Allocating Risk Dollars Back to Individual Cost Elements

Transcription

1 Allocatg Rsk Dollars Back to Idvdual Cost Elemets Stephe A. Book Chef Techcal Offcer MCR, LLC (0) x 0th Aual DoD Cost Aalyss Symposum Wllamsburg VA -6 February MCR, LLC Approved for Publc Release

2 Abstract Asymmetry of rsks ad opportutes for most WBS elemets leads users of commo estmatg methods, such as "rollg up" (.e., addg) most-lkely costs of the varous elemets ad labelg that sum the pot estmate, to uderestmate actual program cost. Ucertates actual costs make t useful to model costs as radom varables ad to express program cost estmates terms of percetles of ts probablty dstrbuto. After the pot estmate of the program s cost s determed by whatever method ad defto are cosdered approprate, t s sesble to establsh a "maagemet reserve" of addtoal fuds to overcome uatcpated cotgeces due to rsks ad other cotgeces that may threate to deplete the budget pror to program completo. Percetles of the total-cost probablty dstrbuto ca serve as gudeles for the sze of a approprate maagemet reserve. If the pot estmate falls at the 0th percetle level of the cost probablty dstrbuto, a prudet maagemet reserve ca be establshed by addg addtoal dollars to the pot estmate a amout that s requred to brg the total amout of avalable dollars to the 50th, 70th, or eve 80th percetle, depedg o the crtcalty of the program. These addtoal dollars are ofte referred to as rsk dollars. Rsk dollars the maagemet reserve pool, ever very popular amog fuders, occasoally costtute a otceably large percetage of the pot-estmate-based caddate fudg base. Eve f that s ot the case, fudg orgazatos are typcally reluctat to set asde large amouts of moey for maagemet reserve, belevg that such pots of slush fuds lead to sloth, waste, effcecy, ad geerally slack maagemet. It s therefore ecessary to provde logcal ustfcato for such requests by dsplayg a defesble way a allocato of the requested rsk dollars amog the varous cost elemets. Ths presetato suggests a mathematcal procedure that allows the aalyst to allocate rsk dollars amog program elemets a maer that s logcally ustfable ad cosstet wth the orgal goals of the cost-estmatg task. Because a WBS elemet s eed for rsk dollars arses out of the asymmetry of the ucertaty the cost of that elemet, a quattatve defto of eed must be the logcal bass of the rsk-dollar computato. I geeral, the more rsk there s a elemet s cost, the more rsk dollars wll be eeded to cover a reasoable probablty (e.g., 0.70) of beg able to complete that elemet of the program. Correlato betwee rsks must also be take to accout to avod double-bllg for correlated rsks or suffcet coverage of solated rsks.

3 Cotets What Are Rsk Dollars? What s Your Pot Estmate? What Level of Cofdece Do You Need? Why Allocate Rsk Dollars? The Poltcal Reaso The Proect-Maagemet Reaso How Should We Allocate Rsk Dollars? The Dfferece betwee Ucertaty ad Rsk How May Rsk Dollars Does Each WBS Elemet Need? Summary

4 Cotets What Are Rsk Dollars? What s Your Pot Estmate? What Level of Cofdece Do You Need? Why Allocate Rsk Dollars? The Poltcal Reaso The Proect-Maagemet Reaso How Should We Allocate Rsk Dollars? The Dfferece betwee Ucertaty ad Rsk How May Rsk Dollars Does Each WBS Elemet Need? Summary

5 The Term Pot Estmate Must be Formally Defed A Necessty f the Pot Estmate s to Serve as a Bass to whch Rsk Dollars wll be Appeded By Pot Estmate, Do You Mea the Most Lkely Cost? ( Mode ) 50th-Percetle Cost? ( Meda ) Expected Cost? ( Mea ) the Roll-Up of Most Lkely Costs of Each WBS Elemet? Somethg Else? Whe Estmatg Costs of Complex Hardware ad/or Software Systems, These Numbers are Almost Always Dfferet (Especally the Somethg Else ) To Illustrate the Ideas, Ths Dscusso Wll Cosder the Pot Estmate to be the Roll-Up (.e., Sum ) of the WBS-Elemet Most Lkely Costs 5

