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Adventures in industry. Sue Lewis Southampton Statistical Sciences Research Institute University of Southampton. sml @ Outline. Experiments on many factors - with Jaguar Cars - using two-stage group screening - to find the important factors

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Adventures in industry
Adventures in industry

Sue Lewis

Southampton Statistical Sciences Research Institute

University of Southampton

[email protected]


  • 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

Factors affecting performance
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

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

Classical solution
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

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

Gathering information from experts
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

Web based system gisel
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

Making a decision on groupings
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

Ten factors for the experiment
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

Plan for the first stage 10 factors
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


Half-replicate (I=123456) in 4 sessions of 8 runs

Results of first stage experiment
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

Second stage experiment
Second Stage Experiment


  • 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


Aim: mean sound output

close to target

with reduced variation



Gear pump
Gear pump

gear pack

Aim: reduce mean leakage and variation in leakage

- under varying pressure and speed

Possible approaches
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/reassemblyexperiments (Shainin)

    In our examples: cannot reuse components

Our approach
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


  • 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

Finding a design
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

Results from the studies
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


  • 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

Some related references
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.

Some related references1
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.