Water Sciece ad Egieerig, Dec. 2008, Vol. 1, No. 4, 107-113 ISSN 1674-2370, http://kkb.hhu.edu.c, e-mail: wse@hhu.edu.c Reliability model of orgaizatio maagemet chai of South-to-North Water Diversio Project durig costructio period Feg Jigchu* 1, Zhou Yag 1, Hog Yuzhe 1, Zhao Shixi 2, Re Xiaoqiag 1 1. Busiess School, Hohai Uiversity, Najig 210098, P. R. Chia 2. Office of the South-to-North Water Diversio Project Costructio Committee uder the State Coucil, Beijig 100053, P. R. Chia Abstract: I order to aalyze the idispesability of the orgaizatio maagemet chai of the South-to-North Water Diversio Project (SNWDP), two basic forms (series coectio state ad mixed state of both series coectio ad parallel coectio) of the orgaizatio maagemet chai ca be abstracted. The idispesability of each form has bee studied ad is described i this paper. Through aalysis of the reliability of the two basic forms, reliability models of the orgaizatio maagemet chai i the series coectio state ad the mixed state of both series coectio ad parallel coectio have bee set up. Key words: South-to-North Water Diversio Project; reliability model; maagemet chai; parallel coectio; series coectio DOI: 10.3882/j.iss.1674-2370.2008.04.012 1 Itroductio The maagemet chai of the SNWDP durig the costructio period facilitates the passage of maagemet orders, busiess trasactios, message trasfers, etc. The reliability of the maagemet chai directly affects the smoothess ad effectiveess of these processes. For this reaso, it is ecessary to study the reliability of the maagemet chai i regard to govermetal maagemet relatioships, cotract relatioships, cliet relatioships, supervisory ad guaraty relatioships, ad relatioships withi the SNWDP orgaizatio. The SNWDP depeds o the reliability of each relatioship withi the hierarchy of the maagemet chai as well as the reliability of relatioships amog etities at equivalet maagemet levels (both series coectio ad parallel coectio). I the preset work, based o the two basic patters of series coectio ad parallel coectio of the maagemet chai of the SNWDP, studies o the reliability of the orgaizatio maagemet chai have bee coducted ad reliability models of the orgaizatio maagemet chai i both the series coectio state ad the mixed state of series coectio ad parallel coectio have bee set up. This work was supported by the Natioal Sciece ad Techology Pla (Major Project of the Eleveth Five-Year Pla, Grat No. 2006BAB04A13). *Correspodig author (e-mail: feg.jigchu@163.com) Received Jul. 9, 2008; accepted Dec. 1, 2008
2 Purposes of reliability study of orgaizatio maagemet chai The purposes of settig up the reliability idex of the orgaizatio maagemet chai ad the optimum models are as follows: (1) To cotribute to improvig the stability of the maagemet chai etwork: The maagemet chai of the SNWDP, iflueced by several elemets, is a complicated dyamic system ad is very radom. As a probability idex, the reliability degree ca effectively evaluate the systemic workig stability of the maagemet chai of the SNWDP. (2) To provide techology for the pla of the maagemet chai: The maagemet chai etwork of the SNWDP should have the requisite smoothess ad workig capacity to guaratee that each relatioship is regular ad effective, thereby stregtheig its flexibility ad certaity. Moreover, the reliability of the orgaizatio maagemet chai ehaces emergecy mechaisms for accidetal icidets. (3) To cotribute to improvig the efficiecy of the maagemet chai: I order to satisfy the miimum reliability of the maagemet chai ad esure the fulfillmet of essetial tasks, the itegrated structure is appraised ad fuctio strategies are compared. 3 Basic forms of orgaizatio maagemet chai The maagemet chai of the SNWDP durig the costructio period cosists of the orgaizatio maagemet chai, the work breakdow structure (WBS) maagemet chai, ad the mix of the two. The relatioships of the mai body of the SNWDP iclude: the govermetal maagemet relatioship ad trade relatioship betwee the govermet ad the project legal persoel; the cliet relatioships betwee the project legal persoel ad the aget costructio or maagemet eterprises; ad the cotract relatioship betwee the project legal persoel, cosultatio eterprises, work cotract eterprises, supervisio compaies, ad supply eterprises. Accordig to each relatioship of the mai body, the orgaizatio of the SNWDP durig the costructio period has several forms of maagemet chais, as show i Figure 1. Accordig to various relatioships i the orgaizatioal structure of the SNWDP, the maagemet chai ca be described i basic forms, while the mai factors ca be represeted by dots, expressed as letters or umbers. Cruodes are coected to a strig accordig to some method ad order, thus formig a maagemet chai (Che et al. 2004; Wag et al. 2002; Wu 2003). The basic patter of the maagemet chai of the SNWDP has two forms. Oe is series coectio, ad the other is parallel coectio. The orgaizatio maagemet chai of the SNWDP is complicated, ad it is difficult to calculate its reliability, so it is ecessary to abstract its basic forms (series coectio state ad mixed state of both series coectio ad parallel coectio). By studyig the reliability of the basic forms, a evaluatio of the reliability of the orgaizatio maagemet chai of the SNWDP ca be coducted. 