Issues, methods and organization for costing the CLIC accelerator project, with particular focus on BDS & MDI Philippe Lebrun Special BDS-MDI meeting CERN, 7 June 2010

CLIC Cost & Schedule WG Mandate Establish and optimize the cost of the CLIC complex at the nominal colliding beam energy of 3 TeV, as well as that of an optional first phase with a colliding beam energy of 500 GeV Define and optimize the general schedule for the 3 TeV and 500 GeV projects defined above Estimate the electrical power consumption of the 3 TeV and 500 GeV projects defined above Identify possible modifications of parameters and/or equipment leading to substantial capital and/or operational cost savings, in order to define best compromise between performance and cost Develop collaboration with ILC project on cost estimate methodology and cost of common or comparable systems, aiming at mutual transparency Document the process and conclusions in the CDR in 2010 April 2009

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

CLIC 3 TeV cost estimate 2007 (H. Braun & G. Riddone)

Contents Cost estimate methods Organization & tools for costing CLIC Feedback to technical design & optimization Large series, manufacturing techniques & learning curves Elements of cost risk analysis Coping with exchange rates & cost escalation

Cost estimate methods Analytical –Based on project/work breakdown structure –Define production techniques –Estimate fixed costs –Establish unit costs & quantities (including production yield and rejection/reprocessing rates) –In case of large series, introduce learning curve (see later) Scaling –Establish scaling estimator(s) and scaling law(s), including conditions & range of application Empirical « First-principles » based –Define reference project(s) and fit data, mutatis mutandis In most cases, hybrid between these methods

Basic sizing laws in normal-conducting magnet design Coil sizingYoke sizing Basics T. Zickler

Typical unit costs in normal-conducting magnet design T. Zickler

Example of preliminary design for costing of normal-conducting magnet PBS and 2 Pre-Damping Ring QUADRUPOLE 30 T/m Length758 mm Weight1720 kg Power17.4 kW N. of units408 Cost/unit148 kCHF TOTAL COST60384 kCHF M. Modena & A. Vorozhtsov

An example of empirical scaling: cost of cryogenic helium refrigerators

K helium refrigerator for LHC Compressor station (~ 4 MW) Cost ~ number of compressor units ~ linear with capacity Cold box Cost ~ volume < linear with capacity

Ph. Lebrun CLIC analytical costing based on PBS Component level List of systems standardized Contact experts per system Coordinators per domain/subdomain Identified for analytical costing based on level 5 description

CLIC sub-domain coordinators

CLIC 3 TeV Beam Delivery Systems

CLIC 3 TeV Machine-Detector Interface

CLIC 3 TeV Experimental Area Not to be considered here !

CLIC 3 TeV Post-Collision Line Should this appear here?

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

Ph. Lebrun CLIC Study Costing Tool CLIC Study Costing Tool developed & maintained by CERN GS-AIS Operational, on-line from C&S WG web page (access protected) Includes features for currency conversion, price escalation and uncertainty Demonstrations to users in C&S WG meetings

Cost drivers, models and optimization Limitation of PBS/WBS-based approach: does not look at interplay between technical systems ⇒ risk of local (« mountain lake ») optimization Hence importance of communication among experts to develop global view –cost WG –informal discussion with system specialists, –understanding of rationale behind scaling laws –pluridisciplinary models –feedback to project team Cost scaling models only exist for limited number of components or subsystems Targeted cost studies by industrial companies important for –providing up-to-date, relevant data –establishing limits of validity of scaling laws –exploring technical alternatives & breakthroughs

Applying the scaling method to multi-MW klystrons

Scaling klystron cost E. Jensen

Optimizing klystron initial cost E. Jensen

Optimizing klystron cost including replacement E. Jensen

Tunnel size, a cost driver for CLIC... J. Osborne …itself driven by ventilation… …sized by power dissipation

CLIC two-beam modules Complexity, number, integration CLIC 3 TeV (per linac) Modules: Accelerating str.: 71406PETS: MB quadrupoles: 1996DB quadrupoles: CLIC 3 TeV (per linac) Modules: Accelerating str.: 71406PETS: MB quadrupoles: 1996DB quadrupoles: CLIC 500 GeV (per linac) Modules: 2124 Accelerating str.: 13156PETS: 6578 MB quadrupoles: 929DB quadrupoles: 4248 CLIC 500 GeV (per linac) Modules: 2124 Accelerating str.: 13156PETS: 6578 MB quadrupoles: 929DB quadrupoles: 4248 G. Riddone

CLIC vs LHC components: different solutions for different series numbers Flexible cells, manual work Flexible workshops Automatic chains CLIC AS CLIC PETS CLIC Quads CLIC TBM AS quadrants AS discs