6 The Roll-Up Pot Estmate Pctures WBS- ELEMENT TRIANGULAR COST DISTRIBUTIONS MERGE WBS-ELEMENT COST DISTRIBUTIONS INTO TOTAL-COST NORMAL DISTRIBUTION* Most Lkely $ Most Lkely... $ ROLL-UP OF MOST LIKELY WBS-ELEMENT COSTS $ MOST LIKELY TOTAL COST Most Lkely $ Note: The roll-up of WBS elemet most lkely costs s ot equal to the most lkely total cost. * Whe the Number of WBS Elemets s Large 6

7 Whe WBS Elemets Are Few... WBS-ELEMENT TRIANGULAR COST DISTRIBUTIONS MERGE WBS-ELEMENT COST DISTRIBUTIONS INTO TOTAL-COST LOGNORMAL DISTRIBUTION Most Lkely $ Most Lkely... $ ROLL-UP OF MOST LIKELY WBS-ELEMENT COSTS MOST LIKELY TOTAL COST $ Note: The roll-up of WBS elemet most lkely costs s stll ot equal to the most lkely total cost. Most Lkely $ 7

8 Rsk Dollars Amout of Addtoal Dollars (beyod the Pot Estmate) Requred to Fud Program at a Approprate Level of Cofdece If Pot Estmate s the Roll-up of Elemets Most Lkely Costs, Lots of Rsk Dollars Wll Be Needed to Reach 50% Cofdece Level ad Eve More to Reach 80% Level If Pot Estmate s the Most Lkely Total Cost, Some Addtoal Rsk Dollars Wll Usually Be Requred to Reach 50% Cofdece Level ad Some More Wll be Needed to Reach 80% Level If Pot Estmate s the 50th-percetle Cost, Addtoal Rsk Dollars Wll Be Requred to Reach 80% Cofdece Level If Pot Estmate s the Expected Cost, Addtoal Rsk Dollars Wll Be Requred to Reach 80% Level Pot Estmates Ca be Selected for other Characterstcs Sometmes Called Maagemet Reserve (Seergly) Slush Fud 8

9 Cotets What Are Rsk Dollars? What s Your Pot Estmate? What Level of Cofdece Do You Need? Why Allocate Rsk Dollars? Why Allocate Rsk Dollars? The Poltcal Reaso The Proect-Maagemet Reaso How Should We Allocate Rsk Dollars? The Dfferece betwee Ucertaty ad Rsk How May Rsk Dollars Does Each WBS Elemet Need? Summary 9

10 Why Allocate? Your Request to Fudg Authorty Our Pot Estmate s $ΩM, but We Also Foresee a Need for $ΘM as Maagemet Reserve Commo Resposes from Fuders What? Do t You Kow How Much Your Program s Gog to Cost? Do You Eve Kow How You are Gog to Maage the Program? That s a Rather Large Slush Fud - What Are You Gog to Do Wth It? Your Aswer We are Pushg the State of the Art a Number of Techology ad Software Areas ad There are Several Other Rsk Issues Due to the Iovatve Nature of Ths Program. I ll Show You How We Pla to Use Our Maagemet Reserve to Maage the Varous Rsk Issues ad Make Our Program Executable. 0

11 How Wll the Rsk Dollars Actually Be Spet? Not the Way You Thk After All, They re Rsk Dollars They ll Be Spet o Rsks that Tur Out to Be Crtcal All the Rsk Dollars Must be Retaed by the Program Maager Utl Specfc Need Materalzes That s Why t s Called Maagemet Reserve The Why are We Dog the Allocato Now? We re Not Really Allocatg the Moey Now We re Merely Proposg that Some (or All) WBS Elemets May Need Extra Moey Proporto to Ther Rskess We are Makg that Extra Moey Part of our Cost Estmate The Race Is Not to the Swft, or the Battle to the Strog,... (Ecclesastes, 9:), but That s the Way to Bet

