Strategic Engineering Designing Systems for an Uncertain Future 21st Century COE Program System design: Paradigm Shift from Intelligence to Life Keio University June 10, 2006 Olivier L. de Weck deweck@mit.edu Assistant Professor of Aeronautics & Astronautics and Engineering Systems Olivier L. de Weck, 2006 Page 1 Motivation: Iridium Satellite System 'Motorola unveils new concept for global personal communications: base is constellation of low-orbit cellular satellites', Motorola Press Release on Iridium, London, 26 June 1990. ‘Last week, Iridium LLC filed for bankruptcy-court protection. Lost investments are estimated at $5 billion.’ Wall Street Journal, New York, 18 August 1999. Iridium Satellite Millions of subscribers US (forecast) US (actual) 120 100 80 60 40 20 0 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Year Difficult to properly size capacity of large system Market assumptions can change when 7-8 years elapse between conceptual design and fielding (1991-1998) Olivier L. de Weck, 2006 Page 2 Outline Customization of the F/A-18 Aircraft Introduction to Strategic Engineering Research Projects: Staged Deployment of Satellite Constellations Flexible Automotive Product Platforms Time Expanded Decision Networks (TDN) Engineering Education Olivier L. de Weck, 2006 Page 3 Customization of the F/A-18 Aircraft Olivier L. de Weck, 2006 Page 4 Mission (and Configuration) Change Swiss Mission (1993) U.S. Navy Mission (1978) fighter and attack aircraft carrier based 3000 flight hours 90 min average sortie max 7.5g positive ~15 year useful life interceptor land based 5000 flight hours 40 min average sortie max 9.0g positive ~30 year useful life “Redesign” (Switch) Standard U.S. Navy F/A-18 C/D Configuration Modified Swiss F/A-18 C/D Configuration Olivier L. de Weck, 2006 Page 5 F/A-18 Redesign Strategy 1. 2. 3. 4. specify new Swiss mission usage spectrum apply new spectrum to existing U.S. Navy Configuration identify and prioritize “hot spots” that most need change redesign and implement local changes at “hot spots” Olivier L. de Weck, 2006 Page 6 F/A-18 Wing Carry-Through Bulkheads Olivier L. de Weck, 2006 Page 7 F/A-18 Center Barrel Section Y453 Y470.5 Y488 Wing Attachment 74A324001 Olivier L. de Weck, 2006 Page 8 F/A-18 Center Fuselage Buildup (1) Olivier L. de Weck, 2006 Page 9 Center Barrel Change Consequences Substitution from Aluminum to Titanium Intended Consequence: - Increased fatigue life of individual components from 3000 5000 hours achieved Unintended Consequences: - Increased aircraft empty weight by ~O(100) lbs - Shifted C.G. of aircraft by ~ O(1) inch - Stiffened fuselage (1st bending mode) ~(0.1) Hz - Rendered manufacturing processes obsolete not expected or wanted Olivier L. de Weck, 2006 Page 10 F/A-18 Complex System Change F/A-18 System Level Drawing Fuselage Stiffened Original Change Flight Control Software Changed Manufacturing Processes Changed Center of Gravity Shifted Gross Takeoff Weight Increased Olivier L. de Weck, 2006 Page 11 F/A-18 Lessons Learned Changes increased cost per aircraft by O(~$10M) Changing a system after its initial design is often required to accommodate new requirements expensive, and time-consuming if change was not anticipated in the original design Change propagation some changes are local and remain local other changes start local, but propagate through the system in complex, unanticipated ways switching costs include: engineering redesign cost, change in materials, manufacturing changes, change in operational costs Olivier L. de Weck, 2006 Page 12 Introduction to Strategic Engineering Olivier L. de Weck, 2006 Page 13 What about the Future ? Typical Engineering Design Mindset: “Give me a set of requirements today, a timeline and a budget and I will design and deliver the best possible product/system/project for you by tomorrow.” 