Experimental learning curves LHC superconducting dipole magnets Unit cost c(n) of nth unit produced c(n) = c(1) n log 2 a with a = « learning percentage », i.e. remaining cost fraction when production is doubled Cumulative cost of first nth units C(n) = c(1) n 1+log 2 a / (1+log 2 a) with C(n)/n = average unit cost of first nth units produced

Learning coefficients P. Fessia

Ph. Lebrun Effect of learning coefficient on average unit cost up to rank N

Saturation of learning process has little impact on total cost

Ph. Lebrun Cost variance factors Technical design –Evolution of system configuration –Maturity of component design –Technology breakthroughs –Variation of applicable regulations Industrial execution –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 responsible Tracked and compensated Decreasing control of project responsible Outside project control Procurement Contract adjudication Technical definition Reflected in scatter of offers received from vendors (LHC experience)

DOE cost element template

Ph. Lebrun Observed tender prices for LHC accelerator components Adjusted to mean (1.46) and total number (218) of sample

Sampling from an exponential PDF (m=0,  =1) In response to an invitation to tender, consider n (valid) offers distributed according to an exponential PDF: application of the CERN purchasing rule will lead to select the lowest bidder What is the PDF of the lowest bidders, i.e. of the prices effectively paid? In the following, reasoning on the integral PDF

From distribution of offers to distribution of prices (adjudication to lowest bidder) 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 LHC accelerator components: 48 contracts, 218 offers, i.e offers/contract on average From exponential fit of statistical data on offers, m = 1.46,  = 0.46 Estimated 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

Rolling up the cost uncertainties The probability distribution function for the total project cost is critically dependent on the degree of correlated uncertainties between the estimates for the individual cost elements. Failure to include correlations in the estimates (or assuming no correlation) results in underestimating the risk in the cost estimate. If C is the global correlation coefficient, σ 2 = C 2 * (Σ σ i ) 2 + (C-1) 2 * Σ σ i 2 As an illustration, if all the σ i are identical σ i = σ 0 /N where σ 0 is the standard deviation of the sum assuming full correlation, and N is the number of cost elements, then σ 2 = C 2 * (σ 0 /N) 2 * N 2 + (C-1) 2 * N *(σ 0 /N) 2 = C 2 *σ (C-1) 2 *σ 0 2 /N → C 2 *σ 0 2 as N → ∞ ⇒ the standard deviation of the sum with global correlation C is σ → C*σ 0

Exchange rates and cost escalation Exchange rate fluctuations should ideally reflect evolution of purchasing power of currencies, but –Economic parities offset by financial effects –Variety of escalation indices in each currency Choose « reference currency » (CHF) and apply relevant escalation indices in reference country (Office Fédéral de la Statistique) Currency A Time 1 Currency B Time 1 Exchange rate 1 Currency A Time 2 Currency B Time 2 Exchange rate 2 Escalation Index a Escalation Index b ?

Swiss vs CERN indices

Method for CLIC cost risk assessment 1. For each cost element k Separate cost risk factors in three classes, assumed independent –Technical design maturity & evolution of configuration Represented by relative standard deviation  design (k) Judgement of « domain responsible » Rank in three levels yielding different values of  design (k) –Known technology  0.1 –Extrapolation from known technology0.2 –Requires R&D0.3 –Price uncertainty in industrial procurement Represented by relative standard deviation  industry (k) Estimate n number of valid offers to be received Apply  industry (k) = 0.5/n –Economical & financial context Risk outside project cost assessment Deterministic, compensated a posteriori by adequate indexation Estimate risk on cost c(k) of cost element k –Relative standard deviation  (k) is the r.m.s. sum of  design (k) and  industry (k) –Absolute uncertainty on cost element  c (k) =  (k) x c (k)

Method for CLIC cost risk assessment 2. For total project Cost of project C =  c(k) Estimate uncertainty on project cost  C =   c(k) –Assumes full correlation between c(k), therefore maximizes uncertainty Apply only additive uncertainty [C, C+  C] Compensate economical & financial effects a posteriori –Choice of CHF as reference currency –Applications of compound indices from Office Fédéral de la Statistique (CH) Arts et métiers – Industrie for technical components Construction for civil engineering

Tentative time line September-December 2009 –First round of cost domain review –Identification of major cost drivers –Feedback to technical systems March 2010 –Freeze configuration for CDR –Identify R&D topics for TDR April-July September 2010 –Input from cost domains, upload in Costing Tool –Cost roll-up November 2010? –Internal review –Decision to publish January 2011? –External review March 2011 –Final write-up