m v 2 .7 3 . 3 4 . 0 4 . ?

m L 2 .7 ,3 4 .0 4 .7C s t o o 1 .3 1 ,7 2 .0 2 ,3m L 3 .1 .8 4 6 . 4C4 my 1 , 9 2 . 4 2 . 9 3 . 4m L 2 . 6 3 . 3 3 . 9 & 6

s m o 2.@ 2.5 3 0 3 5mL 2.@ 2 .5 3 .0 S J 6 m v 1 .6 1 .9 2 . 2.7

m L 1 .5 ~ .9 2 ,~ 2o?C? my I . I 1 .4 1 .7 1 .9m L 1.2 1 .5 L 8 2 ,1

C a m u 0 . 8 1 . 0 1 . 1 1 . 3m L 0 .9 1 .1 1 ,4 1 ,6C9 my 0.5 0 .6 @.? @ 9m L 0.7 0 .8 1 .@ 1 ,2

T h e e r r o r p o ~ i b i l i t y i n t h e class Ct i s d e f i n e d as1 , e = 1 ,E (e ) ffi 0 , e ~ l ,

a n d t h a t i n t h e c l a s s C , o is d e f in e d a s0 , e ~ 0 ,~ e ) = I , e - 0 .

(5 )

(6)3 2 L og ic al c on n ec~es o ] e~o r possi bd i ~ es

T w o t a s k s a r e a s s u m e d t o b e i n d e p e n d e n t o f e a c h o t h e r .( i ) ~ c o n n e c t i v e .T h e f u n c t io n F i s u s e d a s t h e A t o c o n n e c t i v e o f e r r o r p o s s i b il it ie s :

1F x , y ) = 1 { 1 - x l x m ~ ~ L _ y ) / y ) m } , , 0 < x , y ~ 1, 7 )w h e r e ~ ( o , o ) = F ( x , o ) = F ( o , y ) = o .

P a r ~ e l t as k s a r e e o n n e ~ e d b y a n a n d g a te i n a f a ul t t re e . T h e e r ro rp o ~ b ~ U e s o f p a ra U e | t as k s a r e o p ex o at ed b y t h e ~ c o n n e c ti v e a n d t h ee x t e n s io n p r i n ~ p l e i n o r d e r t o o b t ~ n t h e e rr o r p o s s i b ~ t y o f t h e w h o l e t a sk .( fi ) o R c o n n e c t i v e .The fun~on G i s u s e d a s t h e o a c o n n e c t i v e o f e r r o r p o s s i b il it ie s :

{ ( x / ( 1 - x ) ) 3 ( y / ( 1 _ y ))3 }~ t3c ( x , Y ) = I + { ( ~ / 0 - x ) ) + ( y / 0 _ y ) ) 3 ) ~ , o ~ x , y < 1 , ( s )w h ere c ( 1 , 1 ) - ~ ( x , 1 ) = 6 ( 1 , y ) = 1.

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F uz zy hum an rdiabHily ~uudysis 17 3Series tasks are c onn ected by a n or ga te in a fault tree. Th e e~ror possibili tiesof se r ies tasks a re opera ted by the oR connect ive and the ex tension pf indple inord er to obtain the e rro r possibi li ty of the w hole task.

3.3. Dependence between consecutive tasksOnly th e depende ~ce b e tween para ll e l t asks as shown m Figure 3 i s in t roduced .Th e de p en d en ~ be tween ser ies t asks m ay ~ found in [3] , bu t i t i s no t cons ideredin our case s tudy. I t i s assumed that the t , sk B is performed after the task A isdon e. I f a hum an op era tor fail s in the task A , then h e is apt to fail in the task B.If he succeed s in ~ e task A, then he is a lso liable to succeed in the tas k B.Ho wev er f f he succeeds in the t ask A, he succeeds in the who~e t ask whe ther he~,ucceeds or not in the task B. So i t is not necessary to con ~d er th e la t ter e~ e .Let g ~ be the e r ror poss ib il ity of the t ask A, En be tha t o f the t ask B and R be

the fuzzy causal relat ion represent ing the dependence.( i) Th e case that the er ror o f the task A influences the erro r of the task B.Let E ~ be thq~ erro r possibil ity of the task B influenced by the erro r o f the taskA. Under logk~ cons idera t ion , g~ can be es t imated as EA AND R . In thisE~ is the e rro r possibil ity of the whole task:

( i i ) The case that the error of the task A does not inf luence the error of thetask BTh e po rt ion o f the e ~ o r possibili ty of the task A which doe s not inf luence theer ror of the t ask B is ob ta ined by

l o )wh ere E ~ i s th i s p ort i onTh e er ror possibi li ty of the whole task E in this case is obtain ed ~y

g = F ( E , E B ) . 11)(i i i ) The error possibi l i ty E as a whole.The error possibi l i ty E is obtained by

E = c ( E , ( t 2 )

Fig 3 Depend ence between paraHd tasks

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2 4 E Onisawa . Nishiweki3.4. valuation