90% of thinking and design effort is spent on this But, in essence, we are always forecasting: what customers will require in 18 months what capacity our facility will need in 3 years what variants we will produce in 8 years how many missions we will fly in 12 years What if our forecast is wrong? (it usually is) Perhaps system will function technically …. But system will not deliver optimal value, or architectural “lock-in” occurs, or it will fail financially if its configuration is not easily changed Olivier L. de Weck, 2006 Page 14 Traditional (Systems) Engineering System Validation Customer Needs Marketing Requirements Definition Product System Ytarget System Functional Testing Systems Engineering Conceptual Design System Yactual Subsystem Development Subsystem Ytarget Component Design Preliminary Design Components Ytarget Detailed Design Fielding/ Launch Final Assembly Subsystem Yactual Subsystem Integration Components Yactual System Operation Component Testing Olivier L. de Weck, 2006 Page 15 Implicit Assumptions of TSE The customer knows what his/her needs are The requirements are known and time-invariant The system or product can be designed as one coherent whole and is built and deployed in one step There is only one system or product designed at once The system will operate in a stable environment as far as regulations, technologies, demographics and usage patterns are concerned Olivier L. de Weck, 2006 Page 16 But reality tells us that … Customer knows some of his/her needs but not all The true requirements often change after the system is fielded and experience is gained Constraints on capital expenditures and operating budgets frequently only allow a “piecemeal” implementation Often multiple variants of a system must be designed and built, possibly based on some common standard Environment is not static, but dynamic macro economic/budgetary changes (e.g. prime interest rate) regulatory changes (e.g. new CAFÉ standards) new technologies emerge (e.g. hydrogen fuel cells for cars) demographic shifts (e.g. aging population in Western nations) changing customer preferences (e.g. weighting of fuel economy) disruptive events (natural, man-made) Olivier L. de Weck, 2006 Page 17 Strategic Engineering Strategic Engineering is the process of designing systems and products in a way that deliberately accounts for customization and future uncertainties such that their lifecycle value is maximized. Olivier L. de Weck, 2006 Page 18 Strategic Engineering Framework - CDI – - Operate - – RDI – – Operate - Time Baseline System Baseline System Variant B Variant B Variant C Variant C Space Variant B2 Variant B2 Variant C2 Variant C2 … … … … … Development Gen 2 Baseline Gen 2 Baseline Operations (Stage 1) Development Operations (Stage 2) Olivier L. de Weck, 2006 Page 19 Alternatives 1. Ignore the future and design for `optimal’ immediate or short-term use (= TSE) 2. Come up with a `best guess’ of the most likely future scenario and design to it (= forecasting + TSE) 3. Develop a range of potential future outcomes and design such that the system will be robust optimal on `average’ across all future scenarios protected against the worst case scenario risk averse opportunistic take advantage of the `best case’ scenario most flexible to adapt to any scenario flexible Interested in how to do 3. Strategic Engineering Olivier L. de Weck, 2006 Page 20 Strategic Engineering “Toolbox” Traditional Systems Engineering Methods (QFD, DSM,…) Forecasting, Change Propagation Analysis System Architecting Principles, “Illities” Modularity, Flexibility, Scalability, Reconfigurability,… Real Options “in” Projects Standardization Product/System Platforms Staged Development and Deployment Optimization: Dynamic Programming, Multiobjective, … … all these attempt to address part of the problem, when do these methods apply, is there a unifying framework …? Olivier L. de Weck, 2006 Page 21 de Weck Research Approach theory Non-dimensional lifecycle analysis Generic Lifecycle Cost Modeling Time-expanded decision networks Generic System Modeling (OPM) Meta-platforming Comparative Analysis NASA: Launch Vehicle Selection & Evolution NASA: Interplanetary Supply Chain & Logistics DARPA/AFRL: Space Tug Mission Scenarios BP: Exploration & Production Standardization Iridium and Globalstar: Staged Deployment GM: Flexible Automotive Product Platforms ARM: Hydrogen Enhanced Combustion Engine BP: Commercial Office Building Staging application Olivier L. de Weck, 2006 Page 22 Staged Deployment of Satellite Constellations Funded by Alfred P. Sloan Foundation Reference de Weck, O.L., de Neufville R. and Chaize M., “Staged Deployment of Communications Satellite Constellations in Low Earth Orbit”, Journal of Aerospace Computing, Information, and Communication, 1, 119-136, March 2004 Olivier L. de Weck, 2006 Page 23 Design (Input) Vector X Design Space Astrodynamics Satellite Design Network X1440= Constellation Type: C Polar, Walker Orbital Altitude: h 500,1000,1500,2000 [km] Minimum Elevation Angle: emin 2.5,7.5,12.5 [deg] Satellite Transmit Power: Pt 200,400,800,1600,2400 [W] Antenna Size: Da 1.0,2.0,3.0 [m] Multiple Access Scheme MA: MF-TDMA, MF-CDMA [-] Network Architecture: ISL yes, no [-] C: h: emin: Pt: DA: MA: ISL: 'walker' 2000 12.5000 2400 3 'MFCD' 0 This results in a 1440 full factorial, combinatorial co design space Olivier L. de Weck, 2006 Page 24 Objective Vector (Output) J Performance (fixed) Data Rate per Channel: R=4.8 [kbps] Bit-Error Rate: pb=10-3 Link Fading Margin: 16 [dB] Capacity Cs: Number of simultaneous duplex channels Cost Lifecycle cost of the system (LCC [$]), includes: - Research, Development, Test and Evaluation (RDT&E) - Satellite Construction and Test - Launch and Orbital Insertion - Operations and Replenishment Olivier L. de Weck, 2006 Page 25 Multidisciplinary Simulator Structure Constants Input p x Vector Vector msat h, e min Constellation T, p ISL Spacecraft nspot Satellite Network msat Launch Module LV Cost nGW Link Budget LCC Rs Capacity Cs Pt , Da , MA msat Satellite Mass Number of Satellites T p Number of orbital planes nspot Number of spot beams nGW Number of gateways LV Launch vehicle selection Output J Vector Note: Only partial input-output relationships shown Olivier L. de Weck, 2006 Page 26 Governing Equations – Satellite Simulator a) Physics-Based Models Energy per bit over noise ratio: Eb PG r G t N 0 kLspace Ladd.Tsys.R (Link Budget) b) Empirical Models msat 38 0.14 Pt mprop 0.51 (Spacecraft) Scaling models derived from FCC database Springmann P.N., and de Weck, O.L. ”A Parametric Scaling Model for Non-Geosynchronous Communications Satellites”, Journal of Spacecraft and Rockets, May-June 2004 Olivier L. de Weck, 2006 Page 27 Traditional Systems Engineering The traditional approach for designing a system considers configurations (architectures) to be fixed over time. Designers look for a Pareto Optimal solution in the Trade Space given a targeted capacity. If actual demand is below Lifecycle Cost [B$ FY 2002] capacity, there is a waste If demand is over the capacity, market opportunity may be missed 1 10 Iridium actual Iridium simulated Globalstar actual Globalstar simulated Demand distribution Probability density function Pareto Front b P a D b f D ( )dD waste a 0 f D ( D) for all D under cap 0 10 3 10 4 5 6 10 10 10 Global Capacity Cs [# of duplex channels] 7 10 f D ( )dD 1 Olivier L. de Weck, 2006 Page 28 Staged Deployment Adapt to uncertain demand with a staged deployment strategy: A smaller, more affordable system is initially built This system has the flexibility to increase its capacity if demand is sufficient and if the decision makers can afford additional capacity Economic Advantage Some capital investments are deferred to later The ability to reconfigure and deploy the next stage is a real option Olivier L. de Weck, 2006 Page 29 Step 1: Partition the Design Vector Constellation Type: C xflexible xbase Astrodynamics Orbital Altitude: h Minimum Elevation Angle: emin Satellite Transmit Power: Pt Satellite Design Antenna Size: Da Network Multiple Access Scheme MA: Network Architecture: ISL Stage II Stage I C: h: emin: Pt: DA: MA: ISL: Rationale: Keep satellites the same and