Research Article Research on a Risk Assessment Method considering Risk Association

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1 Mathematcal Problems Egeerg Volume 26, Artcle ID 996, 7 pages Research Artcle Research o a Rsk Assessmet Method cosderg Rsk Assocato Zha Zhag, Ka L, ad Le Zhag 2 School of Busess Admstrato, Northeaster Uversty, Sheyag, Cha 2 School of Ecoomcs ad Maagemet, Bejg Jaotog Uversty, Bejg, Cha Correspodece should be addressed to Le Zhag; zhagle eu@sa.com Receved 26 August 26; Revsed 2 October 26; Accepted November 26 Academc Edtor: Ya-Wu Wag Copyrght 26 Zha Zhag et al. Ths s a ope access artcle dstrbuted uder the Creatve Commos Attrbuto Lcese, whch permts urestrcted use, dstrbuto, ad reproducto ay medum, provded the orgal work s properly cted. Regardg rsk assessmet problems wth multple assocated rsks, a rsk assessmet method (RAM) s proposed ths paper. Accordg to the rsk-assocated assessmet formato offered by expert pael, a comprehesve assocated matrx s costructed to detfy the fluece relatoshp amog rsks so as to determe the herarchcal structure of rsks. The, based o the determed dvded or udvded rsk herarchcal structure as well as the possblty ad loss of rsks provded by expert pael, each value at rsk (VAR) s calculated through kowledge related to probablty theory. Fally, the feasblty ad effcecy of the proposed method are demostrated through a calculatg case.. Itroducto Rsk assessmet s quatfyg the probable degree of fluece or loss brought by a certa evet or thg [. Rsk assessmet s a mportat segmet of rsk maagemet, for stace, facal rsk maagemet, credt rsk maagemet, egeerg rsk maagemet, ad other aspects; t plays a sgfcat decso-support role for rsk maagers to adopt reasoable rsk preveto measures ad strateges [2 4. Over the years, may scholars at home ad abroad have attached great mportace to researches o RAM ad there have already bee some outstadg research achevemets [, lke aalytc herarchy process about rsk assessmet [, 6, hazard degree calculato method [7, 8, rsk matrx method [9 ad artfcal eural etwork [2,, ad so o. Though all the RAMs metoed above have solved varous kds of rsk assessmet problems from dfferet perspectves, most of them do ot take rsk-assocated stuatos to accout. However, realty there are usually coectos amog rsks. For example, Baraoff ad Sager [4 aalyzed the assocated stuato betwee resource rsk ad producto rsk lfe-surace compaes. Abdellaou et al. [ fd that assocated rsks are valued dfferetly tha correspodg reduced smple rsks. Thus, research o RAM cosderato of rsk assocato has academc ad practcal applcato values. Now, there are few researches of ths aspect. Lao et al. [6 adopted Bayesa Network approach to evaluate IT outsourcg rsk meawhle cosderg the assocato betwee IT outsourcg rsk factors ad IT outsourcg rsks; Büyüközka ad Rua [7 proposed a Choquet tegrals-based software developmet rsk evaluato approach regardg the assocato amog developmet evromet rsk, code costrat rsk, ad egeerg rsk durg the developmet of software. However, these RAMs maly focus o specfc rsk assessmet problems rsk-assocated stuatos wth o uversal RAM proposed. Therefore, based o prevous researches, we establsh outsourcg rsk herarchy, troduce the teracto betwee dfferet levels of rsk, ad gve a RAM cosderato of multple rsk-assocated stuatos. Therearefoursectosthspaper.ISectowe elaborate the research backgroud ad the problems that eed to be explored or studed ad the clarfy the objectves ad sgfcace of the proposed method. I Secto 2 we descrbe the RAM cosderg rsk assocato detal. I Secto we use a calculatg case to prove feasblty ad effcecy of the proposed method. Fally Secto 4 we summarze the cocluso ad the ma cotrbutos of ths

