A Model for Assessing Impacts of Small and Medium Enterprises Lack of Systems Engineering Capability on Systems Development Projects

Transcription

1 A Mdel fr Assessing Impacts f Small and Medium Enterprises Lack f Systems Engineering Capability n Systems Develpment Prjects Thmas V. Huynh aval Pstgraduate Schl Mnterey, CA 93943, USA thuynh@nps.edu Xuan-Linh Tran University f Suth Australia Adelaide, SA 500, Australia Xuan-Linh.Tran@unisa.edu.au Abstract. A small and medium enterprise (SME) has systems engineering (SE) capability if it has and applies sund SE prcesses and tls in its wrk. T assess impacts f SMEs lack f SE capability n the perfrmance f a systems develpment prject, we mdel the prject as a netwrk and extend Gherghe and Avamu s quantitative vulnerability assessment mdel t include the netwrk cmplexity and interperability. Cmplexity is reflected by the average degree f the netwrk, and interperability in this wrk is reflected by the mean number f the members f the prject capable f prviding SE capability t the prject. The resulting mdel shws that a criterin fr a successful executin f a system develpment prject may be vilated by the netwrk instability, which depends n the netwrk cmplexity and interperability. Fr illustratin purpses, we apply this apprach t a simplified Australian Defense system develpment prject in which the Australian SMEs play an imprtant rle. ITRODUCTIO A team is needed t execute a prject t develp a prduct/system. In the U.S., Australia, Japan, and Eurpe, as pinted ut in (Huynh and Tran 008), a prject team t develp a system r a prduct fr a custmer (fr example, a Defence rganizatin) nrmally cnsists f a prime cntractr, subcntractrs, and small and medium enterprises (SMEs). The prime cntractr, wh is respnsible fr the delivery f the system the prject is intended t develp and field, respnds t the custmer; the subcntractrs are under cntract t the prime cntractr; and the SMEs can be under cntract t prvide a unique service r prduct t the prime cntractr and/r the subcntractrs. Fr a prject t develp and field a largescale, cmplex system t be successfully executed, all members f the team must have capabilities needed in the develpment f such a system. The lack f a required capability f any team member, in particular the SE capability f the participating SMEs, brings risk t the prject. Systems engineering (SE) capability means applicatin f sund SE prcesses and tls. A prject risk can be failure f the resulting system t prvide the required perfrmance, failure t timely deliver the system, and failure t keep the system develpment cst under cntrl. We assume the prime cntractr r large subcntractrs generally have the required SE capability t effectively execute their prject effrts. If sme f the remaining members, in particular the SMEs, f the team are knwn nt t have adequate SE capability t carry ut their effrts effectively, it will then be necessary t determine impacts f their inadequate SE capability n the prject. We treat a prject as a cmplex system. Whereas there is n generally accepted frmal definitin f a cmplex system (Mitchell 006), a number f definitins have been attempted. A cmplex system is ne in which there are multiple interactins between many different cmpnents. (Weng et al. 999) Within the cntext f this wrk, we cnsider a cmplex system t cnsist f a large number f elements making up the system that interact with each ther. The elements f the system cnsidered in this wrk are the prject team members (cmpanies). A cmplex prject is ne in which

2 there are a large number f cmpanies wrking tgether t develp a system, which itself culd be a large-scale, cmplex ne. The large size f a prject team whse members are all linked thrugh cntracts is a cmplex prject. The view expressed in (Huynh and Osmundsn 006) is that nt nly des the cmplexity f a system induce vulnerability f the system (Gherghe, A. V. and Vamanu 004) but als lacking interperability amng the elements that make up the system degrades the perfrmance f the system. Interperability is the ability f tw r mre systems r cmpnents t exchange infrmatin and t use the infrmatin that has been exchanged. (IEEE 990) Bradly defined, interperability is the ability f systems, units, r frces t prvide services t and accept services frm ther systems, units, r frces, and t use t enable them t perate effectively tgether. (Hura et al. 000) Within the cntext