change only arrangement in space 'walker' 2000 12.5000 200 W 1.5 m 'MFCD' 1=yes xIbase = xIIbase C: h: emin: Pt: DA: MA: ISL: Olivier L. de Weck, 2006 'polar' 1000 7.5000 200 W 1.5 m 'MFCD' 1=yes Page 30 Step 2: Search Paths in the Trade Space Lifecycle cost [B$] h= 400 km e= 35 deg Nsats=1215 h= 2000 km e= 5 deg Nsats=24 family h= 400 km e= 20 deg Nsats=416 Constant: Pt=200 W DA=1.5 m h= 800 km e= 5 deg Nsats=54 ISL= Yes h= 400 km e= 5 deg Nsats=112 Total: 40 Paths System capacity Olivier L. de Weck, 2006 Page 31 Step 3a: Model Uncertainty [GBM] D - demand Dt – time period e- SND random variable m, s - constants DD mDt se Dt D DD 2 var s Dt D 5 x 10 Demand [Nusers] DD E mDt D 1.6 1.4 1.2 Geometric Brownian Motion Model GBM model, Dt = 1 month, Do = 50,000, m = 8% p.a., s = 40% p.a. – 3 scenarios are shown 1 0.8 0.6 0.4 0 5 Time [years] 10 15 Demand can go up or down between two decision points Infinitely many scenarios can be generated based on this model Olivier L. de Weck, 2006 Page 32 Step 3b: Binomial Lattice Model u es Dt d 1 u euDt d p ud Discretized Random Walk Total p 25=32 scenarios p p Sample scenario 1-p (1-p) P(i) p 1 p k Olivier L. de Weck, 2006 n k Page 33 Step 4: Calculate cost of paths We compute the costs of a path with respect to each Cap2 demand scenario We then look at the weighted average of every allowable path for cost over all scenarios rule: We always adapt to demand when demand exceeds capacity Cap1 Decision Costs The costs are discounted: the present value of LCC is considered Initial wait Deploy wait wait deployment 2nd stage Olivier L. de Weck, 2006 Page 34 Step 5: Identify optimal path System Lifecycle Cost [B$] 10 1 For a given targeted capacity, we compare our solution to the traditional approach Our approach allows large savings (30% on average) A4 A3 Best Path LCC of rigid design 2.01 Traditional design A2 1.36 10 E [LCC(pathj)*]= Best Deployment Strategy A1 0 10 2 10 3 10 E[DLCC]=$650 million value of real option 4 Capacity [thousands of users] n E LCC ( path j ) pi LCC scenarioipath j i 1 Olivier L. de Weck, 2006 Page 35 Takeaway from Satellite Project Identified best initial configuration, as well as potential growth stages Stage A1 21 satellites 3 planes h=2000 km Stage A2 50 satellites 5 planes h=800 km Stage A3 112 satellites 8 planes h=400 km Previous work focused on optimal coverage for static requirements only, arrive at very different solution Requires extra upfront investment (e.g. extra fuel, tunable antenna patterns), technical details remain Olivier L. de Weck, 2006 Page 36 Flexible Automotive Product Platforms sponsored by General Motors 2003-2005 Suh E.S., de Weck O.L., Chang D., “Flexible Product Platforms: Framework and Case Study”, Research in Engineering Design, submitted Nov.2, 2005 Olivier L. de Weck, 2006 Page 37 Research Context & Questions Sharp increase in number of models (variants) offered in the U.S. automotive market [Detroit News, Jan 2005]: 1947: 33 1990: 198 2009: 277 (estimate) Sales volumes per variant drop on average Market fragmentation Platform strategy adopted by most manufacturers Many uncertainties: - Styling & performance preferences shifting, regulations, new technologies future sales volumes are uncertain - How to design platforms to be flexible to respond to future developments? Model 3-4 years Model 3-4 years Model 3-4 years Platform ~ 10-15 year life Olivier L. de Weck, 2006 Page 38 Typical Vehicle Architecture (Platform) – General Motors Unique Carryover Modified Common “Platform” • Traditional product platform concept: • Unique Elements: Variant-specific customized elements • Common Elements: Commonly shared elements among product family • Rise of new elements class • Flexible (“Cousin”) Elements: Elements used (with modification) in more than one variant to satisfy variant-specific requirement Olivier L. de Weck, 2006 Page 39 Change Propagation Analysis Design Automotive Platforms to accommodate future changes in styling and demand of individual variants Identify BIW