2 2 Mathematcal Problems Egeerg paper ad also the lmtatos ad further research work to be carred out. 2. Theores ad Methods 2.. Descrpto of Problems. I rsk assessmet problems, the occurrece of a certa rsk may lead to aother rsk, that s, the assocato amog rsks. The followg symbols are used to express the set ad quatty of a rsk assessmet problem cosderato of rsk-assocated stuatos: () R{R,,...,R m }:thesetofrsks,wherer meas the rsk umber,,2,...,m () E{E,E 2,...,E }: the set of the expert pael, where E k meas the expert umber k, k,2,..., () w (w,w 2,...,w ): the weght vector of experts, where w k meas the mportace or weght of the expert E k ; t satsfes w k, k w k, k,2,..., (v) A k [a k j m m: rsk-assocated matrx offered by the expert E k,wherea k j meas the evaluato value offered by the expert E k for the drect fluece degree of the rsk R o the rsk R j,whchfve-pot scalesadopted.meas ofluece, meas weak fluece, 2 meas rather weak fluece, meas medum fluece, 4 meas rather strog fluece, ad meas strog fluece (v) λ k : the thresholds offered by the expert E k for comprehesve fluece degree. Settg up thresholds s to reject the fluece relatoshp that s sgfcat ad has lttle comprehesve fluece degree accordg to expert pael. λ k, k,2,..., (v) P k :theprobabltyofoccurreceoftherskr offered by the expert E k, k,2,...,,,2,...,m (v) l k : the loss after the occurrece of the rsk R offered by the expert E k, k,2,...,,,2,...,m (v) P G : the comprehesve probablty of the occurrece of the rsk R.,2,...,m (x) L G : the comprehesve loss of the rsk R,,2,...,m (x) z : the VAR of the rsk R,,2,...,m We propose the detaled procedure of RAM cosderato of rsk assocato. Frstly, several rsk-assocated matrxes offered by expert pael are combed as group rskassocated matrx, whle several thresholds of comprehesve fluece degree offered by expert pael are combed as group threshold; secodly, rsk relatoshp detfcato s performed through methods lke matrx trasform ad there are usually two stuatos, dvded ad udvded rsk herarchcal structures the result of rsk relatoshp detfcato. If the udvded rsk herarchcal structure s set as stuatoa,eachvalueatrskwouldbecalculatedaccordg totheoccurreceprobabltyadlossofeachrskoffered by the expert pael; f the dvded rsk herarchcal structure s set as stuato B, the expert pael are requred to offer the occurrece probablty of bottom rsk ad codtoal probablty accordg to the rsk herarchcal structure. Furthermore, the comprehesve probablty of the occurrece of eachrskwouldbecalculatedthroughcodtoalprobablty formula ad total probablty formula specfcally so as to calculate each value at rsk cosderato of loss of each rsk Rsk Relatoshp Idetfcato. Accordg to the descrpto of problems above, detfcato methods of relatoshp amog several rsks (or rsk herarchcal structures) are lsted below. Frstly, rsk-assocated matrxes (A,A 2,...,A )are combed as a group-assocated matrx A G [a G j m m, amog whch the calculatg formula of a G j s a G j { ka k j w k, t j 2 {, t { j > 2,j,2,...,m. () I formula (), t j meas the umber of experts who score thedrectfluecedegreeoftherskr o the rsk R j as. Furthermore, the group-assocated matrx A G s trasformed to regulated group-assocated matrx B G [b G j m m,amog whch the calculatg formula of b G j s b G j a G j max { h ag h },j,2,...,m. (2) Secodly, comprehesve fluece matrx wth drect assocato C[c j m m s set up ad the calculatg formula s CB G (I B G ). () Meawhle, thresholds (λ,λ 2,...,λ ) of comprehesve fluece degree are combed as a group threshold λ G, ad the calculatg formula s λ G k w k λ k. (4) Accordg to the group threshold λ G, the comprehesve fluece matrx C [c j m m s trasformed to λ G -cut matrx C λ [α j m m,where α j {, c j λ G {,j,2,...,m. (), c { j <λ G Assume D [d j m m as - comprehesve assocated matrx, whch d j { α j +, j { α { j, j,j,2,...,m. (6)