L e t F . ) + = e , ~ ) , e d ~ ) ) b e a n ~ - ~ t o f E .( i) T h e c e n t e r e o o f E :Y l =Co.( ii ) Po t en t i a l i t y f o r e r r o r . D e f ine

J 2 - - . ~ ~ 1 - 0 . 5 ) o : d o :w h e r e e 2 ( ~ ) = 0 .5 . J 2 i s e v a l u a t e d w h e n J l ~ 0 . 5 .( ii i) Fuzz ine ss o f e r r o r poss ib il i ty . D e f ine

~ e 2 ~ ) - e o ) ~ d ~J 3 = t

o ( l - co ) o : d o :w he re 2(o:) ~ eo for o: G [0, 1) .( iv ) T h e r e l a t i ve po t en t i a l i t y and the r e l a t i ve f uzz ine ss . D e f ine

J e2(o:) - 0.5)o: d o :2' - f : (e~(~ )- o .5)~d~uw h e r e 2 ( ) = 0 .5 , an d

~ e 2 a ) - e o ) ~ d ~J y _--

( 2 ( o : ) - e o ) o : o :

0 3

1 4 )

0 5

( 1 6 )

1 7 )

T h e d e n o m i n a t o r s i n E q s . ( 1 6 ) a n d ( 1 7 ) a r e t h e e v a l u a t i o n o f t h e s t a n d a r d e r r o rposs ib i li t y E ' i n t he c l a ss which e , be lon gs t o . L e t ( E ' ) ~ - -- (e~( o:), e~ ( o :) ) be an~ - c u t o f E ' . T h e s t a n d a r d e r r o r p o s s i b i li ty E ' h a s t h e f o l lo w i n g p o s s i b il it yd i s t r i bu t ion :

1E ( e ) = I + 2 0 x l e - Col~ 1 8 )

w h e r e o is t h e e v ~ u a t i o n J 1 e n d m i s t he va lue i n t he c l a s s which eo be lo ng s t o .T h e p a r ~ n e t e r m i s d e t e m f i n e d b y T a b l e 5 .E q u a t i o n s ( 1 6 ) a n d ( 1 7 ) i m p l y t h e r e l a t i v e e v a l u a t i o n i n t h e c l a s s w h i c h e ,~ l o n g s t o . T h e p o t e n t ia l it y a n d t h e f u zz in e ss o f E a r e c o m p a r e d w i t h t h o s eo f E .

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Fu zzy hum an ~el~a ~l~ analys~s ~ 54 on t i le acd t

I n t h i s s e ~ o n t h e r e li a b il it y a n al ys is o n t h e C h e m o b y l a c c i d e n t J~ p e r f o r m e d b y, s i n g e r r o r p o s si b il it y a n d t h e r e s u l t is c o m p a r e d w i t h t h e r e su l t o f t h ep r o b a b ~ s t i c a n a l y s i s . T h e t r i p l e t o f ~ h e h u m a n e r r o r p r o b a b i l i t y f o r t h ed e r iv a t io n o f t h e e r r o r p o ~ b i f i t y is t h e s i n e a s t h e o n e u s e d in th e p ro b a b il is ~ c. ~ a l y si s . T h a t i s, t h e ~ p l e t o f t h e h u m a n e r r o r p r o b a b i l it y o f ' A ' i s [6 1 0 - 4 ,3 x 10 s , 1 .5 x 10 - 2] a n d ~ e t r ip l e t s o f t h e h u m a n e r r o r p r o b a b il i ti e s o f t h e o t h e rtg S k 8 a r e e a c h [ 2 x 1 0 - 3 , 1 0 - 2 , 5 x 1 0 - 2 ] . T h e m o d i f i c a t i o n b y t h e s t r e ~ f a c t o r i sp e r f o r m e d i n F i g u r e 4 ( a ) .F i g u r e s 4 ( a ) a n d 4 ( b ) s h o w t h e f a u lt t re e s w h i c h c o r r e s p o n d t o F i g u r e s 2 (a ) a n d2(b) , respect ively . F igure 5 shows the fuzzy causal re la t ions in th is analys is .F igu res 6 (a ) and 6 (b ) show the e r ro r pos s ib i l i t i e s o f the top even t s in the f au l tt r ees show n in F igu res 4 (a ) an d 4 (b ) , r e spec t ive ly . ~ e subsc r ip t 1 i s g iven to theresul t in F igure 6(a) and the subscr ip t 2 i s g iven t~ ~he resu l t in F igure 6(b) .C o m p a r i n g t h e r t ~ u l t o f t h e ~.3 analys is and that of the probabi l is t ic analys isthe fo l low ing i s cons ide red .(1) J l~ > J12 . This resu l t i s in fer red by the resu l t o f the probabi l is~ie analys is .2 ) E l 0 ) < E 2 0 ). Th is imp l ies tha t i t i s l e s s pos s ib le fo r the hu m an operator om a k e a n e r r o r i n th e c a s e o f F ig u r e 4 ( b ) t h a n ir~ t h e c ~ e o f F i g u r e 4 ( a ).(3 ) E t ( 1 ) > E2(1 ). Th i s imp l ies tha t i t i s m ore l ike ly fo r the hu m an o per a to r tom a k e a n e r r o r i n th e c a s e o f F ig u r e 4 ( a ) t h a n i n t h e c a se o f F i g u r e 4 ( b ).Th ese r esu l ts a r e a l so in fe r r ed by the r esu l t o f the p robab i l i s ti c ~ r~alysis . F ro mthe above cons ide ra t ion the s ame resu l t a s the p robab i l i s t i c ana lys i s i s ob ta ined :

