Adventures in industry

Sue Lewis

Southampton Statistical Sciences Research Institute

University of Southampton

sml@maths.soton.ac.uk

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

Cold Start Optimisation

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

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

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

• 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

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

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)

• 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

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

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

Investigation of different groupings

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

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

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

Experiments on assembled products

Aim: mean sound output close to target

with reduced variation

armature

diaphragmmagnet

front case

Acoustic sounder Hosiden Besson

Gear pump

Aim: reduce mean leakage and variation in leakage

- under varying pressure and speed

gear pack

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

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

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

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

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

Software to Implement the Methods (DEAP)

Software to Implement the Methods (DEAP)

Results from the studies

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0.8

1.0

Mea

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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

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

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 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.