12 Cotets What Are Rsk Dollars? What s Your Pot Estmate? What Level of Cofdece Do You Need? Why Allocate Rsk Dollars? The Poltcal Reaso The Proect-Maagemet Reaso How Should We Allocate Rsk Dollars? The Dfferece betwee Ucertaty ad Rsk How May Rsk Dollars Does Each WBS Elemet Need? Summary

13 Roll-Up Issues Impact Rsk-Dollar Allocato Method Mathematcal Facts Most-Lkely Proect-Elemet Costs Do Not Sum to Most Lkely Total Proect Cost th Percetles of Proect-Elemet Costs Do Not Sum to th Percetle of Total Proect Cost If Proect-Elemet Costs are Correlated, the Correlatos Must be Take to Accout whe Summg Elemet Costs (usually by Mote Carlo) to Obta the Dstrbuto of Total Proect Cost These Mathematcal Facts Guaratee that There s o Smple Way (or eve a Uque Rght Way) to Allocate Rsk Dollars Back to the WBS Elemets

14 To Allocate the Rsk Dollars Calculate Total Amout of Rsk Dollars Requred 50 th Rsk$ 50 th -percetle Total Cost, Mus Roll-Up; or 80 th Rsk$ 80 th -percetle Total Cost, Mus Roll-Up Of Course, Other Percetles (70 th,, 90 th, etc.) May Be Cosdered Approprate for a Proect, as Well as Other Deftos of the Pot Estmate Allocato of Rsk Dollars to Proect Elemets Must Put Rsk Dollars Where They are Needed We Must Defe a Elemet s Need Order to Determe How May Rsk Dollars are Needed Need Dollar Need of Proect-elemet (to Be Defed Precsely Later) Corr Correlato Betwee Rsk-dollar Requremets of Proect Elemets ad

15 Our Specfcatos o the Rsk-Dollar Allocato Procedure. Those WBS Elemets Havg More Cost Rsk Shall be Allocated More Rsk Dollars, Relatve to ther Pot Estmates. Iter-Elemet Correlato Shall be Take to Accout whe Calculatg a Elemet s Rsk- Dollar Allocato Correlated Elemets Shall Share Rsk Dollars Rsk Dollars Shall ot be Double-Allocated. The Rsk-Dollar Allocato Shall Not Result a WBS-Elemet s Estmate Beg Reduced Below ts Pot Estmate Ths Meas that Rsk Dollars Shall Not be Subtracted from a Pot Estmate Therefore the Fewest Possble Number of Rsk Dollars Allocated to ay WBS Elemet wll be Zero 5

16 Impact: No Elemet s Estmate s Reduced Below ts Pot Estmate 50th Percetle Estmate 80 th Percetle Estmate Pot Estmate The Rsk-Dollar Allocato Shall Not Result a WBS-Elemet s Estmate Beg Reduced Below ts Pot Estmate Eve f The Pot Estmate Exceeds the 50 th Percetle Estmate The Pot Estmate Exceeds the 80 th Percetle Estmate 6

17 Example: System X WBS-Elemet Tragular Cost Dstrbutos Atea 0.0. Facltes* Evrometal Cotrol Electrocs Power Dstrbuto Commucatos Platform 6. Computers * Vertcal scale (probablty desty) dfferet ths graph oly Software 7

18 System X Tragular Dstrbutos WBS Elemet L M H Mea** Sgma. Atea Electrocs Platform Facltes Power Dstrbuto Computers Evrometal Cotrol Commucatos Software SUMS 50* 756** 79.* * Pot Estmate (Not the Same as the Most Lkely Total Cost) ** Mea Expected Cost (Note: Sum of WBS-Elemet Meas s Equal to the Total-Cost Mea.) 8

19 System X Iter-Elemet Correlatos Correlato Matrx WBS Elemet WBS Elemet

20 Computato of Total Cost Stadard Devato ( T ) WBS Elemet L M H Mea** Sgma WBS Elemet Atea. Electrocs. Platform. Facltes 5. Power Dstrbuto 6. Computers 7. Evrometal Cotrol WBS Elemet Commucatos Software SUMS * * Use the WBS-Elemet Sgma Values ad the Iter-Elemet Correlatos to Compute T : T

