Download Presentation
## Process Capability

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Process Capability**• Cp = (design tolerance width)/(process width) = (max-spec – min-spec)/ /6x • Example: • Plane is “on time” if it arrives between T – 15min and T + 15min. • Design tolerance width is therefore 30 minutes • x of arrival time is 12 min • Cp = 30/6*12 = 30/72 = 0.42 • A “capable” process can still miss target if there is a shift in the mean. • Motorola “Six Sigma” is defined as Cp = 2.0 • I.e., design tolerance width is +/- 6x or 12 x 3 3 process width Design tolerance width min acceptable max acceptable Problem Solving, Design, and System Improvement**There are multiple solutions to most parametric design**problems Analytical Expression for Brownie Mix “Chewiness” Chewiness = FactorA + FactorB Where FactorA = 600(1-exp(-7T/600)) + T/10 And FactorB = 10*Time HYPOTHETICAL FactorA FactorB Temperature Time 200F 400F 26 min 20 min Option 1 Option 2 Options 1 and 2 deliver the same value of “chewiness.” Why might you prefer one option over the other? Problem Solving, Design, and System Improvement**Parametric Tuning**• Existing system that basically works. • Adjustments involve setting values of parameters. • In ideal case, have a nice analytical model and can optimize mathematically. This is rare in practice. • Examples: • Physical Processes • Almost any continuous manufacturing process, e.g. chemical processing, food processing • Products • Windshield wiper spray parameters • Catapult settings • Engine control settings • Services • Direct mail parameters (drop locations, mailing dates, placement of graphics) • Boarding process at airline gate • Call center procedures • Automated check-in process at hotel • Ad placement on Yahoo Problem Solving, Design, and System Improvement**Taguchi Methods**• Any deviation from the target value is “quality lost.” • Use of statistical experimentation to find robust combinations of parameters. • Field is called “Design of Experiments” or “DOE.” • Systematically explore space of possible parameter values. • Based on analysis of relative influence of parameters on mean and variance of performance variable, select “robust design.” • A robust design is relatively insensitive to random variability in internal and external variables. Quality Quality Loss Loss = C(x-T)2 Good Performance Metric Performance Metric, x Bad Maximum acceptable value Minimum acceptable value Target value Target value Problem Solving, Design, and System Improvement**Methodology for Achieving Robust Design**• Identify key variables and metrics • Articulation of performance metrics, goals • Causal diagram • Hypothesized sources of variability • Analytical models where available • Conduct exploratory experiments • Reduce variability • Design changes • Instructions/aids for user • Use logic, analysis, and rough experiments to focus further experimentation • Avoid wasting experiments on clearly infeasible regions of design space. • Perform focused experimentation within narrow ranges of variables • Use “Design of Experiments” techniques if combinatorically intractable • See Ulrich and Eppinger “Robust Design” chapter for details. • “Control” variability in laboratory setting • Focus on identifying combination of settings that minimize variability in performance. • Select final values for design variables. Problem Solving, Design, and System Improvement**Take Aways**• Products and processes are causal systems • Typically have lots of variables • Internal variables are set by the manufacturer/provider • Target settings and associated variance • External variables are set by the environment or the user • Target settings and associated variance (variance often much harder to control than with internal variables) • Impossible to eliminate all variability • GOAL: find target settings for variables such that variability in other values of these variables has minimal effect on output/performance….a “robust design.” • Methodology for achieving robust design • Causal model, even if not explicitly analytical • Early exploratory experimentation • Control of variability and increased robustness through design changes • Focused experimentation to refine settings Problem Solving, Design, and System Improvement