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Adventures in industry
Sue Lewis
Southampton Statistical Sciences Research Institute
University of Southampton
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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 useeg 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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control x noise interactions
Control
Re
sp
on
se
HighLow
Noise
High
Low
For conventional factorial designs large number of factors large number of runs
Also main effects and control x control interactions
Want to detect
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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
Control
Re
sp
on
se
HighLow
Noise
High
Low
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• 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
Grouping factors
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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
Two Stage Group Screening
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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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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 NoisePlug type* TemperaturePlug gap* Injector tip leakageAir fuel ratioInjection timing
Control – less likelySpark during crankSpark time during run-upHigher idle speedIdle 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 timingGroup 3: Spark time during crank & During run-upGroup 4: Higher idle speed & Idle flare
Noise factors: Group 5: Injector tip leakageGroup 6: Temperature
Design:Half-replicate (I=123456) 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
Aim: mean sound output close to target
with reduced variation
armature
diaphragmmagnet
front case
Acoustic sounder Hosiden Besson
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Gear pump
Aim: reduce mean leakage and variation in leakage
- under varying pressure and speed
gear pack
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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
0.4
0.6
0.8
1.0
Mea
n Le
akag
e
Endfloat-0.1 0.1 0.3
Pressure110
50
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
O’Neill, 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.