Improvement Curves: An Early Production Methodology Brent M. Johnstone 11 June 2015 1
Hours per Unit Misspecification of Slopes 10,000 80% Slope 75% Slope Predicting 75% Slope, But Achieving Only 80% Slope Understates Estimated Hours By 59% At Unit #150 1,000 100 1 10 100 Cumulative Quantity Choice Of Learning Slope Selection Is Critical Parameter In Manufacturing Labor Estimates. Incorrect Ex Ante Predictions Lead to Over or Understatements of Projected Hours 2
Issues With Choosing Slopes A Simple Projection of Actual Experience To Date Is No Guarantee of Success In general, the empirical findings caution against simplistic uses of either industry experience curves or a firm s own progress curves. Predicting future progress rates from past historical patterns has proved unreliable. (pg. 237) Dutton, Thomas (1984) Even with both an excellent fit to historical data (as measured by metrics like R 2 ), and meeting almost all of the theoretical requirements of cost improvement, there is no guarantee of accurate prediction of future costs. [E]ven projections based on producing an almost identical product over all lots, in a single facility, with large lot sizes, and no production break or design changes, do not necessarily yield reliable forecasts of labor hours. Out-ofsample forecasting using early lots to predict later lots has shown that, even under optimal conditions, labor improvement curve analyses have error rates of about +/- 25 percent. (pg. 94) RAND (2008) Existing Literature Provides Little Guidance On Ex Ante Selection 3
Hours per Unit S-Curves Observed Learning Curves Are Rarely Straight Logarithmic Functions But Exhibit S Shape Depending On Maturity Of Product 100,000 Phase 1 - Development Multi-missioned flight articles Low delivery rate High incidence of change Incomplete tool families High scrap & rework Phase 2 - Production Configuration Implement changes from test program Complete tool family Acceleration of production rate Progressive reduction of minor engineering changes Affordability / producibility improvements initiated Reduced scrap, rework & obsolescence 10,000 Phase 3 - Stabilization Aircraft design stabilized Reach peak production rates Reduced setup costs with large lot sizes Continued scrap & rework reductions Ongoing tech modernization program 1,000 1 10 100 1000 10000 Cumulative Units Initially Observed Based On World War II Experience (Carr, 1946) 4
Early Production Issues Choice of Learning Curve Slope Is Particularly Difficult In Early Production When There Is Limited Actual Cost History Development Actuals Are High & Observed Slopes Usually Very Flat Early Production Actuals Begin Sharp Decrease As Initial Problems Are Being Worked In the Build Engineering Changes / Corrections Tooling Changes / Improvements Reduction In Nonconformances (Scrap, Rework & Repair) Supply Chain Disruptions Overcome Problem For Estimating: What Kind Of Learning Curve Slope Can We Expect To See? How Long Will This Steep Phase Last? If We Are On A Recovery Slope, What Are We Are Recovering To and How Quickly? 5
Hours per Unit S-Curve & Basic Slopes Cochran (1960) Suggested A Straight-Line Basic or Characteristic Slope Whose Total Cost Equals Total Cost For S-Curve 10,000 S Curve Basic Curve 1,000 80% Basic Slope 100 1 10 100 1,000 Quantity 6
Basic Slopes Processes Job Machine Shop 1 Sheet Metal Stamp 1 Composite Automated Layup 3 Electrical Fabrication 2 Job Machining Large Parts 1 Electrical Subassembly 2 Composite Handlay 3 General Subassembly 1 Major Aircraft Assembly 1 Typical Slope % 95% 92% 92% 90% 88% 85% 85% 83% 80% Sources: 1 Cochran (1968) 2 Delionback (1975) 3 Kassapoglou (2013) Basic Slopes Vary With Manufacturing Processes 7
Hours per Unit S-Curve vs Basic Slope Unit Cost On S-Curve Is Initially Larger Than Basic Slope Extensive Changes To Engineering, Tooling As Well As High Nonconformance Drive Cost Of Early Units S-Curve Recovers To Basic Slope After Initial Engineering, Tooling Issues Are Resolved Cochran Suggested Crossover Point Occurred Around 30 th Unit Empirical Analysis Shows Recovery Between 30 th And 100 th Unit 10,000 S Curve Basic Curve Cost of Early Units Reflects Premium Due To Engineering, Tooling Changes & High Levels of Scrap & Rework 1,000 Crossover Point Where S-Curve Unit Cost Equals Basic Slope Unit Cost 100 1 10 100 1,000 Quantity 8