f this wrk, we cnsider interperability as the ability f the different members f a prject team t prvide, receive, and prcess data and infrmatin amng themselves t generate the infrmatin necessary fr the develpment f the system the prject intends t prduce. Whereas this wrk is fcused n SE capability n the part f SMEs needed fr them t interperate with the cmpanies they are interacted with thrugh cntractual bligatin, the apprach in this wrk can be applied t any ther capability required f the cmpanies in a prject team. The presence f bth cmplexity and interperability f a prject precipitates a number f questins: Hw d the cmplexity and interperability measures play? Des a larger, mre cmplex prject require a higher degree f interperability amng the members f the prject t achieve a desired purpse? Or des it matter? On the ne extreme, if a prject has a large degree f cmplexity, but the members f the prject are nt interperable, then will the prject achieve its purpse (t prduce the required system n time and within budget)? On the ther extreme, if a prject has a maximum degree f cmplexity and all the members are interperable, then will the purpse be achieved by the prject? Or will there be a limit t the achievement f the prject? Hw d these measures play against each ther between these tw extremes? We will attempt t answer these questins in the cntext f a defense system develpment prject. Gherghe and Vanamu (004) develp the s-called Quantitative Vulnerability Assessment (QVA) mdel t diagnse the vulnerability f cmplex systems and t dynamically mnitr the time evlutin f the vulnerability f the systems. This QVA mdel makes use f the ntins f classical statistical physics, Thm s structural stability and mrphgenesis (Thm 975, 983), catastrphe thery (Zeeman 977), and system thery (Thm 975). Previusly, the QVA mdel was adpted t assess the perfrmance f a cmplex, distributed fusin ad hc sensr netwrk (Huynh and Osmundsn, 006). In this wrk we adpt and extend the QVA mdel t incrprate cmplexity and interperability and assess the perfrmance f a system develpment prject. Our gals in this paper are: ) Explain ur explratry wrk tward understanding f impacts f cmplexity and interperability n the executin f a system develpment prject. ) Elucidate the develpment f a mdel that results frm the incrpratin f cmplexity and interperability in the QVA mdel. 3) Illustrate the resulting mdel with a simplified Australian Defense system develpment prject in which the Australian SMEs play an imprtant rle. The rest f the paper is rganized as fllws. We describe the systems develpment prject and discuss its representatin as a netwrk. We next cmbine randm netwrk thery (Bllbas, 985; ewman et al. 00) with the Gherghe and Vanamu mdel (Gherghe and Vanamu 004) t incrprate cmplexity and interperability. We then discuss the criterin f prject executin success in the assessment f an Australian defence prject in relatin t SMEs SE capability. We cntinue with a discussin f the impacts f cmplexity and interperability n the prject executin success. Finally, we end with sme remarks. ETWORK MODEL OF PROJECTS A prject is assumed t have participating rganizatins, nt all f which have a

3 relatinship with ne anther. T represent the prject as a netwrk we cnsider the participating rganizatins as the ndes f the netwrk and their mutual relatinships as the links cnnecting the participating rganizatins. Figure shws an example f a prject represented as a netwrk. The netwrk represents a typical structure f a prject team in the U.S., Australia, Japan, and Eurpe. des D and P represent, respectively, a custmer (Defence rganizatin) and the prime cntractr. des Sub, Sub, and Sub3 dente the subcntractrs under cntract t the prime cntractr. Sub is cnnected t Sub_S, Sub_S, and Sub_S3, which represent three SMEs under cntract t supprt Sub. des Sub_S, Sub_S, Sub_S3, and Sub_S4 represent fur SMEs supprting Sub. Sub3 is supprted by the tw SMEs represented by des Sub3_S and Sub3_S, supprted by three SMEs. te that the custmer and the prime cntractrs can als be supprted by SMEs, depicted by S_D, S_D, P_S, and P_S. The links dente the relatinships respnsibility, cmmunicatin, interperability, etc. amng the different ndes. Links als exist amng the SMEs, such as the link between Sub_S3 and Sub_S. Figure. A netwrk f team members in a simplified prject (Huynh and Tran 008) MODEL DEVELOPMET System Cmplexity