3 Mathematcal Problems Egeerg Matrx D reflects the preferece of the expert pael for fluece degree amog each rsk wth drect fluece relatoshp. The fluece of the rsk R o tself s. Accordg to matrx D, herarchcal structure of each rsk s dvded. Assume H H J,2,...,m, (7) where H {R j d j }ad J {R j d j }. H meas the rsk set correspodg to the elemet valued the lst umber the matrx D; J meas the rsk set correspodg totheelemetvaluedtherowumber the matrx D. If formula (7) works for a certa, R should be regarded as the bottom elemet D ad the lst umber ad the row umber D should be deleted to form a ew matrx. Durg the process, f the bottom elemet caot be foud, rsk assessmet should be performed regardg stuato A. If there s bottom elemet, searchg bottom elemet the ew matrx should be performed utl all the elemets the matrx are deleted. The the herarchcal structure of matrx D should be bult up accordg to the order of deletg. Fally, rsk assessmet should be performed for stuato B. 2.. Rsk Assessmet. RAMs for stuatos A ad B are lsted below. Stuato A. As for the stuato that rsk herarchcal structure caot be dvded, each rsk s regarded as elemets of the same layer to process. Frstly, the probablty of occurrece of rsk offered by the expert pael (P,P2,...,P )scombed as comprehesve probablty of occurrece of rsk P G,ad the calculatg formula s P G k w k P k,2,...,m. (8) Secodly, the loss of rsks (l,l2,...,l )offeredbythe expert pael s combed as comprehesve loss of rsks L G, ad the calculatg formula s L G k w k l k,2,...,m. (9) Fally, o the bass of the comprehesve probablty of occurrece of rsk P G ad comprehesve loss of rsks L G,the value at rsk s calculated, ad the calculatg formula s z P G L G,2,...,m. () Stuato B. Asforthestuatothatrskherarchcalstructure ca be dvded, R f {R,,...,R m } s assumed as the set of rsk o the layer umber f, adr f s set as the rsk umber o the layer umber f, f,2,...,m; P k (p k,pk 2,...,pk d ) s the probablty vector of the occurrece oftherskothefrstlayer(thebottomlayer)offeredby the expert E k,wherep k j s the probablty of occurrece of the rsk R j offered by the expert E k ; d f s the umber of rsks o the layer umber f. R j,f s assumed as the rsk umber j o the layer umber f related to the rsk R f, j,2,...,d f f ; df f stheumberofrsksothelayer umber f related to the rsk R f. R f Ts assumed as the occurrece of the rsk R f,adr f Fmeas that the rsk R f does ot happe. I cosderato of two codtos, R j,f T ad R j,f F,therewllbe2 df f codtoal probabltes related to R f T. Furthermore, assumg that P k (R f T R,f T,,f T,..., R f d T)s the probablty of occurrece of the rsk R f offered by the expert E k wth the rsks,f f R,f,,f,...,R f d happeg smultaeously, k,f f,2,...,; P k (R f T R,f T,,f F,..., R f d f,f T) s the probablty of occurrece of the rsk R f offered by the expert E k wth the rsks R,f,,f,,f,...,R f d happeg smultaeously but o rsk,f f,f, k,2,...,;..., P k (R f T R,f F,,f F,...,R f d F)stheprobablty of occurrece of the,f f rsk R f wthout R,f,,f,...,R f