Process Capability

1
Process Capability

• Cp (design tolerance width)/(process width)
  (max-spec min-spec)/ /6?x
• 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 30/612 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 /- 6?x or 12 ?x

3?
3?
process width
Design tolerance width
min acceptable
max acceptable
2
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
10Time
HYPOTHETICAL
FactorA
FactorB
Temperature
Time
200F
400F
20 min
26 min
Option 1
Option 2
Options 1 and 2 deliver the same value of
chewiness. Why might you prefer one option over
the other?
3
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

4
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.

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
5
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.

6
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