108 Feg Jigchu et al. Water Sciece ad Egieerig, Dec. 2008, Vol. 1, No. 4, 107-113
Figure 1 Model of maagemet chai of SNWDP durig costructio period 3.1 Basic form i series coectio state Oe of the basic forms of the orgaizatio maagemet chai of the SNWDP is the series coectio state, show i Figure 2. Figure 2 Basic form of orgaizatio maagemet chai of SNWDP i series coectio state Feg Jigchu et al. Water Sciece ad Egieerig, Dec. 2008, Vol. 1, No. 4, 107-113 109
3.2 Basic form i mixed state of both series coectio ad parallel coectio The other basic form of the orgaizatio maagemet chai of the SNWDP is the mixed state of both series coectio ad parallel coectio, show i Figure 3. Figure 3 Basic form of orgaizatio maagemet chai of SNWDP i mixed state of both series coectio ad parallel coectio 4 Costructed fuctio of miimum reliability ad ivalidatio probability of orgaizatio maagemet chai 4.1 Basic uit reliability The reliability of the orgaizatio maagemet chai of the SNWDP depeds o both ode reliability ad arc reliability. It is ecessary to aalyze ad compute the reliability of each ode ad arc i the orgaizatio maagemet chai. The computatio load of the reliability of the maagemet chai is directly proportioal to the umber of cruodes ad arcs. Because some cruodes ad arcs belog to the same project or the same mai body, ad their activities are correlated, it is difficult to distiguish them. It is also difficult to compute the reliability of cruodes ad their followig arcs, thus greatly icreasig the computatio load (Awakul ad Ogulaa 2002; Lyeis et al. 2001). I order to compute coveietly ad reduce the computatio load, ode i ad its followig i-j arc are combied to costruct a basic uit of the orgaizatio maagemet chai, expressed by (i,. For those fial cruodes without followig arcs, it is assumed that a followig arc exists. Moreover, both the umber ad the reliability are assumed to be 1. I the basic uit of the orgaizatio maagemet chai, the relatioship betwee cruodes ad arcs is coectio i series. The reliability of (i, is R ij = rr (1) i i-j where R is the reliability of the basic uit (i,, r i is the reliability of cruode i, ad r i-j is the ij reliability of arc i-j. 110 Feg Jigchu et al. Water Sciece ad Egieerig, Dec. 2008, Vol. 1, No. 4, 107-113
4.2 Basic uit ivalidatio probability Accordig to the reliability of the basic uit of the orgaizatio maagemet chai, the ivalidatio probability is P ij = 1 Rij = ri(1 rij - ) + (1 ri) rij - + (1 rij - )(1 ri) (2) where P ij is the ivalidatio probability of a basic uit of the orgaizatio maagemet chai, ad other symbols are the same as i Eq. (1). The basic uits i the orgaizatio maagemet chai are comparatively clear ad idepedet, so, if it is difficult to compute the exact cruode reliability ad arc reliability, the reliability of a basic uit ca be computed directly with the approximate estimatio method, thus makig the computatio of reliability of the maagemet chai more coveiet. At the same time, the umber of basic uits of the maagemet chai is just half of the total umber of cruodes ad arcs, so the computatio load ca be greatly reduced. 4.3 Costructed fuctio of miimum reliability If variable x ij expresses the coectedess of the orgaizatio maagemet rig, the xij = 1 if ( i, is a ormal ope path, ad (3) xij = 0 if ( i, is a abormal ope path Therefore, P(x ij = 1) = R ij is the probability of the orgaizatio maagemet chai i the ormal state, ad P(x ij = 0) = R ij is the probability of the orgaizatio maagemet chai i the abormal state. As the cruodes of the orgaizatio maagemet chai are idepedet, Ex ( ) = 1 Px ( = 1) + 0 Px ( = 0) = R (4) ij ij ij ij where E(x ij ) is the expectatio value of the BULL variable. Therefore, the probability of the orgaizatio maagemet chai i the ormal state is equal to the expectatio value. Suppose that there are S kids of miimum path from l to m, expressed as T, T,, T,, T, which are formed by rigs i series. The formula is 1 2 S T ( x) = Π x (5) ( i, T where T ( x) is the costructed formula of the miimum path, ad x ij is the coectedess of the maagemet rig. From l to m, the costructed formula of the etire orgaizatio maagemet chai ca be expressed as: S S π ( x) = UT( x) = 1-Π 1- Π xij (6) = 1 O the basis of Eq. (6), the formula of the miimum reliability of the orgaizatio maagemet chai ca be costructed as follows: ij Feg Jigchu et al. Water Sciece ad Egieerig, Dec. 2008, Vol. 1, No. 4, 107-113 111