d offered by the,f f expert E k, k,2,...,;forcoveece,p k (R f T R,f T,,f T,..., R f d f,f T), Pk (R f T R,f T,,f F,..., R f d f,f T),..., Pk (R f T R,f F,,f F,..., R f d f,f F) are recorded as P k (R f T T,T,...,T), P k (R f T T,F,...,T),..., P k (R f T F,F,...,F)for abbrevato. Frstly, the probablty vectors P (p,p 2,...,p d ), P 2 (p 2,p2 2,...,p2 d ),..., P (p,p 2,...,p d ) are combed as the comprehesve probablty vector P (p,p 2,...,p d ) ad the calculatg formula s p j w k p k j j,2,...,d. () k Secodly, the codtoal probabltes P (R f T T,T,...,T), P 2 (R f T T,T,...,T),..., P (R f T T,T,...,T)are combed as the comprehesve codtoal probablty P G (R f T T,T,...,T);thecodtoalprobabltes P (R f T T,F,...,T), P 2 (R f T T,F,...,T),..., P (R f T T,F,...,T) are combed as the comprehesve codtoal probablty P G (R f T T,F,...,T);...;thecodtoalprobabltesP (R f T F,F,...,F), P 2 (R f T F,F,...,F),..., P (R f T F,F,...,F) are combed as the comprehesve codtoal probablty P (R f T F,F,...,F),adthecalculatg formulas are as follows: P G (R f T T,T,...,T) k w k P k (R f T T,T,...,T), (2a)

4 4 Mathematcal Problems Egeerg P G (R f T T,F,...,T) k w k P k (R f T T,F,...,T),. P G (R f T F,F,...,F) k w k P k (R f T F,F,...,F). (2b) (2b df f ). P G (R,f F,,f F,..., R d f f,f F, R f T)P G (R,f F)P G (,f F) P G (R f d f,f F)P G (R f T R,f F,,f F,..., R f d f,f F). (4b df f ) Accordg to formulas () (2b df f ),totalprobablty formula s adopted to calculate the comprehesve probablty P G of occurrece of each rsk specfcally (from the bottom layer); for stace, the formula to calculate the comprehesve probablty of occurrece of rsk o the layer umber f s where P G P G (R,f T,,f T,..., R d f f,f T, R f T)+P G (R,f T,,f F,..., R d f f,f T, R f T)+ +P G (R,f F,,f F,...,R d f f,f F, R f T), P G (R,f T,,f T,..., R d f f,f T, R f T)P G (R,f T)P G (,f T) P G (R f T R,f T,,f T,..., R f d T),,f f P G (R,f T,,f F,..., R d f f,f T, R f T)P G (R,f T)P G (,f () (4a) Fally, accordg to formulas () (4b df f ),thecomprehesve probablty P G of occurrece of each rsk s calculated. Furthermore, accordg to formula (), each value at rsk z s calculated.. The Calculatg Case for Stuatos A ad B I the followg part, 2 calculatg cases for stuatos A ad B are used to expla the RAM proposed above. Case for Stuato A. I order to mprove ts compettve ablty, Laog GTE Bopharmaceutcal Compay wats to outsource ts clcal expermet busess. Before outsourcg, the compay eeds rsk assessmet o ths outsourcg actvty. The compay sets up a pael of experts cludg experts (E,E 2,...,E ), ad accordg to experece ad busess profcecy of each expert, the weght vectors of experts provded by the compay are w (.2,.2,.,.,.). Throughrelevataalyssad arragemet of feedback suggestos from questoares, the group of experts determe 2 kds of outsourcg rsks: bad book (R ) ad cotract modfcato ( ). These 2 rsks caot be dvded to a herarchcal structure. It should be calculated by usg formulas (8), (9), ad (). The experts gve the value as Tables ad 2 show. Byusgformulas(8),(9),ad(),wecaget P G k w k P k , L G w k l k k , F) P G (R d f f,f T)P G (R f T R,f T,,f F,..., R d f f,f T), (4b) z P G LG , P G 2 k w k P k ,