Representatin. If the size f a prject is a factr f cmplexity, then cnnectivity amng the cmpanies (prject team members) reflects the cmplexity f the prject. Tw cmpanies are cnnected if ne has a capability t meet the needs f the ther, and that is nt always certain. One can never be certain that a prject team frmed ab initi will functin as desired. Relatinships amng the team members can be influenced by plitics, plicy (dictated by Defence), budget, incrrectly assessed capabilities, cmplicated (pssibly unpredictable) relatinships (thus interdependencies) amng the cmpanies (Hass, 008). Cmplexity f a prject can thus be assessed thrugh its structure (i.e., its degree) and interdependencies amng the members f the prject and the level f uncertainty in the relatinships amng the cmpanies. There is thus an element f stchasticity f frming a prject with the SMEs and the prime and subcntractrs. T discuss mdelling in general terms, we cnsider a system f elements (which are the cmpanies in this case). Every pair f elements is assumed t be cnnected with a cnstant prbability p c. It represents the prbability that tw rganizatins are in a cntractual bligatin. We assume randmness when the prject is frmed, when we wuld nt knw which SMEs are ging t be tied t which ther rganizatins; that is, cnnectivity amng the prject members is nt knwn a priri. Fr instance, a culture clash that can happen after the cntract is signed can result in a severed relatinship (cnnectivity). Let I,, 3,, be the index set. Let L be the number f links element i i has with L ther elements, i i I. L, knwn i as the degree f element i (ewman et al. 00), fllws a binmial distributin with parameters p c and (Bllbas 985). The prbability that nde i has degree is then given by P: P( Li ) pc pc. () Emplying the ntin f cmplexity and the ntatins used in (Aslaksen 004), let dente the cmplexity f the system, defined as the mean number f links supprted by an element f the system, P. A simple 0

4 cmputatin, using (), leads t p. () c is thus a measure f cnnectivity f the system; the mre cmplex the system is, the higher the value f. It is als knwn as the average degree f the system (ewman et al. 00). System Interperability Measure. Interperability amng the cmpanies in a prject exists when they each have capabilities t supprt each ther in the executin f the prject. In this wrk interperability between SMEs and the larger cmpanies they supprt is f interest; and f particular interest is interperability that requires the SMEs t have SE capability t supprt the effrt f the cmpanies t which they are cnnected. We can think f each element as having a s. A (+)- spin, dented by s, where, spin element is interperable with any ther (+)-spin element; it is nt interperable with a ()-spin element. Likewise, tw ()-spin elements are nt interperable. In this wrk, elements are cmpanies. Tw cmpanies which have SE capabilities that allw the tw t wrk tgether are said t have (+)-spins. After the team is frmed we may learn that certain members d nt have the SE capability as advertised; in this case, these members have (- )-spins. Let ps be the prbability that an element has a (+)-spin; p s is assumed t be cnstant. Let Y be the number f (+)-spin elements. Then Y fllws a binmial distributin with parameters and p, and, k k hence, PY k ps ps k, which is the prbability that k elements are interperable. Let dente the interperability f the system (prject), defined as the mean number f interperable elements in the system, n0 kp k leads t. A simple cmputatin then p. (3) s Stability f Cmplex and Interperable Systems. Let each element be identified by its degree and spin, i.e., by a dublet, (,) s, where,, and s,. An element is said t be in state if (i.e., its average degree is at least equal t ) and s. It is in state, if either ( and s ) r ( 0 and s ). Let X and X dente the elements in state and state, respectively. Clearly, X X. (4) Adpting the quantitative vulnerability assessment (QVA) mdel (Gherghe and Vanamu 004) and its assciated ntatins, we nw describe the dynamics f the system. Let X, X dente the state f the system. The state f the system wuld underg a smallest transitin accrding t the prcess X, X X, X X, X (5) where and are the state transitin prbabilities. Specifically, is the prbability that the number f elements in state is decreased by ne and that in state is increased by ne; is the prbability that the number f elements in state is decreased by ne and that in state is increased by ne. The prcess (5) admits a distributin functin f the system state, f X, X, which satisfies the master equatin f X, X X, X f X, X t X, X X, X f X, X X, X f X, X (6) Let dente the s-called membership fractin (Gherghe and Vanamu 004), defined by X X. (7) Thus, if the elements f the system are

