Abstracts of

ENBIS-DEINDE 2011

Spring Conference

Torino (Italy), 16-18 March 2011

Joint ENBIS-DEINDE 2011 Spring Conference

PROGRAMME CHAIR:Grazia Vicario (Politecnico di Torino, Italy)

SCIENTIFIC COMMITTEE:Alessandro Balsamo (Istituto Nazionale di Ricerca Metrologica - INRIM, Italy)Stefano Barone (University of Palermo, Italy)Shirley Coleman (University of Sheffield, United Kingdom)Alistair B Forbes (National Physical Laboratory, United Kingdom)Mauro Gasparini (Politecnico di Torino, Italy)Peter Goos (University of Antwerp, Belgium)Ron S Kenett (KPA Ltd, Israel)Raffaello Levi (Politecnico di Torino, Italy)Jeremy Oakley (University of Sheffield, United Kingdom)Giovanni Pistone (Collegio Carlo Alberto, Moncalieri, Torino, Italy)Olivier Roustant (Ecole des Mines de Saint-Etienne, France)Henry Wynn (London School of Economics, United Kingdom)

LOCAL CHAIR:Roberto Fontana (Politecnico di Torino, Italy)

The Enbis Deinde 2011 Spring Conference has been organized by the Department of Math-ematics of Politecnico di Torino.The Sponsors and the Supporters of the Conference are:

• Fondazione “Franca e Diego de Castro”;

• Regione Piemonte, Direzione Cultura, Turismo e Sport, Settore Promozione Turistica- Analisi della Domanda e del Mercato Turistico;

• Fiat Group Marketing & Corporate Communication S.p.A.;

• SAS.

ENBIS DEINDE 2011

Contact address: enbis-deinde2011@calvino.polito.itWeb site: http://calvino.polito.it/enbis deinde 2011/

c© — Copyrights 2011 —

DIMAT - Dipartimento di Matematica - Politecnico di Torino

10129 Torino, Corso Duca degli Abruzzi, 24

Workshop DEINDE was first introduced in the early nineties as a forum for re-searchers and practitioners alike to discuss topics related to industrial experimen-tation.

In the course of the past editions qualified experts gave presentations coveringexperimentation on large systems, dimensional scatter control on body in white,process optimization, experiments on mixtures, parameter prediction via simula-tion, characterization of dedicated software, experimentation in the food and drugindustry, computer experiments.

The ninth edition held on April 2007 at the Department of Statistics & AppliedMathematics ”Diego de Castro” of the University of Torino, was a joint initiativeof DEINDE and ENBIS (European Network for European Network for Businessand Industrial Statistics) organizations, sharing common areas of interest.

The Tenth Workshop intends to bring together both leading experts and researchers,creating a forum to cover recent progress and to stimulate exchanges among re-searchers and practitioners.

It will also encourage informal contacts and discussions among participants, inorder to provide a forum for sharing ideas, experiences and knowledge.

Lectures will be presented highlighting peculiarities of specific subjects, the mainfocus being however presentation of a broad spectrum of methodologies and theirapplications, aimed at generating discussion about their use.

Participation is therefore encouraged of delegates with a broad spectrum of inter-ests, ranging from research and development to management and application.

Table of contents

F. Aggogeri, G. Barbato , E. M. Barini, G. Genta and R. Levi. Factorsaffecting measurement uncertainty in industrial . . . . . . . . . . . . . . . . . 7

A. Baldi Antognini and M. Zagoraiou. Model-based experimental designs forOrdinary and Universal Kriging emulators . . . . . . . . . . . . . . . . . . . . 9

G. Barbato, G. D. Panciani, F. Ricci, S. Ruffa and G. Vicario. Formtolerance verification using the Kriging method . . . . . . . . . . . . . . . . . 10

S. Barone. Strengths and limitations of Variation Mode and Effect Analysis . . . 12

I. Ben-Gal, D. Kedem and G. Singer. Sensoring Design via Rough Set Theoryand Error Correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

R. Berni and G. V. Lombardi. Agricultural multi-functional vehicles and en-vironment: choice experiments and random utility models for investigatingrenewable energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

L.Borgarello, E. Galliera, A. Avanzo and A. Fagiano. Roller bench urbancycles identification for light commercial vehicles fuel consumption . . . . . . 16

R. Borgoni, L. Radaelli, V. Tritto and D. Zappa. On the reduction of aspatial monitoring grid: proposals and applications to semiconductor processes 18

L. Buslig, J. Baccou, V. Picheny and J. Liandrat. Adaptive design ofexperiments: application to environmental safety studies . . . . . . . . . . . . 20

L. Corain, F. Mattiello and L. Salmaso. Multivariate Permutation Methodsfor Improving the Quality of Industrial Processes . . . . . . . . . . . . . . . . 22

A. Corazza, M. P. DAmbrosio and V. Massaro. Mercury dosing solutionsbased on innovative Hg compounds for efficient lamps: mixture optimizationusing a DOE approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

R. Fontana and A. Braunstein. Algebraic generation of orthogonal fractionalfactorial designs: some results based on integer linear programming . . . . . . 24

L. Gao, P. Giudici and S. Figini. Bayesian efficient capital at risk estimation . 25

P. Hammersberg and H. Olsson. Weld quality improvements using a parameterdesign approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