21 System X Total-Cost Percetles (as Output by Crystal Ball ) Probablty Desty Mote Carlo Statstcs Value Trals 0000 Mea,79.95 Meda, Std Dev 87.8 Rage M Rage Max,09.8 Rage Wdth,65.59 System X Total-Cost Frequecy Dstrbuto 68.59,67.5,850.7,.7, Percetle Cost 0% %,00.6 0%,5.05 5%,6.75 0%,00.9 5%, %,9.55 5%,50.8 0%, %, %, %, %,8.7 65%,9.6 70%, %, %,8.7 85%, %,. 95%,6.7 00%,09.8

22 Rsk-Dollar Defto COST-ELEMENT TRIANGULAR DISTRIBUTIONS MERGE ELEMENT COST DISTRIBUTIONS INTO TOTAL-COST DISTRIBUTION 80% PROBABILITY L B H $ L B H $... L B H $ POINT ESTIMATE (ROLL-UP OF MOST LIKELY WBS-ELEMENT COSTS) RISK DOLLARS $ 80th PERCENTILE COST Notes:. Addto of rsk dollars creases cofdece that total estmate (pot estmate plus rsk dollars) s suffcet to execute program.. Pot estmate may also be chose to be the 50 th Percetle ( Meda ), Expected Cost ( Mea ), or Most Lkely Cost ( Mode ), as well as the Roll-Up Estmate.

23 Statstcal Facts About Rsk Impact of Rsk o Cost s Modeled as Ucertaty Cost Ucertaty Cost Meas That Cost Dstrbutos Rage Over Wde Itervals More Ucertaty Meas a Wder Rage Less Ucertaty Meas a Narrower Rage Sgma (), or Stadard Devato, the Statstcal Measure of Rage of Cost Dstrbuto, Is Uversal Measure of Ucertaty Questo: Is a Good Measure of Rsk?

24 How Does Measure Ucertaty? s the Mea (.e., Average ) Squared Dstace from the Mea of the Dstrbuto ( ) ( ) xμ f x dx where μ Mea ( Expected Value ) of Dstrbuto f(x) Probablty Desty Fucto If Iter-Elemet Correlatos are Zero TOTAL k k K If Correlato Betwee Proect Elemets ad TOTAL k k

25 5 Algebrac Aalyss of the Total Cost Stadard Devato Larger Imples More Ucertaty, Whch Tur May Imply Greater Need for Rsk Dollars Cosder the Followg Algebrac Rearragemet of the Total-Cost Value: Let s See What the Algebrac Rearragemet Meas the Case of WBS Elemets k k k kk k k k kk k k TOTAL

26 6 Total Cost Stadard Devato for WBS Elemets, Chart of k k k kk k k TOTAL

27 7 Total Cost Stadard Devato for WBS Elemets, Chart of ( ) ( ) ( ) k k TOTAL ) ( ) ( ) (

28 8 Total Cost Stadard Devato for WBS Elemets, Chart of ( ) k k TOTAL ) ( ) ( ) ( Porto of Total Cost that s Assocated Wth WBS Elemet

29 Try Ths: Use Values to Allocate Rsk Dollars Based o Ucertaty Cosder the Followg -Elemet Verso of the Represetato of the Total-Cost Value, the - Elemet Verso of whch Appears o the Prevous Chart: TOTAL The Porto of the Total-Cost Value that s Assocated, ether Drectly or va Correlato, wth WBS Elemet k s Gve by the Followg Expresso: ASSOC( k ) k k 9

30 -Based Allocato Formula Ucertaty Base TOTAL Fracto of Rsk Dollars to be Allocated to Elemet k Should Therefore be: ASSOC( k ) TOTAL Amout of Rsk Dollars to be Allocated to Elemet k s Therefore k k k k Total Amout of Ucertaty Porto for Ucertaty Base Rsk Dollars k 0