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0.95 ~x ~ 1.0,0 . 0 ~ : < 0 .9 5 ,0 .6 < x ~ 1 .0 ,0 .5 ,~x J2~ an d Y3~.> .Y3~ in sp i t e o f J11 > J l z , J21 > J22 an d J 3 1 > II32 T h i sa lSO SHOW S h a t s m a l l J | d o e s n o t a l w ay s m ea n g o o d r e l i ab i li t y .(6 ) J 2 ~ an d J 3~ a s w e l l a s J l ~ a r e a rg e . T h i s r e s u l t s h o w s t h a t t h e p o t e n t i a l i t yf o r e r r o r is h ig h . H o w e v e r l a rg e J 3 d o e s n o t n e c e s ~ l y y i e ld w i th c o n fi d e n ce t h a tt h e h u m a n o p e r a t o r m a k e s a n e r r o r c e r ta i n ly .I f J 2 , J 3 , J 2 ' a n d J ' 3' a r e a l s o e v a l u a t e d , t h e g o | l o w in g re s u l t is o b t a i n e d :Re l i ab i r l i t y i n F i g u re 4 (b ) i s n o t n o ces s a r i l y mu ch b e t t e r t h an t h a t i n F i g u re 4 (a ) .F i g u r e 6 ( b ) s h o w s t h a t t h e h u m a n o p e r a t o r h a s e n o u g h p o s s i b i l i t y t o m a k e a ne r r o r . 1 h e r e is r o o m f o r i m p r o v e m e n t o f t h e m a n a g e m e n t a n d a d m i n is t ra t iv ec o n t r o l s y s t e m e v e n i n t h e c a s e o f F i g u r e 4 ( b ) .I t is f o u n d t h a t e r r o r p o s s ib i li ty c a n b e i n t e r p r e t e d f r o m m a n y p o i n t s o f v ie w . I ti s d i mcu l t t o g a i n s u ch an i n t e rp re t a t i o n i n p ro b ab i l i s t i c an a |y s i s .1 0 ~ 1 0

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Fu zzy hum an rd~ bility malysis 27, C e r i S e

T h i s p a p e r c o m p a r e d t h e r e s u l t o f f u z z y r e l i a b i l i V / a n a l y s i s u s i n g e r r o rp o s s ib i li ty w i t h t h a t o f p r o b a b i li st ic a n a ly s is o n t h e C h e m o b y l a c d d e n t . T h i s ~ s es t u d y s h o w e d t h e f o l l o w i n g v a l i d it y o f ~ r e l ia b i l it y a n a l y s i s : e r r o r p o s s ib i H v /c a n b e i n t e r p r e t e d f r o m ~ n a n y p o i n t s o f v i e w a n d i t i s d if fi cu l t t o g a i n s u c h a ni n t e rp r e t a t io n i n p r o b a b ~ s t i c a n a l y s is . T h e b e l i e f t h a t a s m a l l e rr o r p r o b a b ~ t ys h o w s g o o d r e li a b i li ty i s d a n g e r o u s i n r e l ia b i l it y a n a l y si s. S o m e b i g a c c i d e n t s h a v es h o w n t h i s c o n s i d e r a t i o n . ~ i ~ i s p a p e r s h o w s t h a t i t i s n e c e s s a r y t o a p p l y ~t h e o r y t o r e l i a b i l i t y a n a l y s i s ,

R e f e m n c u[1] Z. H u and J . Zhang, A preliminary human factor analysis on the accident a t the Chem obylnuclear power plant, Private Communication to Prof. Y. Ni~waki IA EA (1987) .[2] Interna tional N uclear Safety AdvB ory Grou p, Sum mary report o a th post-accide~t reviewmeeting on th e Ch em obyl accident, Safety Series No . 75-1NSAG -1, International Atom ic Ene rgyAgency, Vienna (1986).[9] T . Ontu twa , An approach to human re liab i li ty in man-mac | f ine sys tem us ing e~o r ~ i b ~ y ,Fuzzy Sets and Systems 27 (1988) 87-103.[4] A.D . Sw ain and H.E. Gut tmann , Handbook o f Hu ma n Reliability Amdysis with Empluisis onNuclear Pow er P lant Appficmions (NUREG/CR-1278, 1980).[5] USSR S tate Comm ittee on the U rina tion of Atom ic Energy, 131e accident a t the Chem obylnuclear power plant and its consequences, Information compiled for the IAEA experts ' meeting,

Vienna, 25 -29 August (1986).