5 Mathematcal Problems Egeerg Table E E 2 E E 4 E P(R T) P( T) Table 2 l k E E 2 E E 4 E R L G 2 w k l k 2 k , z 2 P G 2 LG () The rsk value of cotract modfcato s much bgger tha the value of bad bookg. The compay should cosder ths result to desg the outsourcg pla. Case 2 for Stuato B. O the same backgroud, through relevat aalyss ad revew of feedback suggestos from questoares, the pael of experts determes outsourcg rsks: bad book (R ), cotract modfcato ( ), decreased servce qualty ( ), hdde costs ( ), ad damaged compay mage ( ). The rsk-assocated matrxes offered by the experts are as follows: A R [ [ R 2 2, A A 4 A R R R [ [ [ [ [ [ R R 4 R 4 2,,. (6) Frstly, accordg to formula (), the rsk-assocated matrxes (A,A 2,...,A ) are combed as the groupassocated matrx A G [a G j : A G R [ [ R (7) Secodly, accordg to formula (2), the group-assocated matrx A G s trasformed to regulated group-assocated matrx B G [b G j ;amely, A 2 R R 4 2 [ [, B G R R.6 [.4.27 [ (8)

6 6 Mathematcal Problems Egeerg Table : Probablty ad codtoal probablty of occurrece of rsks offered by experts. R Fgure : Herarchcal structure of rsks. Accordg to formula (), group comprehesve fluece matrx C[c j s costructed; that s, E E 2 E E 4 E P(R T) P( T R T) P( T R F) P( T R T) P( T R F) P( T T) P( T F) P( T T, T) P( T T, F) P( T F, T) P( T F, F) C R [ [ R (9).42 Furthermore, accordg to the stuato of the compay, the thresholds about comprehesve fluece matrx provded by experts separately are λ., λ 2., λ., λ 4., λ.. Accordg to formula (4), the group threshold s λ G.. Accordg to formula (), the comprehesve fluece matrx C s trasformed to - comprehesvefluecematrxd[d j ;thats, D R [ [ R. (2) Accordg to matrx D ad formula (7), the herarchcal structureofkdsofrskssdvdedasshowfgure. Accordg to the herarchcal structure of rsks show Fgure, combed wth the hstorcal data ad realty of the market, the pael of experts offered the probablty of occurrece of the bottom rsk R,thecodtoalprobablty of occurrece of the rsks o the secod layer ad, ad the codtoal probablty of occurrece of the rsks o the thrd layer ad,asshowtable.thelossof rsks offered by experts (ut: te thousad Yua) s lsted Table 4. Furthermore, accordg to formulas () (4.2 df f ), the comprehesve probablty of occurrece of rsks P G s calculated,showthesecodlstoftable.forexample, the probablty of occurrece of the rsk s P G 2 P G(R T)P G ( T R T) + P G (R F)P G ( T R F).284. Accordg to formula (9), the loss of rsks Table 4: Loss of rsks offered by experts. l k E E 2 E E 4 E R Table : Probablty of occurrece of rsks, loss of rsks, ad value at rsk. P G l G z R (l,l2,...,l ) s combed as the comprehesve loss of rsks L G, as show the thrd lst of Table. Fally, accordg to formula (), each value at rsk z s calculated as show fourth lst of Table. Thus, the calculatg results of rsk assessmet provde decso support for rsk maagemet of the bopharmaceutcal compay. 4. Cocluso A rsk assessmet method cosderato of rsk-assocated stuatos s provded ths paper. Based o varous kds of evaluatg formato about rsks offered by the group of experts, ths method calculates each value at rsk through detfcato of herarchcal structure of rsks by adoptg kowledge related to probablty theory. Accordg to calculato aalyss, the proposed method s feasble ad proved to have certa applcato value. For structured rsk assessmet problems, the proposed method s geeral. However, the requremets of dfferet dustres ad dfferet types of busess for servce outsourcg are ot the same. So the method we gve ths paper may ot be drectly applcable