31 Now for the Bad News Ufortuately, Ths Clever Procedure s No Good* as a Measure of Ucertaty Caot Dstgush Betwee Hgh-Ed Rsk ad Low-Ed Ucertaty 50th vs. 50th PE 80th Both Dstrbutos Have the Same Value, but the Oe o the Left (wth the Hgh-Ed Rsk) Needs Lots of Rsk Dollars to Reach ts 50 th Percetle ad Eve More to Reach ts 80 th Percetle The Oe o the Rght s More tha Fully Fuded to ts 80 th Percetle by ts Pot Estmate (PE) *Of course, that wo t stop people from usg t! 80th PE

32 Ths Problem wth s Not New C.-C. Ho ad W. Che (Iteral Reveue Servce), Selected Sem- Varace Estmators of Uderreportg Nofarm Sole Propretor Icome, Proceedgs of the Amerca Statstcal Assocato, Secto 8, 996, pages Full varace cosders extremely hgh ad extremely low uderreported recepts or overstated expeses equally udesrable. Sem-varace, o the other had, measures devatos from the mea for observatos below or above the mea. (page 98) We exted the sem-varace estmators descrbed above to a covarace cotext ad develop a sem-varace based correlato coeffcet betwee a par of a selected half of X ad a selected half of Y. (page 99) B.J. Jacobse (Chef Ecoomst, Captal Markets Cosultats, Mlwaukee WI), Mea-Sem-Varace Effcet Froter, 7 pages. Ths result s crtcally depedet o vestor utlty beg a fucto of the stadard devato (or varace) of returs. But why should rsk be defed such a way? Itrospecto would suggest that vestors are prmarly cocered about losg moey, ot makg moey. To take ths behavoral cosderato to accout, we foud the mmal semstadard devato of returs. (pages -)

33 Let s Look at the Need of WBS Elemet k for Rsk Dollars Calculated Need of Ay WBS Elemet s Based o ts Probablty of Overrug ts Pot Estmate (whch here s ts Most Lkely Cost Mode) A Elemet that Has Prepoderace of Probablty Below ts Pot Estmate (such as the dstrbuto o the left) Has Lttle or No Need Proposed Defto of Need of Proect Elemet k at the 80 th Percetle Level Need k 80 th Percetle Cost Mus Pot Estmate Need k 0 If Pot Estmate Exceeds 80 th Percetle Cost 80th 50th 50th Need k 0 Most Lkely Most Lkely Need k >> 0 80th

34 Need-Based Allocato Formula Total Need Base (Aalogue of Total-Cost ) Need Base Need Need Need Porto for Proect Elemet k (Aalogue of Porto of Total-Cost that s Assocated wth Elemet k) k Need Need k Rsk Dollars Allocated to Proect Elemet k ( k Need Need k Base) Rsk Dollars A percetage of total rsk dollars Now We Have to Calculate the Need of Each WBS Elemet

35 Tragular Cost Dstrbuto 50% Desty DENSITY L M H $ Cost Probablty Desty Fucto Three Parameters L, M, H Completely Specfy Dstrbuto Mea, Meda, Mode, Sgma, All Percetles ca be Expressed Terms of L, M, ad H 5

36 Expected Value ad Percetles of Tragular Dstrbutos Expected Value L M H p th Percetle T p Dollar Value at whch { } p P Cost T p L p ( M L)( H L) f p M H L L H ( p)( H L)( H M ) f p M H L L 6

37 Example: 50 th ad 80 th Percetles of Usual Tragular Dstrbutos WBS Elemets that May Very Well Need Rsk Dollars at Both the 50 th ad 80 th Percetle Levels Have Tragular Dstrbutos Shaped Lke Ths: 50% L M H Dstrbutos Lke Ths Have M-L < (.50)(H-L) ad, of course, M-L < (.80)(H-L). Therefore 50 th Percetle T th Percetle T.80 H H $ Cost (.50 )( H L)( H M ) (.0 )( H L)( H M ) 7

38 WBS-Elemet Need Calculated for the Case M-L < (.50)(H-L) At the 50 th -Percetle Level Need > 0 Always f the Most Lkely Cost s Take as the Pot Estmate Need 50 th - Percetle Elemet Cost, Mus Most Lkely Elemet Cost Need H (. 50)( H L)( H M) M At the 80 th -Percetle Level Aga, Need > 0 Always ths Stuato Need 80 th - Percetle Elemet Cost, Mus Most Lkely Elemet Cost ( )( )( ) Need H.0 H L H M M 8

