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Adventures in industry

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Sue Lewis

Southampton Statistical Sciences Research Institute

University of Southampton

- 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

- Softwarefor implementing the methods

Cold Start Optimisation

- Control (or design) factorsâ€“ 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

Want to detect

control x noise interactions

Also main effects and control x control interactions

For conventional factorial designs

large number of factors ïƒ¨ large number of runs

- 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

Grouping factors

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

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

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 â€“ but experts often at different sites

- 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

Factors under Consideration

Summary of Opinions on Air to Fuel Ratio

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

Control â€“ very likelyNoise

Plug type* Temperature

Plug gap* Injector tip leakage

Air fuel ratio

Injection timing

Control â€“ less likely

Spark during crank

Spark time during run-up

Higher idle speed

Idle flare

* hard-to-change: grouped together

Investigation of different groupings

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 (I=123456) in 4 sessions of 8 runs

Included large interactions

(Afr & Injection timing) x Temperature

(Higher idle speed & Idle flare) x Injector tip leakage

- both grouped control x noise interactions

ïƒ¨ 6 factors to investigate at the 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

Acoustic sounder

Hosiden Besson

Experiments on assembled products

front case

armature

Aim: mean sound output

close to target

with reduced variation

magnet

diaphragm

gear pack

Aim: reduce mean leakage and variation in leakage

- under varying pressure and speed

- 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

- set factors to values specified in the design
- Disassembly/reassemblyexperiments (Shainin)
In our examples: cannot reuse components

- 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

- 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

To design the experiment

- must decide which set of products to assemble
- There is a hugenumber 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

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

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

- 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

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.

Oâ€™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.