1. 1 Update on cost-related issues Philippe Lebrun Joint CLIC-ILC meeting on costs CERN, 12 June 2009 Peter’s notes: Thursday, 16july09 PHG - 16july09: added slide #

2. 2 Progress since TILC’09 CLIC Study Costing Tool –Production version operational [G. Riddone] –Tested on preliminary (partial) cost estimate Analytical cost estimate –PBS of CLIC 500 GeV being established –Discussions with Domain Coordinators started –Establish list of cost drivers & possible alternatives Currency conversion & escalation –Reference currency CHF –Escalation based on two compound indices for industrial prices (≠ consumer prices) of Swiss Federal Statistical Office [input from A. Unnervik, CERN Purchasing] Cost risk analysis –Compromise between accuracy and simplicity –Variance due to industrial procurement: method based on LHC data refined [input from P. Garbincius] –Proposed plan for common CLIC-ILC document CLIC general schedule –Input commissioning and operation of phase 1 [K. Foraz] PHG - 16july09: should we have side to side comparison with ILC status/progress?

3. 3 Analytical basis is PBS Component level not yet defined List of systems standardized Contact experts per system Coordinators per domain/subdomain Identified for analytical costing based on level 5 description PHG - 16july09: ambitious to try to get all this correct from start Do you have a process which allows changes later? Can you add more categories? Does your system deal with Quantity = 0?

4. 4 Cost vs energy What are we comparing? Cost E cm 3 TeV in one phase (CLIC reference) 500 GeV as phase 1 of 3 TeV 500 GeV optimized (ILC comparison) 3 TeV in two phases PHG - 16july09: what comparison do we need? Understand what should be the same – are they? What should be different – why?

5. 5 Industrial price indices (CH) PHG - 16july09: should probably say somewhere what ILC did for RDR for 3 regions, construction (~ 3/8), non-construction (~ 5/8), and “weighted average” escalation for 2006-2007

6. 6 Cost variance factors (assumed statistically independent) Evolution of configuration –Maturity of design –Technology breakthroughs –Variation of applicable regulations Technical execution –Off-the-shelf or special product –Qualification & experience of vendors –State of completion of R&D, of industrialization –Series production, automation & learning curve –Rejection rate of production process Structure of market –Mono/oligopoly –Mono/oligopsone Commercial strategy of vendor –Market penetration –Competing productions Inflation and escalation –Raw materials –Industrial prices International procurement –Exchange rates –Taxes, custom duties Engineering judgement of project team Reflected in scatter of offers received from vendors (LHC experience) Tracked and compensated PHG - 16july09: this is “history”, not subject to statistical variation in not projected into future

7. 7 Scatter of LHC offers as a measure of cost variance Available data: CERN purchasing rules impose to procure on the basis of lowest valid offer ⇒ offers ranked by price with reference to lowest for adjudication by FC Postulate: scatter of (valid) offers received for procurement of LHC components is a measure of their variance due to technical, manufacturing and commercial aspects Survey of 218 offers for LHC machine components (48 contracts) Prices normalized to that of lowest valid offer, i.e. value of contract Exponential PDF fitted to observed frequency distribution with same mean value PHG - 16july09: “Postulate”, at first look, looks good. Is that a commonly accepted estimating method?

8. 8 LHC tender prices for accelerator components Adjusted to mean (1.46) and total number (218) of sample PHG - 16july09: for exponential σ = 1-

9. 9 From distribution of offers to distribution of prices Consider two valid offers X1, X2 following same exponential distribution with P(Xi<x) = F(x) = 1 – exp[-a(x-b)] ⇒ m = b + 1/a and  = 1/a Price paid (lowest valid offer) is Y = min(X1, X2): what is the probability distribution of Y? Estimate P(Y<x) = P(X1<x or X2<x) = G(x) Combined probability theorem P(X1<x or X2<x) = P(X1<x) + P(X2<x) – P(X1<x and X2<x) If X1 and X2 uncorrelated, P(X1<x and X2<x) = P(X1<x) * P(X2<x) Hence, P(X1<x or X2<x) = P(X1<x) + P(X2<x) – P(X1<x) * P(X2<x) and G(x) = 2 F(x) – F(x) 2 = 1 – exp[-2a(x-b)] ⇒ Y follows exponential distribution with m = b + 1/2a and  = 1/2a By recurrence, if n uncorrelated valid offers X1, X2,…Xn are received, the price paid Y = min (X1, X2,…Xn) will follow an exponential distribution with m = b + 1/na and  = 1/na