39 Example: 50 th ad 80 th Percetles of Other Tragular Dstrbutos WBS Elemets that Probably Do t Need Rsk Dollars at the 50 th, but Mght or Mght Not Need Them at the 80 th Percetle Level, Have Tragular Dstrbutos Shaped Lke Ths: 50% L If Dstrbutos Lke Ths Have M-L > (.80)(H-L),80 th Percetle T.80 L (.80 ) Cost ( M L)( H L) If Dstrbutos Lke Ths Have M-L < (.80)(H-L), 80 th Percetle T.80 H (.0)( H L)( H M) M H 9

40 WBS-Elemet Need Calculated for the Case M-L > (.80)(H-L) At the 80 th -Percetle Level Need 80 th - Percetle Elemet Cost, Mus Most Lkely Elemet Cost Need L (.80) ( M L)( H L) M If Need < 0, We Set Need 0 If Need > 0, We Use that Postve Number as the Need of the Elemet At the 50 th -Percetle Level It Must Be True that M-L > (.50)(H-L), so We Apply the Followg Formula... Need L (. 50) ( M L)( H L) M Ths Number s Always Negatve the Stuato Descrbed, so We Set Need 0 0

41 Need Calculated Cases whe M-L > (.50)(H-L), but M-L < (.80)(H-L) At the 50 th -Percetle Level Need 50 th - Percetle Elemet Cost, Mus Most Lkely Elemet Cost Need ( )( ) L (. 50 ) M L H L M Ths Number s Always Negatve the Stuato Descrbed Because (.50)(M-L)(H-L) > (.50) (H-L) Meas that L(.50)(H-L)-M (.50)(H-L)-(M-L) < 0 Therefore We Set Need 0 At the 80 th -Percetle Level Need 80 th - Percetle Elemet Cost, Mus Most Lkely Elemet Cost Need H (.0 )( H L )( H M ) M If Need < 0, We Set Need 0 If Need > 0, We Use that Value as the Need of the Elemet

42 Total Amout of Rsk Dollars Needed for 50% Cofdece (says Crystal Ball ) 50 th Rsk$ 50 th -Percetle Total Cost, Mus Roll-Up Pot Estmate 50 th Rsk$ ) Recall Output of Crystal Ball Software:

43 Allocato of System X Rsk Dollars to WBS Elemets at 50 th Percetle

44 Example: System X WBS-Elemet Tragular Cost Dstrbutos Atea 0.0. Facltes* Evrometal Cotrol Electrocs Power Dstrbuto Commucatos Platform 6. Computers * Vertcal scale (probablty desty) dfferet ths graph oly Software

45 Total Amout of Rsk Dollars Needed for 80% Cofdece (says Crystal Ball ) 80 th Rsk$ 80 th -Percetle Total Cost, Mus Roll-Up Pot Estmate 80 th Rsk$ ) Recall Output of Crystal Ball Software: 5

46 Allocato of System X Rsk Dollars to WBS Elemets at 80 th Percetle 6

47 Not So Fast! We re Not Fshed Yet Statstcal Fact: Actual WBS-Elemet 50 th Percetles Do Not Sum to the 50 th Percetle of Total Cost But Our (so-called) 50 th Percetle Estmates Really Do Sum to the 50 th Percetle of Total Cost Why? Because We Calculated the 50 th Percetle of Total Cost Frst The We Dvded the 50 th Percetle Total-Cost Amog the WBS Elemets Proporto to ther Rskess, wth Iter- Elemet Correlatos Take to Accout Therefore the Numbers You See Summg to the 50 th Percetle of Total Cost are NOT the Actual 50 th Percetles of Each of the WBS Elemets Same Assertos Hold True for 80 th ad All Other Cost Percetles 7

48 8 Note: Actual Percetles Represeted by Term 50 th Percetle Estmates pth Percetle ( )( ) L H L M p L L H L M p f ( )( )( ) M H L H p H L H L M p f