Change Propagation Network flexible elements Developed 7-step process Body-in-White Platform Key Design Variables Olivier L. de Weck, 2006 Page 40 Embed Flexibility W27 *Assume it meets quality, manufacturing, and safety requirements Flexible/Unique Upper Passenger Compartment H122 H50 L48 Flexible Lower Rear Passenger Compartment Common Lower Front Passenger Compartment Inflexible BIW Design Critical Components (Example) Flexible BIW Design Unique Unique Body Outer Panel Common Unique Unique Body Inner Panel Common Flexible (Blanking) Olivier L. de Weck, 2006 Page 41 Cost of Design Alternatives Design Inflexible BIW Flexible BIW Component Fabrication Inflexible Flexible BIW Assembly Line Inflexible Flexible Design Inflexible BIW Flexible BIW Initial Investment (Line + Tooling) 100.00 134.17 Refurbish Cost (Every 5 Years) 10.58 17. 99 Switch Cost (Styling Only) 31.99 5.35 Switch Cost (Styling + Length) 42.33 5.51 Length Change Above Belt Line H122 H5 W27 Forecast: Profit Differenct (Inflexible - Flexible 25,000 T rial s Frequency Chart 24,973 Displayed .023 572 .017 429 .011 286 .006 143 L48 .000 0 5.00 7.25 9.50 11.75 14.00 Normalized Profi t Olivier L. de Weck, 2006 Page 42 Takeaway Automotive Platforms Product Platforms …. “Bandwidth” can be increased by carefully embedding flexibility in the design Key is to propagate exogenous, functional uncertainties into design variables and find critical physical components Critical components are those that are change multipliers, or whose change would cause large switching costs Design for flexibility might cause larger upfront investment and larger variable costs Crossover between rigid and flexible design as a f(uncertainty) typically occurs Olivier L. de Weck, 2006 Page 43 Wrap-Up Olivier L. de Weck, 2006 Page 44 Time-expanded Decision Networks wait wait switch switch state node chance node decision node start end … Period 1 Period 2 Period N Olivier L. de Weck, 2006 Page 45 Path Optimization in TDN For each uncertain scenario, find the optimal path through the TDN max NPV, min LCC, … example start end … Period 1 Period 2 Period N Olivier L. de Weck, 2006 Page 46 Principles of Strategic Engineering A rigid design will be optimal (max NPV) if future events unfold exactly as forecasted A robust design can minimize the standard deviation of outcomes (reduce risk), but will usually also lower the expected NPV and max achievable NPV The larger the degree of uncertainty, the more valuable flexibility will be. Flexible designs can increase the E[NPV], while limiting downside and maximizing upside The larger the switching costs from one configuration to another the more likely that the current system will be continued due to “architectural lock-in”, despite operational sub-optimality Olivier L. de Weck, 2006 Page 47 Strategic Engineering Map Degree of NPV Uncertainty s E[NPV] “we are betting the farm” Flexible Design Strategically Redesign “we can adapt” Optimize for Expected Requirement “we know what’s coming” Robust Design “we will be ok no matter what” Relative Switching Costs DC/LCCr Olivier L. de Weck, 2006 Page 48 Future Work: Where do various systems fall ? Degree of NPV Uncertainty ? s communication satellites E[NPV] commercial aircraft wireless sensor networks automotive platforms consumer products water supply system highway infrastructure Relative Switching Costs DC/LCC Olivier L. de Weck, 2006 Page 49 The migration of strategic thinking Warfare ~500 A.D. Sun Tzu The Art of War Carl von Clausewitz (1780-1831) Management since ~1960s Michael E. Porter Competitive Strategy: Techniques for Analyzing Industries and Competitors Engineering since 2000? target domain: Army Firm System/ Product Olivier L. de Weck, 2006 Page 50 Last Slide Engineering Education Teaching Pedagogy Eng. Systems Studies 16.810 (U) Satellite Constellations (exits) Automotive Platforms (new) Oil & Gas Exploration (new) Eng. Design & Rapid Proto. Active Learning City Planning Game (exists) Auto Market Simulator (new) Others (TBD) Courses