Adventures in industry

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Adventures in industry

• Sue Lewis
• Southampton Statistical Sciences Research
  Institute
• University of Southampton

sml_at_maths.soton.ac.uk
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Outline

• Experiments on many factors
• - with Jaguar Cars
• - using two-stage group screening
• - to find the important factors
• Experiments on assembled mechanical products
• - where values of factors cannot be set
• - with Hosiden Besson, Sauer Danfoss, Goodrich
• Software for implementing the methods

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Cold Start Optimisation
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Factors Affecting Performance

• Control (or design) factors can be set by the
  engineers
• Noise factors - cannot be controlled in use
• eg ambient temperature
• - can be controlled in an
  experiment
• Aim find the control factor settings that
• Optimise the performance (engine starts -
  resistance)
• Minimize variability in performance
• - due to the varying noise factors
• - Deming, Taguchi

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Want to detect
control x noise interactions
Also main effects and control x control
interactions
For conventional factorial designs large number
of factors ? large number of runs
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Classical Solution

• Run an experiment to estimate only main effects
• - identify the important factors
• For the important factors, run an experiment
• - to estimate both main effects and
  interactions
• Disadvantage could miss factors that interact
  with noise

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Grouping factors

• Arrange the factors in groups
• Label the factor levels
• high - larger response anticipated
• low - smaller response anticipated
• For each group define a new grouped factor with
  two levels
• high - all factors in group high
• low - all factors in group low
• Experiment on the grouped factors

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Two Stage Group Screening
Stage 1 perform an experiment on the grouped
factors to decide which groups are important -
estimate main effects and/or interactions
Stage 2 dismantle those groups found to be
important and experiment on their individual
factors - estimate both main effects and
interactions


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Gathering Information from Experts

• Opinions on
• Factors that might be included in the experiment
• - and their levels
• The likely importance of each factor
• The direction of each main effect
• Any insights/experience on interactions
• Local brainstorming but experts often at
  different sites

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Web-based System (GISEL)

• Gathers opinions/suggestions on factors and their
  levels
• - via a dynamic questionnaire
• - with free form comments
• Keeps a record of opinions, experiments and
  results
• Guides factor groupings via software that
• - explores the resources needed for various
  strategies and factor groupings
• - estimates the risk of missing important
  factors through simulation of experiments

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Factors under Consideration
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(No Transcript)
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Summary of Opinions on Air to Fuel Ratio
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Making a decision on groupings

• Assess possible grouping strategies
• - resource required
• - risk of missing an important factor
• Individual factors are classified as
• Very likely to be active
• Less likely to be active
• Not worth including
• Probabilities assigned
• eg 0.7 and 0.2

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Ten Factors for the Experiment

• Control very likely Noise
• Plug type Temperature
• Plug gap Injector tip leakage
• Air fuel ratio
• Injection timing
• Control less likely
• Spark during crank
• Spark time during run-up
• Higher idle speed
• Idle flare
• hard-to-change grouped together

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Investigation of different groupings
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Plan for the First Stage (10 factors)

• Control factors
• Group 1 Plug type Plug gap
• Group 2 Air to fuel ratio Injection timing
• Group 3 Spark time during crank During run-up
• Group 4 Higher idle speed Idle flare
• Noise factors
• Group 5 Injector tip leakage
• Group 6 Temperature
• Design
• Half-replicate (I123456) in 4 sessions of 8 runs

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Results of First Stage Experiment

• Included large interactions
• (Afr Injection timing) x Temperature
• (Higher idle speed Idle flare) x Injector tip
  leakage
• - both grouped control x noise interactions
• ? 6 factors to investigate at the Second Stage
  Experiment

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Second Stage Experiment

• Design
• Half-replicate in 32 runs (I ABCDEF)
• - for the individual factors
• - could have been smaller
• Preliminary findings include
• Air to Fuel Ratio x Temperature is large
• Possible three factor interaction

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• Experiments on assembled products

