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MIT ESD 71 - An Engineering Systems Analysis of Space Station Assembly & Supply

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1© 2006 Brandon Owens, Engineering Systems Division, Massachusetts Institute of Technology1An Engineering Systems Analysis of An Engineering Systems Analysis of Space Station Assembly & SupplySpace Station Assembly & SupplyApplication PortfolioESD.71 – Engineering Systems Analysis for DesignDecember 5th, 2006Brandon Owens© 2006 Brandon Owens, Engineering Systems Division, Massachusetts Institute of Technology2The Engineering System: A LEO Space Station• Assembled and supplied by Space Shuttle over a 10 year period– Comprised of multiple segments, each requiring a Space Shuttle launch• An astronaut crew is needed to process payload– The maximum amount of payload that can be processed is directly proportional to the crew size– Crew is transferred to and from station on Space Shuttle and Soyuz• Processed payload is assumed to be worth $21,000/kg2© 2006 Brandon Owens, Engineering Systems Division, Massachusetts Institute of Technology3Model of the Engineering SystemProduction Function:Ypayload returned= MIN [(η x NShuttle Flightsx MShuttle return capacity at given inclination), Pcrew]Input Cost Function:C = CShuttle variable cost x NShuttle Flights+ CSoyuz variable costx NSoyuz FlightsCash Flows:Cash Flowi= V x (Ypayload returned)i–Cifor all iNet Present Value:NPV = ∑Cash Flowi/(1+r)ifor all i © 2006 Brandon Owens, Engineering Systems Division, Massachusetts Institute of Technology4Uncertainties of the Engineering System• Launch Vehicle Flight Rate– Determines the amount of payload returned• Launch Vehicle Success Rate– Success criteria for missions to space stations are among the most stringent of missions to LEO– Launch sequencing is critical for space station assembly & supply• Annual Budget of Space Programs– Proposed by President, approved by Congress• Presidential Agendas– Presidents define goals of space station programs & reserves the right to change them• And Many More3© 2006 Brandon Owens, Engineering Systems Division, Massachusetts Institute of Technology5Model of the Key Uncertainty• The uncertainty analyzed is the annual Space Shuttle Launch Rate– Historical data from 1983 to 2006 (after the initial test flights) used to derive average and standard deviation– Launch rate is assumed to decay to 2.5 flights per year over the 10 years of assembly and supply56.4%Standard Deviation Annual Flight Rate (%)2.63Standard Deviation Annual Flight Rate6Median # of Flights per Year9Maximum # of Flights over a Year0Minimum # of Flights over a Year4.67Average # of Flights per Year00.511.522.533.544.550246810Time (Years)Annual Launch Rate (Flights/year)ST= SevTÆ ln(ST/S)/T = vv = -6.24%/year© 2006 Brandon Owens, Engineering Systems Division, Massachusetts Institute of Technology6System Design Alternatives• Alternative 1 (A1)– 28.5° orbital inclination– Crew of four astronauts– Station only able interface with U.S. vehicles• Alternative 2 (A2)– 51.6° orbital inclination– Crew of seven astronauts—4 from the U.S. and 3 from Russia• Requires two $20M Soyuz launches per year• Alternative 3 (A3)– 51.6° orbital inclination– Maximum crew size of seven (A3A) with option to terminate Russian participation (A3B)• Option leads to an extra charge of $5M per Soyuz flight• In the decision analysis, the option can be exercised after five years• In the lattice analysis, the option can be exercised in the 0, 2nd, 4th, 6th, or 8thyear4© 2006 Brandon Owens, Engineering Systems Division, Massachusetts Institute of Technology7Two-Stage Decision Analysis of Uncertainty• Three events are possible at each stage– E1 = The Space Shuttle averages 5 launches/year– E2 = The Space Shuttle averages 4 launches/year – E3 = The Space Shuttle averages 3 launches/year• The probability of each event is as follows:– P(E1) = 0.625– P(E2) = 0.042– P(E3) = 0.333– The probability of events in the second stage are assumed to be independent of events in the first stage30E3and E335E2and E340E2and E240E1and E345E1and E250E1and E1Successful Space Shuttle Missions over the 10 Year PeriodCombinations of Events© 2006 Brandon Owens, Engineering Systems Division, Massachusetts Institute of Technology8Binomial Lattice Analysis of Uncertaintyu = e(σ√∆T)= 2.22 d = e(-σ√∆T)= 1/u = 0.45 p = 0.5 + 0.5(v/σ) √∆T = 0.4220.090.430.192.100.950.4310.364.672.100.9551.0823.0010.364.672.10251.78113.4051.0823.0010.364.67Step 5Step 4Step 3Step 2Step 1Step 0OUTCOME LATTICE (Annual Launch Rate)5© 2006 Brandon Owens, Engineering Systems Division, Massachusetts Institute of Technology9Results• According to the Decision Analysis:– The option adds no value when A1or A2is available• According to the Lattice Analysis: – The option adds no value when A1is available– The option is worth $109M when A1is not available and should be executed at Time Step 0• Decisions are sensitive the assumed parameters for both techniquesLattice AnalysisDecision Analysis$(1,592M)$(1,547M)$(1,588M)$(3,598M)$(3,707M)$(3,581M)EV(A3)EV(A2)EV(A1)4 Crew4 Crew4 Crew4 Crew4 Crew4 Crew7 Crew4 Crew4 Crew4 Crew7 Crew7 Crew7 Crew4 Crew4 CrewStep 4Step 3Step 2Step 1Step 0CREW SIZE LATTICE© 2006 Brandon Owens, Engineering Systems Division, Massachusetts Institute of Technology10Concluding Remarks• Decision Analysis and Lattice Modeling are useful for gaining qualitative insights into the management of uncertainty in this system• LEO space stations may be too complex and unique to derive useful quantitative information through decision and lattice analyses– Numerous assumptions were necessary to perform trivial calculations– Some of the results (e.g. 252 Space Shuttle launches in one year) will not be taken seriously by those who actually work with the system• Decision Analysis can be more accurate than lattice analysis, but it can add a great deal of complexity to the analysisNo analytic tool is equipped to answer every research question; care must be taken in selecting the right tool for the job6© 2006 Brandon Owens, Engineering Systems Division, Massachusetts Institute of Technology11References• Arianespace, (2004). Ariane V User’s Manual, Issue 4, Revision 0.• Baker, David (editor), (2006). Jane’s Space Directory 2005-2006.• Harland, David M. and John E. Catchpole, (2002). Creating the International Space Station, Springer-Praxis, Chichester, U.K.• Isakowitz, Steven J., (1995). International Reference Guide to Space


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