Graduate Courses 16.888 Multi Sys Des Opt ESD.71 Eng Sys Analysis SDM Program ESD.34 Sys Architecture ESD.36 Sys Project Mgt Age Dissemination Outlets 19 OpenCourseWare http://ocw.mit.edu 25 35 Engineering Systems Learning Center http://i2i.mit.edu Others MIT Professional Institute Seminars, Workshops, Future Work Strategic Engineering in additional Industries Comparative and Non-dimensional Analysis - Focus on TDN Olivier L. de Weck, 2006 Page 51 Backup Charts Olivier L. de Weck, 2006 Page 52 F/A-18 Change Propagation Network Object Process Diagram (OPD) Olivier L. de Weck, 2006 Page 53 Local Change to affect crack growth smax stress Ds Isoperformance Curve: Requirement=CGL=Nc: 25000 Ds smin Parameter Bounding Box 0.5 R=0 Performance Jz = Nc =25000 cycles to failure 0.4 Critical Load Number of Cycles N Crack length a [inch] 3 w=6” Initial Crack Length ao [inch] Center Cracked Panel 2a a DK Ds a sec w da C DK m dN Paris Law: Metal Fatigue 0.3 2.5 2 1.5 1 0.1 0.5 00 C=4e-9 m=3.5 0.2 0.5 1 1.5 Load cycles N [-] 2 2.5 x 10 4 0 8 10 12 14 16 Stress Amplitude D s Olivier L. de Weck, 2006 18 [ksi] 20 22 Page 54 F/A-18 Avionics Suite Olivier L. de Weck, 2006 Page 55 Existing Big LEO Systems Iridium Globalstar Time of Launch 1997 – 1998 1998 – 1999 Number of Sats. 66 48 Constellation Formation polar Walker Altitude (km) 780 1414 Sat. Mass (kg) 689 450 Transmitter Power (W) 400 380 Multiple Access Scheme Multi-frequency – Time Division Multiple Access Multi-frequency – Code Division Multiple Access Single Satellite Capacity Global Capacity Cs 1,100 duplex channels 72,600 channels 2,500 duplex channels 120,000 channels Type of Service voice and data voice and data Average Data Rate per Channel 4.8 kbps 2.4/4.8/9.6 kbps Total System Cost $ 5.7 billion $ 3.3 billion Current Status Bankrupt but in operation Bankrupt but in operation Individual Iridium Satellite Individual Globalstar Satellite Olivier L. de Weck, 2006 Page 56 Satellite System Economics Lifecycle cost T CPF T k I 1 Cops ,i 100 i 1 T C 365 24 60 L i 1 s f ,i Number of billable minutes Numerical Example: I 3 [B$] k 5 [%] Cops 300 [M$/y] T 15 [y] Cs 100,000 [#ch] Nu 3 106 Au 1,200 [min/y] CPF I k Cops Cs Lf Nu Au T CPF 0.20 [$/min] L f 0.068 Cost per function [$/min] Initial investment cost [$] Yearly interest rate [%] Yearly operations cost [$/y] Global instant capacity [#ch] Average load factor [0…1] Number of subscribers Average user activity [min/y] Operational system life [y] Nu Au L f min 365 24 60 Cs 1.0 But with Nu 50,000 CPF 12.02 [$/min] Non-competitive Olivier L. de Weck, 2006 Page 57 Strategic Building Architecture BP Exploration Headquarters, Aberdeen, Scotland Source: J. Fernandez , MIT Olivier L. de Weck, 2006 Page 58 Benchmarking Benchmarking is the process of validating a simulation by comparing the predicted response against reality. 140,000 120,000 100,000 80,000 60,000 40,000 20,000 0 Benchmarking Result 2: Lifecycle cost Lifecycle cost (billion $) Number of simultaneous channels of the constellation Benchmarking Result 1: Simultaneous channels of the constellation actual or planned simulated 1 Iridium 6.00 5.00 4.00 actual or planned 3.00 simulated 2.00 1.00 0.00 2 Globalstar 1 Iridium Iridium and Globalstar Iridium and Globalstar Benchmarking Result 4: Number of satellites in the constellation actual or planned simulated Iridium 1 Globalstar 2 Orbcomm 3 SkyBridge 4 Iridium , Globalstar, Orbcom m , and SkyBridge Number of satellites in the constellation Satellite mass (kg) Benchmarking Result 3: Satellite mass 1,400.0 1,200.0 1,000.0 800.0 600.0 400.0 200.0 0.0 2 Globalstar 70 60 50 40 actual or planned 30 simulated 20 10 0 Iridium 1 Globalstar 2 Orbcomm 3 SkyBridge 4 Iridium , Globalstars, Orbcom m , and SkyBridge Olivier L. de Weck, 2006 Page 59 Platform Leverage Increases Average Vehicle Models per Platform Models/Platform 6 5 DCX 4 Ford 3 Honda 2 Toyota VW 1 0 2002 2003 2004 2005 2006 2007 2008 2009 Year Source: Price Waterhouse Coopers, 2003 Olivier L. de Weck, 2006 Page 60