10. 10 Dispersion on prices due to procurement uncertainties For LHC accelerator components –48 contracts –218 offers, i.e. 4.54 offers per contract on average From exponential fit of statistical data on offers, m = 1.46,  = 0.46 We can therefore estimate the expected relative dispersion on paid prices  = 0.46/4.54 ≈ 0.1 ⇒ based on LHC experience, the relative standard deviation on component prices due to procurement uncertainties can be taken as 50/n %, where n is the expected number of valid offers PHG - 16july09: as an estimator, how does one estimate b = the end point or most probable value? Or does one estimate the average? This is a common question…. PHG - 16july09: yes, I would accept 50%/n as a “rule of thumb”, an approximation to an approximation

11. 11 Towards a method for CLIC cost risk analysis Separate cost risk factors in three classes, assumed independent –Risk of evolution of configuration Judgement of « domain responsible » Rank in 3 levels, numerical values of  config tbd –Price uncertainty in industrial procurement Estimate n number of valid offers to be received Apply  industry = 50/n % –Economical & financial context Deterministic Track currency exchange rates and industrial indices Estimate r.m.s. sum of  config and  industry Compensate economical & financial effects PHG - 16july09: remind me, what are these 3 levels? PHG - 16july09: this is a fixed, exactly calculable correction to convert a prior year’s estimate into TODAY’S estimate based on historical data, not to project into tomorrow’s estimae.

12. 12 Proposed plan of CLIC-ILC document on cost risk analysis Introduction –Observed uncertainty on cost of projects –Why and how to cope with it Identification of cost variance factors –Following time line of project development, from conceptual studies and R&D to technical design, configuration management, industrial procurement –Question of correlated/uncorrelated variance factors Boundary conditions imposed by funding & governing bodies –Major differences (managing escalation) lead to different costing methods The CLIC method The ILC method Discussion & conclusion PHG - 16july09: also ILC has US method and non-US method. We did not pay attention to non-US risk in RDR. PHG - 16july09: there is some ART in developing estimate of uncertainty. CORRELATIONS. CF&S (for example), often includes elements estimated to be added to complete and incomplete estimate as part of the “contingency” – watch it!

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14. 14 CLIC Cost & Schedule WG Communication & reporting lines CLIC Cost & Schedule WG CLIC Steering Committee CLIC Technical Committee Other CLIC WG System group ILC GDE Cost Team Other CLIC WG System group reports to PBS, developments & alternatives Configuration Analytical costing Information, methodology Technical design PHG - 16july09: why doesn’t technical design and analytic costing point at both System group and other CLIC WG? OK this is just CLIC (keeping ILC Cost Team informed), not showing what ILC does

15. 15 Statistical modeling of tender prices Heuristic considerations –things tend to cost more rather than less ⇒ statistical distributions of tender prices X i are strongly skew –PDFs f i (x i ) are equal to zero for x i below threshold values b i equal to the lowest market prices available –commercial competition tends to crowd prices close to lowest ⇒ PDFs f i (x i ) are likely to be monotonously decreasing above threshold values b i The exponential PDF is a simple mathematical law satisfying these conditions f(x) = 0 for x < b f(x) = a exp[-a(x-b)] for x ≥ b Characteristics of the exponential law –only two parameters a and b –thresholdb –mean value m = 1/a + b –standard deviation  = 1/a = m – b –« mean value = threshold + one standard deviation »

16. 16 Exponential vs Gaussian PDFs PHG - 16july09: maybe should also show exponential and symmetric gaussian (differential, not integrals) with same mean and σ

17. 17 LHC cost structure (material) Total 2.2 BEuro PHG - 16july09: I’ll have to make comparable pie for ILC RDR estimate. It’s amazing how close our categories (although not fractions) agree. Note that LHC already had its tunnels, but had to dig more caverns!

18. 18 LHC procurement 90 main contracts in advanced technology

19. 19 DOE cost risk assessment method PHG - 16july09: This is an example of a DOE suggestion table. ILC is now using the somewhat simplified XFEL scheme, but the same general idea: that the % uncertainty inversely scales with maturity of design/fabrication/procurement!