7 Mathematcal Problems Egeerg 7 to all dustres or all types of eterprses, especally some specal dustres. As servce outsourcg progresses, some of the expected outsourcg rsks wll chage, ad o the other had, ew ad upredctable outsourcg rsks wll emerge. I order to esure the smooth realzato of servce outsourcg, the eterprse rsk cotrol durg the whole servce outsourcg process s worth studyg. Also further research s requred for large calculato amout of the rsk occurrece. Competg Iterests The authors declare that there s o coflct of terests regardg the publcato of ths paper. [4 E. G. Baraoff ad T. W. Sager, The relatos amog asset rsk, product rsk, ad captal the lfe surace dustry, Joural of Bakg & Face,vol.26,o.6,pp.8 97,22. [ M. Abdellaou, P. Klbaoff, ad L. Placdo, Expermets o compoud rsk relato to smple rsk ad to ambguty, Maagemet Scece, vol. 6, o. 6, pp. 6 22, 2. [6 X.-W. Lao, W. Tao, ad L. Yua, A Bayesa etwork model uder group decso makg for evaluatg IT outsourcg rsk, Proceedgs of the Iteratoal Coferece o Rsk Maagemet & Egeerg Maagemet (ICRMEM 8), pp. 9 64, Bejg, Cha, November 28. [7 G. Büyüközka ad D. Rua, Choquet tegral based aggregato approach to software developmet rsk assessmet, Iformato Sceces,vol.8,o.,pp.44 4,2. Refereces [ M. Doumpos ad C. Zopouds, Assessg facal rsks usg a multcrtera sortg procedure: the case of coutry rsk assessmet, Omega, vol. 29, o., pp. 97 9, 2. [2 T. M. Wllams, Rsk-maagemet frastructures, Iteratoal Joural of Project Maagemet, vol.,o.,pp., 99. [ S. Pramuthu, O preprocessg data for facal credt rsk evaluato, Expert Systems wth Applcatos,vol.,o.,pp , 26. [4 M. Farrell ad R. Gallagher, The valuato mplcatos of eterprse rsk maagemet maturty, Joural of Rsk ad Isurace,vol.82,o.,pp.62 67,2. [ J.C.We,Z.J.L,L.Q.Shetal., Comprehesveevaluato of water-rush rsk from coal floors, Mg Scece ad Techology (Cha),vol.2,o.,pp.2 2,2. [6 M. Nazam, J. Xu, Z. Tao, J. Ahmad, ad M. Hashm, A fuzzy AHP-TOPSIS framework for the rsk assessmet of gree supply cha mplemetato the textle dustry, Iteratoal Joural of Supply ad Operatos Maagemet,vol.2,o.,pp , 2. [7 B. Bahl ad S. Rvard, Valdatg measures of formato techology outsourcg rsk factors, Omega, vol.,o.2,pp. 7 87, 2. [8C.Oksel,C.Y.Ma,adX.Z.Wag, Structure-actvtyrelatoshp models for hazard assessmet ad rsk maagemet of egeered aomaterals, Proceda Egeerg,vol.2,o., pp., 2. [9 K.L.Astles,M.G.Holloway,A.Steffe,M.Gree,C.Gaass, ad P. J. Gbbs, A ecologcal method for qualtatve rsk assessmet ad ts use the maagemet of fsheres New South Wales, Australa, Fsheres Research, vol.82,o.,pp. 29, 26. [ A. S. Markowsk ad M. Sam Maa, Fuzzy rsk matrx, Joural of Hazardous Materals,vol.9,o.,pp.2 7,28. [ D. Dooho ad M. Gavsh, Mmax rsk of matrx deosg by sgular value thresholdg, The Aals of Statstcs,vol.42, o. 6, pp , 24. [2 A. Khashma, Neural etworks for credt rsk evaluato: vestgato of dfferet eural models ad learg schemes, Expert Systems wth Applcatos, vol.7,o.9,pp , 2. [ E.Agel,G.Tollo,adA.Rol, Aeuraletworkapproach for credt rsk evaluato, The Quarterly Revew of Ecoomcs ad Face,vol.48,o.4,pp.7 7,28.

8 Advaces Operatos Research Volume 24 Advaces Decso Sceces Volume 24 Joural of Appled Mathematcs Algebra Volume 24 Joural of Probablty ad Statstcs Volume 24 The Scetfc World Joural Volume 24 Iteratoal Joural of Dfferetal Equatos Volume 24 Volume 24 Submt your mauscrpts at Iteratoal Joural of Advaces Combatorcs Mathematcal Physcs Volume 24 Joural of Complex Aalyss Volume 24 Iteratoal Joural of Mathematcs ad Mathematcal Sceces Mathematcal Problems Egeerg Joural of Mathematcs Volume 24 Volume 24 Volume 24 Volume 24 Dscrete Mathematcs Joural of Volume 24 Dscrete Dyamcs Nature ad Socety Joural of Fucto Spaces Abstract ad Appled Aalyss Volume 24 Volume 24 Volume 24 Iteratoal Joural of Joural of Stochastc Aalyss Optmzato Volume 24 Volume 24