5 all in state ; and if the elements f the system are all in state. Using (7), we can equivalently represent the X, X state f the system as X, X. X, X It then fllws frm (6) that f f t f. (8) f In the asympttic apprximatin, is assumed t be large, and a series expansin f the righthand side f (8) in up t and including the secnd rder in turns (8) int f J. (9) t where J f f.(0) The statinary states f the system are btained f by setting 0. It then fllws frm (9) t J that 0, which implies J is cnstant. A particular slutin is J 0, in which case, (9), upn integratin, yields dz / e f C. () The cnstant C is determined frm the / d. nrmalizatin cnditin f / Cperative phenmena frequently ccur in many-particle systems exhibiting rdered structures. In physics, cperative phenmena are caused by interactins f a great number f particles such as electrns, atms, etc. (Zwicky 943); a cperative transitin invlves a simultaneus, cllective change f state f the atms and/r electrns in the entire system (Clark 994). In this wrk, assuming the state transitins are a cperative phenmenn (Gherghe and Vanamu 004), we write X e X e U V U V () where is a cnstant, U is the cupling cnstant, V is the influence field, and is a generalized temperature f the system. As pinted ut in (Gherghe and Vanamu 004), the cnstant U, an intrinsic parameter, reflects the degree f interactin amng the elements; the influence field V, an extrinsic parameter, represents the external influence n all elements f the system; and the space f all system states wuld vary with the generalized temperature. The significance f the generalized temperature as it pertains t this wrk will be addressed later in the paper. w, the values f at which f ( ) is ptimum cnstitute the space f all pssible states f the system and are btained f frm 0, which, by virtue f () and (), yields U V cth U. (3) Since is assumed t be large, the state f the system, nw dented by UV,,, is btained frm U V tanh, (4) which is (3) in the large- limit. The system cnditin depends n the number f real rts f (4), which depends n the degree f interactin between the system elements, reflected by the cupling cnstant U, the influence field V, and the generalized temperature f the system (Gherghe and Vanamu 004). Fllwing is a summary f the dependence f the system cnditin n the number f real rts (Gherghe and Vanamu 004): ) One real rt: The system is stable (i.e., f

6 lw and/r acceptable vulnerability.) The ppulatin membership transitins smthly between state and state. ) Three real rts with tw being identical: The system is critically vulnerable. Sharp transitins in membership between states and are pssible. Either state r state may suddenly becme imprbable. 3) Three distinct real rts: The system is unstable (i.e., dangerusly/unacceptably vulnerable.) Sharp transitins in membership between states and are pssible. The frequencies f ccurrence f states and are cmparable. The intermediate rt is generally taken as having n physical meaning and is therefre discarded. In ur wrk, the interactin amng the elements in the system is manifested thrugh interperability f the elements. The cupling cnstant U is thus taken t be assciated with the system interperability measure,. Tw cmpanies in the netwrk (prject) are cnnected if they are under mutual cntractual bligatins. V is taken t be related t the system cmplexity measure,. Instead f using UV,,, as dne in (Gherghe and Vanamu 004), we describe the state f an interperable, cmplex system by,,. Then (4) becmes tanh. (5) w, the mapping x accrding t x transfrms (5) int tanh x x. (6) An analytic diffemrphism (, ), tanh x can be expanded in a Taylr series as tanh x x x 3 x 5 x x 3 x 5, which, tgether with (6), yields 3 3 x x 6 0. (7) The nature f the rts f (7) depends n the sign f 3, (8) : 3 as fllws: ) If 0, then ne rt is real and the thers are a pair f cmplex cnjugate rts. ) If 0, then all rts are real and at least tw are equal. 