Hours per Unit S-Curve vs Basic Slope (Cont d) S-Curve Continues Underneath Basic Slope Until Two Lines Intersect Again At Some Future Point (Unit # 1000 For Aircraft Assembly) T-1000 Chosen As Point Of Full Product & Process Maturity Total Cost For Basic Curve = Total Cost For S-Curve Over 1,000 Units 10,000 S Curve Basic Curve 1,000 S-Curve Intersects Basic Slope at Point of Full Maturity 100 1 10 100 1,000 Quantity 9
Hours per Unit S-Curve History 10,000 1,000 S-Curves & Basic Slopes Can Be Constructed Ex Post From Actual Data But How Do We Identify Them Ex Ante? 100 1 10 100 1000 Aircraft Quantity 10
Using Standards One Possible Answer Is Use Of Industrial Engineering Standards Standard Time Necessary For A Qualified Workman, Working At An Efficient Pace and Experiencing Normal Durability & Delay, To Do A Defined Amount Of Work of Specified Quality Using Standardized Processes & Procedures Types of Standards Defined By MIL-STD-1567A Type I Defined by Engineering Time Study (4M) or Work Sampling Type II All Other Kinds of Standards New Automated Tools To Apply Standards Allow Earlier Introduction Of Type I Standards Into Program At Much Lower Cost Than 1980s-Style MIL-STD-1567A Implementation 11
Hours per Unit Standards-Based Approach Determine Standard Hours For a Task and Draw This As the Floor Below Which the Estimate Cannot Go Type I Standards Are Better For This Approach Than Type II 10,000 NOTIONAL Actual Hours 1,000 T1000 Hours Variance Factor = 2 (Actuals / Standards) 100 Standard Hours 1 10 100 1000 Cum Sequence Number Determine Assumed Realization at T-1000 (Aircraft Assembly) Realization Is Expected or Observed Actual Variation To Standard This Value Is Usually Known From Prior Programs 12
Hours per Unit Standards-Based Approach Draw a Line From T-1000 Back To T-1 Using the Appropriate Basic Slope Suggested By Cochran Or By Empirical Study I.e., Major Aircraft Assembly 80% 10,000 NOTIONAL Actual Hours 1,000 Basic 80% Slope T1000 Hours Variance Factor = 2 (Actuals / Standards) 100 Standard Hours 1 10 100 1000 Cum Sequence Number This Is The Basic Slope To Which You Tend To Recover Over Time At Any Given Time, The Actual Hours May Be Higher or Lower Especially Early In The Program, When The Actual Hours Will Tend To Be Higher 13
Hours per Unit Example Curve Projection 10,000 NOTIONAL Actual Hours Recovery to Basic Slope 1,000 Basic 80% Slope T1000 Hours Assumed Point Where S-Curve & Basic Slope Meet Variance Factor = 2 (Actuals / Standards) 100 1 10 100 1000 Cum Sequence Number Standard Hours 14
Conclusions Use Of I.E. Standards As Floor To Establish Basic Slope Provides Empirical Basis For Choosing And-On Learning Curves Basic Slopes Can Be Derived From Industry Experience Or Prior Program Data Approach Can Be Used As Cross-Check To Verify Projected Learning Curve Slopes 15
References Asher, H. (1956). Cost-Quantity Relationships in the Airframe Industry. Santa Monica, California: RAND Corporation. Carr, G.W. (1946). Peacetime Cost Estimating Requires New Learning Curves. Aviation, Vol. 45, April 1946, pp. 76-77. Cochran, E.B. (1960). New Concepts of the Learning Curve. The Journal of Industrial Engineering, July-August 1960, pp. 317-327. Cochran, E.B. (1968). Planning Production Costs: Using the Improvement Curve. San Francisco: Chandler Publishing Company. Crawford, J. R. (1944). Learning Curve, Ship Curve, Ratios, Related Data. Burbank, California: Lockheed Aircraft Corporation. Delionback, L. (1975). NASA Technical Memorandum TM X-64968: Guidelines for Application of Learning / Cost Improvement Curves. Huntsville, Alabama: NASA. Dutton, J., Thomas, A. (1984). Treating Progress Functions As a Managerial Opportunity. The Academy of Management Review, April 1984, pp. 235-247. Fox, B., Brancato, K., Alkire, B. (2008). Guidelines and Metrics for Assessing Space System Cost Estimates. Santa Monica, California: RAND Corporation. Hofbauer, J., Sanders, G., Ellman, J., Morrow, D (2011). Cost and Time Overruns for Major Defense Acquisition Programs: An Annotated Brief (Washington, D.C.: Center for Strategic and International Studies) 16
References (cont d) Kassapoglou, Christos (2013). Design and Analysis of Composite Structures: With Applications to Aerospace Structures, 2nd edition. Chichester, United Kingdom: John Wiley & Sons. Miller, F. D. (1971). The Cubic Learning Curve A New Way to Estimate Production Costs. Manufacturing Engineering & Management, July 1971, pp. 14-15. MIL-STD-1567A, Military Standard: Work Measurement (1983). Wright, T.P. (1936). Factors Affecting the Cost of Airplanes. Journal of the Aeronautical Sciences, Vol. 3, February 1936, pp. 122-128. 17