Acoustic sounder Hosiden Besson
front case
armature
Aim mean sound output close to target with
reduced variation
magnet
diaphragm
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Gear pump

gear pack
Aim reduce mean leakage and variation in
leakage - under varying pressure and speed
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Possible approaches

• Factorial experiments
• set factors to values specified in the design
• Obtain parts with required factor values by
• - making special components
• - measuring large samples and using components
  with required factor values
• For our examples too slow and costly
• Disassembly/reassembly experiments (Shainin)
• In our examples cannot reuse components

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Our Approach

• Take a sample of each kind of component from
  production
• Measure the relevant component variables
• Assemble the components to form a set of products
  for testing
• to maximise information on the factors of
  interest

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Factors

• Directly measurable on a component
• - eg permeability of the armature in the sounder
• Formed or derived as a function of measured
  quantities
• on two or more components
• - eg gaps between components in the assembled
  product
• - cannot be handled by conventional designs
• Factors that can be set
• - eg the skill of the operator in making
  certain adjustments during the manufacture of the
  sounder

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To design the experiment

• must decide which set of products to assemble
• There is a huge number of possibilities
• Eg For 4 components (pump gear pack) and
  sufficient parts
• to assemble 12 products
• - the number of possibilities is 12x1035
• Needs a non-standard search algorithm that
• - finds an efficient set of assemblies
• - allows for the non-reuse of components
• - accommodates conventional factors

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Finding a design

• Use a specially developed search algorithm with
• - a low order polynomial to describe the
  response
• - a design chosen for accurate estimation of the
  coefficients of the model (D-optimality)
• Software (DEAP) has been developed that
• - assists with product and component definition
• - provides access to the design algorithm

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Software to Implement the Methods (DEAP)
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Software to Implement the Methods (DEAP)
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Results from the studies
The most important factors for improving the
product performance were For the sounder the
pip height and skill of operator For the
pump positioning of the cover and the alignment
of gears
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Conclusions

• Tools and methods developed in collaboration with
  industry for two kinds of experiments
• - large numbers of factors
• - assembled products
• Software at the beta testing stage
• - freely available

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Some related references

• Atkinson, A.C. and Donev, A.N. (1992) Optimum
  Experimental Designs. Oxford Oxford University
  Press.
• Dean, A.M. and Lewis, S.M. (2002) Comparison of
  group screening strategies for factorial
  experiments. Computational Statistics and Data
  Analysis, 39, 287-297.
• Deming, W.E. (1986) Out of the Crisis. Cambridge
  C.U.P.
• Dupplaw, D., Brunson, D., Vine, A.E., Please,
  C.P., Lewis, S.M., Dean, A.M., Keane, A.J. and
  Tindall, M.J. (2004) A web-based knowledge
  elicitation system (GISEL) for planning and
  assessing group screening experiments for product
  development. To appear in J. of Computing and
  Information Science in Engineering (ASME).
• Harville, D. A. (1974) Nearly optimal allocation
  of experimental units using observed covariate
  values. Technometrics 16, 589-599.

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Some related references

• ONeill, J.C., Borror, C.M., Eastman, P.Y.,
  Fradkin, D.G., James, M.P., Marks, A.P. and
  Montgomery, D.C. (2000) Optimal assignment of
  samples to treatments for robust design. Qual.
  Rel. Eng. Int. 16, 417-421.
• Lewis, S.M. and Dean, A.M. (2001) Detection of
  Interactions in Experiments with large numbers of
  factors (with discussion). J. Roy. Statist. Soc.
  B, 63, 633-672.
• Sexton, C.J., Lewis, S.M. and Please, C.P. (2001)
  Experiments for derived factors with application
  to hydraulic gear pumps J. Roy. Statist. Soc. C,
  50, 155-170.
• Shainin, R.D. (1993) Strategies for technical
  problem solving. Qual. Eng., 433-448.
• Taguchi, G. (1987) System of Experimental Design.
  New York Kraus.