3) If 0, then all rts are real. It then fllws frm (8) that the system is stable if either (i) and n cnstraint n the rati r (ii) bth and. (9) / The system is critically vulnerable r dangerusly/unacceptably vulnerable if (9) is vilated. The values f reflecting the stability criterin are then given by / / (0) As afrementined and discussed in (Gherghe and Vanamu 004), the generalized temperature wuld be used t set a cnvenient range fr the parameters U and V. In this wrk, the value f the generalized temperature is used t bund the system cmplexity and interperability. Specifically, given a value f the prbability f interperability, p s, and the prbability f cnnectin, p, the generalized temperature c must be fixed fr a desired size f the netwrk. Alternatively, what is the value f the rati fr all pssible cmbinatins f p c and p s? Fig., displaying the sensitivity f the stability

7 f the prject t, shws that, which reflects the stability criterin (0), reaches stable values fr Fr a prject size, the generalized temperature will thus be chsen t satisfy the cnditin te that, in the case f stability, there is n cnstraint n the rati f the system cmplexity measure t the system interperability measure,, and, therefre, n the rati f the prbability f cnnectin t that f interperability between tw elements, p c ps. In assessing the perfrmance f an interperable, cmplex system r that f a prject, we must thus take int accunt (9) and (0), as we will d s in the fllwing sectin. Figure. The sensitivity f the membership fractin f the prject t θ/. AUSTRALIA DEFECE PROJECT PROBLEM As discussed abve, an Australian defence prject is mdelled as a netwrk. We assume the prject requires K team members with the required SE capability. Recall frm abve that X dentes the team members in state (i.e., they are cnnected and have the required SE capability.) Fr the prject t be successfully executed, they must be at least equal t K,. i.e., X K. Frm (4) and (7) it fllws that X. A successful executin f the prject thus requires that K r () where dentes the standard ceiling functin K and is the percentage f the team with SE capability. Sme interperability, cnditin may nt be met, and the required number f team members that have the required SE capability therefre may nt be achieved, hence the failure f the prject. That is, nt all values f wuld satisfy () and, hence, wuld allw a successful prject, because f the instability f the netwrk resulting frm the system (prject) cnditins that depend n the values f the cmplexity and interperability parameters. We must therefre take int accunt (9) and (0) when we assess the perfrmance f the prject accrding t the criterin (). Fig. 3 displays the interperable membership fractin as a functin f the interperability measure fr three values f the prject cmplexity measure. The dashed line represents the value f required fr a successful executin f the prject. Recall that the cmplexity measure reflects the average degree f the netwrk, i.e., the cnnectivity amng the the members sf the prject. As shwn in Fig. 3, fr a prject with a small cmplexity measure f 0.3, it must have a high measure f interperability f 0.9 fr the prject t meet the required percentage f Fr a prject with a medium cmplexity measure f 0.5, a prject can have a minimum measure f interperability f 0. fr the prject t meet the required percentage f Fr a prject with a large cmplexity measure f 0.7, the success f the prject is nt highly dependent n the interperability measure. Thus, if the members f a prject team are fully cnnected and wrk as a chesive team, the members with lw SE capability r nnexistent capability will nt impact the perfrmance f the prject. But, if the prject team is sparsely cnnected (e.g., the SMEs are cnnected t a few larger cmpanies in a prject), then the SMEs must have the required SE capability. If