49 Note: Actual Percetles Represeted by 80 th Percetle Estmates 9

50 Recall Total-Cost Percetles Output of Crystal Ball Software: (8 th ) (85 th ) 50

51 Observatos o the Rsk-Dollar Allocato Process Uder our Defto of Need, Percetage of Rsk Dollars Allocated to Each WBS Elemet Depeds o our Choce of Pot Estmate of Total Cost Pot Estmate Ca be Defed as Roll-Up of Elemet Most Lkely Costs Expected Cost 50 th -Percetle Cost Most Lkely Total Cost (or Whatever) A Elemet s Need s Based o Its Pot Estmate (however that s defed) Its Rsk Characterstcs (.e, skewess of ts cost dstrbuto) Correlato of ts Rsks wth other WBS-Elemets Rsks Rsk-Dollar Percetage Allocated to Each Proect Elemet Also Depeds o Level of Cofdece (50 th, 80 th, etc.) Cosdered Approprate for Maagemet Reserve 5

52 Cotets What Are Rsk Dollars? What s Your Pot Estmate? What Level of Cofdece Do You Need? Why Allocate Rsk Dollars? The Poltcal Reaso The Proect-Maagemet Reaso How Should We Allocate Rsk Dollars? The Dfferece betwee Ucertaty ad Rsk How May Rsk Dollars Does Each WBS Elemet Need? Summary 5

53 Summary Allocato of Rsk Dollars to WBS Elemets Provdes Supportg Justfcato for a Request for Maagemet Reserve Before Decdg How to Allocate Dollars, Aalysts Must Assg WBS-Elemet Cost Probablty Dstrbutos Calculate Total-Cost Probablty Dstrbuto Agree upo Meag of Pot Estmate of Total Cost Agree upo Cofdece Level Requred for Rsk Coverage Agree upo Specfcatos for Allocato Decso How Rsk-Dollar Allocato Procedure Works Defe Dollar-Valued Need of Each WBS Elemet Calculate Dollar-Valued Need of Each WBS Elemet, Takg to Accout Iter-Elemet Correlatos Sum All Needs to Obta Total Need Base Allocate Rsk Dollars to WBS Elemets Proporto to ther Fractos of the Need Base You Do t Have to Worry About Someoe the Audece Notcg that Your 80 th Percetle Estmates Do t Add Up 5

54 The Speaker Dr. Stephe A. Book s Chef Techcal Offcer of MCR, LLC, resposble for esurg techcal excellece of MCR s products, servces, ad processes by ecouragg process mprovemet, matag qualty cotrol, ad trag employees ad customers cost ad schedule aalyss ad assocated programcotrol dscples. Dr. Book has gve umerous techcal ad tutoral presetatos o cost-rsk aalyss, CER developmet, ad other statstcal aspects of cost ad ecoomcs to DoD, NASA, ad EACE (Europea Aerospace Workg Group o Cost Egeerg) Cost Symposa, the AF/NASA/ESA Space Systems Cost Aalyss Group (SSCAG), the U.S. Army Coferece o Appled Statstcs (ACAS), ad professoal socetes such as the Iteratoal Socety of Parametrc Aalysts (ISPA), Socety for Cost Estmatg ad Aalyss (SCEA), Mltary Operatos Research Socety (MORS), U.K. Assocato of Cost Egeers (ACostE), ad the Amerca Isttute of Aeroautcs ad Astroautcs (AIAA). He was a prcpal cotrbutor to several Ar Force cost studes of atoal sgfcace, cludg the DSP/FEWS/BSTS/AWS/Brllat Eyes Sesor Itegrato Study (99) ad the ALS/Spacelfter/EELV Lauch Optos Study (99) ad has served o atoal paels as a depedet revewer of NASA programs. Dr. Book oed MCR Jauary 00 after years wth The Aerospace Corporato, where he held the ttle Dstgushed Egeer durg ad the posto of Drector, Resource ad Requremets Aalyss Departmet, durg He s the curret edtor of ISPA s Joural of Parametrcs ad the 005 recpet of ISPA s Frema Award for Lfetme Achevemet. Dr. Book eared hs Ph.D. mathematcs, wth cocetrato probablty ad statstcs, at the Uversty of Orego