Stat 470-18

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Stat 470-18

• Today Start Chapter 10

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Additional Homework Question
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Chapter 10Robust Parameter Design

• Robust parameter design is an experimentation
  technique which aims to reduce system variation
  and also optimize the mean system response
• Idea is to use control factors to make the system
  robust to the influences of noise factors

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Example Leaf Spring Experiment (p. 438)

• Experiment was conducted to investigate the
  impact of a heat treatment process on truck leaf
  springs where the target height of the springs is
  8 inches
• Experiment considered 5 factors, each at 2
  levels
• B High heat treatment
• C Heating time
• D Transfer time
• E Hold down time
• Q Quench oil temperature
• In regular production Q is not controllable, but
  can be in the experiment

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Example Leaf Spring Experiment (p. 438)

• 25-1 fractional factorial design was performed
  IBCDE
• Experiment has 3 replicates

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Noise Factors

• Noise factors are factors that impact the system
  response, but in practice are not controllable
• Examples include environmental factors, differing
  user conditions, variation in process parameter
  settings,
• Example refrigerators are manufactured so that
  the interior temperature remains close to some
  target
• Section 10.3 discusses different types of noise
  factorsplease read

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Variance Reduction Via Parameter Design

• Let x denote the control factor settings and z
  denote the noise factor settings
• Relationship between the system response and the
  factors y f(x,z)
• If noise factors impact the response, then
  variation in the levels of z will transmit this
  variance to the response, y
• If some noise and control factors interact, can
  potentially adjust levels of control factors to
  dampen impact of noise factor variation

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Variance Reduction Via Parameter Design

• Suppose there is one noise factor and two control
  factors
• What is variance of y in practice?
• What does this imply?

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Cross Array Strategy

• We will consider two types of design/analysis
  techniques for robust parameter design
• The first one uses location-dispersion modeling
  (e.g., have a model for the mean response and
  another for the variance) similar to the
  epitaxial layer growth experiment in Chapter 3
• The design strategy for this technique is based
  on a cross array

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Cross Array Strategy

• Consider the leaf spring example
• We can view this experiment as the combination of
  two separate experimental designs
• Control array design for the control factors
• Noise array design for the noise factors
• Cross array design consisting of all level
  combinations between the control array and the
  noise array
• If there are N1 runs in the control array and N2
  trials in the noise array, then the cross array
  has N1 N2 trials

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Cross Array Strategy

• Design for control factors
• Design for noise factors

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Cross Array Strategy

• The responses are modeled using the
  location-dispersion approach
• The models include ONLY the control factors
• At each control factor setting, and
  are used as measures of location and
  dispersion
• Factors that impact the mean are called location
  factors and those that impact the variance are
  dispersion factors
• Location factors that are not dispersion factors
  are called adjustment factors

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Example Leaf Spring
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Example Leaf Spring
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Example Leaf Spring
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Example Leaf Spring

• Location Model
• Dispersion Model
• Level settings

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Two-Step Optimization Procedures

• Nominal the best problem
• Select the levels of the dispersion factors to
  minimize the dispersion
• The select the levels of the adjustment factors
  to move the process on target
• Larger (Smaller) the better problem
• Select levels of location factors to optimize
  process mean
• Select levels of dispersion factors that are not
  location factors to minimize dispersion
• Leaf Spring Example was a nominal the best
  problem

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Response Modeling

• There may be several noise factors and control
  factors in the experiment
• The cross array approach identifies control
  factors to help adjust the dispersion and
  location models, but does not identify which
  noise factors interact with which control factors
• Cannot deduce the relationships between control
  and noise factors
• The response model approach explicitly model both
  control and noise factors in a single model
  (called the response model)

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Response Modeling

• Steps
• Model response, y, as a function of both noise
  and control factors (I.e., compute regression
  model with main effects and interactions of both
  types of factors)
• To adjust variance
• make control by noise interaction plots for the
  significant control by noise interactions. The
  control factor setting that results in the
  flattest relationship gives the most robust
  setting.
• construct the variance model, and choose control
  factor settings that minimize the variance

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Example Leaf Spring Experiment (p. 438)

• 25-1 fractional factorial design was performed
  IBCDE
• Experiment has 3 replicates

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Example Leaf Spring Experiment (p. 438)

• 25-1 fractional factorial design was performed
  IBCDE

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Example Leaf Spring Experiment (p. 438)
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Example Leaf Spring Experiment (p. 438)
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Example Leaf Spring Experiment (p. 438)

• Response Model

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Example Leaf Spring Experiment (p. 438)
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Example Leaf Spring Experiment (p. 438)

• Variance Model