8 the cnnectivity cnditin f the prject team falls between these tw extreme situatins, then the required SE capability and the interperability requirement can vary. Figure 3. Interperable membership fractin as a functin f the interperability and cmplexity measures COCLUSIO As an explratry effrt in understanding system cmplexity cupled with interperability, we extend the quantitative vulnerability assessment (QVA) mdel by Gherghe and Avamu (004) t incrprate tw parameters representing cmplexity and interperability. In this wrk cmplexity is reflected by the average degree f the system, and interperability by the mean number f interperable elements. Fr illustratin, we cnsider the prblem f assessing the perfrmance f the prject described abve. The mdel shws that the criterin fr successful prject executin may be vilated by the instability f the system resulting frm the system cnditins that depend n the system cmplexity and interperability. In ur future wrk we will assume a nncnstant prbability f p c and ps and als cnsider system cmplexity factrs ther than the average degree f cnnectivity. In additin, if real wrld data n prjects were available, we wuld explre the validatin f the mdel with the data. Finally, we will explre the feasibility f extending this research t gaining insights int systems integratin. REFERECES Aslaksen, E.W. System Thermdynamics: A Mdel Illustrating Cmplexity Emerging frm Simplicity, Systems Engineering, Vl. 7,. 3, 004, pp B. Bllbas, Randm Graphs, Academic Press, ew Yrk (985). F. Zwicky, On Cperative Phenmena, Phys. Rev., Vl. 43, 943, pp Gherghe, A. V. and Vamanu, D. V., Twards QVA Quantitative Vulnerabiltiy Assessment: A Generic Practical Mdel, Jurnal f Risk Research, Vl. 7, umber 6, 004, pp Hass, K. B. Managing Cmplex Prjects Is t a Simple Matter, PM Wrld Tday, Vl. X, Issue III, March 008, pp. -6. Hura, M., McLed, G., Larsn, E. V., Schneider, J., Gnzales, D., rtn, D. M., Jacbs, J., O'Cnnell, K. M., Little, W., Mesic, R., and Jamisn, L., Interperability: A Cntinuing Challenge in Calitin Air Operatins, Rand Crpratin Reprt MR-35-AF, 000. Huynh, T. V. and Osmundsn, J. S. A Mdel fr Assessing the Perfrmance f Interperable, Cmplex Systems, Prceedings f Cnference n Systems Engineering Research, 7-8 April 006, University f Suthern Califrnia, Ls Angeles, CA. Huynh, T. V. and Tran, X.-L., Applicatin f Orthgnal Array Experiment t Optimal Funding Allcatin in Prjects, Prceedings f Asia-Pacific Cnference n Systems Engineering (APCOSE), September -3, 008, Ykhama, Japan. Institute f Electrical and Electrnics Engineers. IEEE Standard Cmputer Dictinary: A Cmpilatin f IEEE Standard Cmputer Glssaries. ew Yrk, Y: 990. Mitchell, M., Cmplex Systems: etwrk Thinking, Artificial Intelligence, Vl. 70, 8, pp. 94, 006. ewman, M. E. J., Strgatz, S. H., and Watts, D. J., Randm graphs with arbitrary degree distributins and their applicatins, Preprint arxiv:cnd-mat/ v 7 May 00. Thm, R., Mathematical Mdels f Mrphgenesis, Ellis Hrwd Limited Publishers, Chichester, 983. Thm, R., Structural Stability and

9 Mrphgenesis, Benjamin/Cummings Publishing Cmpany, Inc., 975. Weng, G., Bhalla, U. S., and Iyengar, R., Cmplexity in Bilgical Signaling Systems, Science, April 999, pp Zeeman E.C., Catastrphe Thery, Addisn- Wesley, 977. BIOGRAPHY Thmas V. Huynh btained simultaneusly a B.S. (Hns) in Chemical Engineering and a B.A. in Applied Mathematics frm UC Berkeley and an M.S. and a Ph.D. in Physics frm UCLA. He is an assciate prfessr f systems engineering at the aval Pstgraduate Schl in Mnterey, CA. His research interests include uncertainty management in systems engineering, cmplex systems and cmplexity thery, system scaling, simulatin-based acquisitin, and system-fsystems engineering methdlgy. Prir t jining the aval Pstgraduate Schl in 003, he was a Fellw at the Lckheed Martin Advanced Technlgy Center in Pal Alt and Sunnyvale, CA, where he engaged in research in cmputer netwrk perfrmance, cmputer timing cntrl, bandwidth allcatin, heuristic algrithms, nnlinear estimatin, perturbatin thery, differential equatins, and ptimizatin. While he spent 3 years in the aerspace industry, he was als teaching part-time in the departments f Physics and Mathematics at San Jse State University. Dr. Huynh is a member f ICOSE. Xuan-Linh Tran received a B.S. in Applied Mathematics and Cmputer Science frm the University f Adelaide, Australia, and an M.S. in Infrmatin Technlgy frm the University f Suth Australia, Australia. She is currently wrking tward her Ph.D. degree at the University f Suth Australia. Her Ph.D. research is in systems engineering prcesses and tls fr Australian Small and Medium Enterprises in defence. Befre starting her Ph.D. prgram, Xuan-Linh wrked at Defence and Systems Institute (DASI) at the University f Suth Australia as a Research Assciate, cnducting research in requirements engineering and sftware test and evaluatin. Prir t jining DASI, she wrked as sftware develper at Metr Meat Ltd, Adelaide, Australia, and at TP Data AB, Malm, Sweden. Xuan-Linh is a member f ICOSE.