lecture4 - http:/ocw.mit.edu _ MIT OpenCourseWare Spring...

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MIT OpenCourseWare _________ http://ocw.mit.edu ___ 2.830J / 6.780J / ESD.63J Control of Manufacturing Processes (SMA 6303) Spring 2008 For information about citing these materials or our Terms of Use, visit: ________________ http://ocw.mit.edu/terms .
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1 M anufacturing Control of Manufacturing Processes Subject 2.830/6.780/ESD.63 Spring 2008 Lecture #4 Probability Models of Manufacturing Processes February 14, 2008
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2 M anufacturing Note: Reading Assignment • May & Spanos – Read Chapter 4 • Montgomery – Skim/consult Chapters 2 & 3 if need additional explanations or examples beyond May & Spanos
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3 M anufacturing Turning Process
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4 M anufacturing CNC Turning 0.6970 0.6980 0.6990 0.7000 0.7010 0.7020 Run Number Shift changes • Randomness + Deterministic Changes random or unknown Δα Observations from Experiments
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5 M anufacturing CNC Data 0.6235 0.6237 0.6239 0.6241 0.6243 0.6245 0.6247 0.6249 0.6251 0.6253 123456789 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 Outer Middle Inner Operating Points: High Feed=1 Low Feed = 2
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6 M anufacturing Brake Bending of Sheet M M ε σ Output: Angle
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7 M anufacturing Bending Process Springback
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8 M anufacturing Angle changes with depth Δ Y Δ u • Clear Input-Output Effects (Deterministic) • Also Randomness as well Observations from Bending Process 20 30 40 50 60 70 80 90 Aluminum 0.3 In Steel 0.3 In Aluminum 0.6 In Steel 0.6 In
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9 M anufacturing Observations from Injection Molding Run Chart for Injection Molded Part 40.60 40.65 40.70 40.75 40.80 40.85 40.90 40.95 41.00 0 1 02 03 04 05 06 0 Number of Run Width (mm) Average Holding Time = 5 sec Injection Press = 40% Holding Time = 10 sec Injection Press = 40% Holding Time = 5 sec Injection Press = 60% Holding Time = 10 sec Injection Press = 60% 2/3/05 50
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10 M anufacturing Observations from Data • Clearly some measurement “noise”? 20 30 40 50 60 70 80 90 shift 1 shift 2 shift 3
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11 M anufacturing Observations from Data • Systematic/traceable “operator error” Sheet Shearing 0.85 0.87 0.89 0.91 0.93 0.95 0.97 0.99 1.01 shift change shift change aluminum steel steel
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12 M anufacturing Inputs A Random Process + A Deterministic Process How Model to Distinguish these Effects? Process Disturbances (Reducible) Irreducible Disturbances Outputs + "Noise"
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13 M anufacturing • Consider the Output-only, “Black Box” view of the Run Chart • How do we characterize the process? – Using Y(t ) only • WHY do we characterize the process – Using Y(t ) only? Process Y(t) Random Processes
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14 M anufacturing The Why • Did output really change? • Did the input cause the change? • If not, why did the output vary? • How confident are we of these answers? • Can we model the randomness? Process
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15 M anufacturing Background Needed • Theory of Random Processes and Random Variables • Use of Sample Statistics Based on Measurements – SPC basis – DOE: use of experimental I/O data – Feedback control with random disturbances
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16 M anufacturing How to Describe Randomness?
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This note was uploaded on 09/24/2010 for the course MECHE 2.830J taught by Professor Davidhardt during the Spring '08 term at MIT.

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lecture4 - http:/ocw.mit.edu _ MIT OpenCourseWare Spring...

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