where E π ( x) S S Rmi = E π ( x) = E 1-Π 1- Π xij = 1-Π 1- Π Rij (7) T is the expectatio value of π ( x ). 5 Reliability model of orgaizatio maagemet chai 5.1 Reliability model for series coectio state I Figure 2, the model of the orgaizatio maagemet chai i the series coectio state reflects a uidirectioal maagemet relatioship. This orgaizatio maagemet chai icludes seve basic uits: A, B, C, D, AB, BC ad CD. The miimum path set is x AB x BC x CD x A x B x C x D. Accordig to Eq. (7), the miimum reliability of the orgaizatio maagemet chai i the state of series coectio is show by Eq. (8): S Rmi = E 1 Π 1 Π xij = S E 1-Π ( 1 - xabxbc xcd xxxx A B C D ) = = 1 Ex x x xxxx (8) ( ) AB BC CD A B C D 5.2 Reliability model for mixed state of both series coectio ad parallel coectio I Figure 3, the basic patter of the orgaizatio maagemet chai icludes both series coected relatioships ad parallel coected relatioships. The basic patter of this orgaizatio maagemet chai has ie basic uits: A, B, C, D, AB, BC, CD, AC ad AD. The miimum path set is x x x x x x x, x x x x x, x x x ( ) AB BC CD A B C D AC CD A C D AD A D Accordig to Eq. (7), the basic patter reliability of the orgaizatio maagemet chai i the parallel coectio state ca be obtaied: S Rmi = E 1 Π 1 Π xij = E 1 1 Π xij 1 Π xij 1 Π xij = ( i, T1 ( i, T2 ( i, T3 E xabxbcxcdxaxbxcxd + xacxcdxaxcxd + xadxaxd ( xadxaxd) ( xabxb CxCDxxxx A B C D) ( xabxbcxcdxxxx A B C D)( xacxcdxxx A C D) ( xacxcdxxx A C D)( xadxx A D) + ( xabxbcxcdxxxx A B C D) ( xacxcdxaxcxd)( xadxaxd) (9) 112 Feg Jigchu et al. Water Sciece ad Egieerig, Dec. 2008, Vol. 1, No. 4, 107-113
where = 1, 2, 3, T 1 is the path of x AB x BC x CD x A x B x C x D, T 2 is the path of x AC x CD x A x C x D, ad T 3 is the path of x AD x A x D. 6 Coclusios (1) The reliability of the orgaizatio maagemet chai directly iflueces the key idexes of maagemet order, busiess trasactios, ad iformatio trasfer of the mai body of the SNWDP durig the costructio period. Therefore, it is ecessary to study the reliability of the orgaizatio maagemet chai regardig various relatioships, such as those of govermetal maagemet, cotracts, clietage, supervisio, coordiatio ad guaraty. It is also ecessary to set up calculatio models of reliability so as to coduct quatitative aalysis of each relatioship ad iterface ad to overcome the disadvatages of qualitative aalysis, thus makig maagemet of the SNWDP more scietific. (2) The maagemet chai of the SNWDP durig the costructio period cosists of a orgaizatio maagemet chai, a WBS maagemet chai, ad a maagemet chai that is a mix of the two. This paper describes a study o the reliability of two basic forms of the orgaizatio maagemet chai of the SNWDP. Its priciple ad results ca be used as a referece for studies o the reliability of maagemet chais. (3) This study o the reliability of the series coectio state ad the mixed state of both series coectio ad parallel coectio lays the foudatio for settig up models of, aalyzig ad calculatig the reliability of the orgaizatio maagemet chai of the SNWDP. Ackowledgemets The authors are grateful to the Office of the South-to-North Water Diversio Project Costructio Committee uder the State Coucil. Refereces Awakul, P., ad Ogulaa, S. O. 2002. The effect of attitudial differeces o iterface coflicts i large scale costructio projects: A case study. Costructio Maagemet & Ecoomics, 20(4), 365-377. Che, G. H., Wag, Y. J., ad Ha, G. W. 2004. Reliability-based supply chai costructio. Idustrial Egieerig ad Maagemet, (1), 72-74. (i Chiese) Lyeis, J. M., Cooper, K. G., ad Els, S. A. 2001. Strategic maagemet of complex projects: A case study usig system dyamics. System Dyamics Review, 17(3), 237-260. Wag, X. H., Tog, Q., Zhag, Y. Q., ad Yua, Q. H. 2002. A research o the theory of the chai maagemet model i the eterprise. Joural of Shadog Uiversity of Scieces & Techology (Social Sciece), 4(1), 78-80. (i Chiese) Wu, L. M. 2003. The discussio of maagemet chai theory. Joural of Wuha Polytechic Uiversity, 22(4), 83-85. (i Chiese) Feg Jigchu et al. Water Sciece ad Egieerig, Dec. 2008, Vol. 1, No. 4, 107-113 113