A. Jourdan. Fast calculation of the sobols indices using complex linear models . 27

R. S. Kenett. Managing Risks with Data . . . . . . . . . . . . . . . . . . . . . . 29

S. Kuhnt and T. Muhlenstadt. How to choose a simulation model for computerexperiments: A local approach . . . . . . . . . . . . . . . . . . . . . . . . . . 30

6

S. Kuhnt and N. Rudak. Multicriterial Optimization of Several Responses basedon Loss Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Y. Lavi. Integrated models in healthcare . . . . . . . . . . . . . . . . . . . . . . . 32

K. Mylona and P. Goos. A New Approach to the Optimal Design of Blockedand Split-Plot Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

M. Neblik, S. Kuhnt and L. Mest. Computer Experiments for Large LogisticSystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

V. Picheny. Space-time Gaussian processes for the approximation of partiallyconverged simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

M. Scagliarini and S. Evangelisti. Multivariate process capability assessmentwith imprecise data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

F. Tinazzi and G. Guercio. Use of the Design of Experiments to Develop aScalable Route to a Key Chirally Pure Arylpiperazine . . . . . . . . . . . . . 39

Factors affecting measurement uncertainty in industrial

CMM work F. Aggogeri

1, G. Barbato

2 , E. M. Barini

2, G. Genta

2 and R. Levi

2

1

Università degli Studi di Brescia, DIMI, Via Branze, 38 – 25123 Brescia, Italy 2

Politecnico di Torino, DISPEA, Corso Duca degli Abruzzi, 24 – 10129 Torino, Italy

Keywords: CMM, Measurement variability, Design of experiments, Industrial case study.

Abstract

Customer satisfaction requirements and keen competition typical of today’s markets make

reliable quality systems a must in industry. Stringent quality assurance programs are required,

capable of ensuring consistency of manufacturing performances. Proactive quality management

implies less time spent in inspection, as preventing production of faulty items is a more cost

effective policy than weeding out defectives. Flexibility and speed of operation, crucial in order

to obtain a competitive lead, require both reliable measuring systems, and methods.

Analysis of main factors affecting measurement variability, and defining an approach to assess

reliability of measurement systems, such as Coordinate Measuring Machines (CMM), were

aimed at in a program carried out within an industrial environment. Measurements of complex

parts often exhibit uncertainties exceeding substantially reasonably expectations, according e.g.

to stated Maximum Permissible Error – MPE (ISO 10360-2:2001). Furthermore, checks of

geometric tolerances often exhibit larger discrepancies than those pertaining, for example, to

measurements of length or diameter (see e.g. Aggogeri et al., 2008). Origins of trouble may be

traced to constraints such as tight time schedules, leading operators to increase probe speed, and

cut down both frequency of probe qualification and part soaking time, in order to reduce overall

measurement task cycle time.

The case considered, concerning experimental evaluation of measurement variability on a

CMM, entailed unraveling a fairly complex pattern of effects. The investigation, aimed at

identification of major components of uncertainty in verification of geometric tolerances,

concerned a platform, object of previous studies (see e.g. Aggogeri et al., 2008). Measurements

were carried out by qualified operators in the certified metrological laboratory of an automotive

component manufacturer, supplying precision parts and subassemblies to leading European

automakers. Key parts undergo 100% CMM inspection, according to standard company policy.

The measurement process was investigated with an (originally) balanced design, aimed at

estimation of effects on measurement variability of probe speed, probe qualification and piece

temperature. Probe speed and qualification process affect part flow in a critical way. By

increasing the former by 30% and dispensing with the latter at every batch change, production

rate may be increased by as much as 5%. If piece temperature effect on measurement variability

does not exceed given limits, CMM may be placed right on the production line, thus avoiding

shuttling parts to and from metrological laboratory, and related soaking time. While the study

focuses on an example pertaining to automotive supply chain, the methods applied lend

themselves to application in other sectors as well.

Factors were considered at two levels; two quantitative, namely probe speed (0.9 and 1.2 mm/s),

piece temperature (19 and 23 °C), and another qualitative, probe qualification (Y, N) indicating

whether qualification is performed immediately before every measurement task as specified, or

dispensed with altogether. Six tolerance verification tasks were considered, namely four

concerning position (concentricity) and two orientation (perpendicularity), specification limit

for all being 0.100 mm. Two different probes with spherical tips were used, one 4 mm dia. on a

50 mm stylus and another 5 mm dia. on a 80 mm stylus, according to features inspected.

7

Exploratory data analysis (Tukey, 1977) highlighted the effect of systematic probe qualification

prior to task on measurements, particularly in terms of reproducibility and repeatability, owing

to geometrical tolerances and their references being located on different sides of the piece. In

the light of these considerations the effect of the factors and their interactions were assessed,

showing among others a sizable effect of speed on measurement variability only when the probe

has been qualified. Main effects are summarized in Figure 1 (a), temperature however plays a

substantial role too, as shown in Figure 1 (b). Contrasts are also depicted in the normal

probability plot of Figure 1 (c), according to the method proposed by Johnson (1964).

Final considerations highlight the importance of factor selection, trials layout and exploratory

data analysis in industrial investigations, leading to identification of major effects, and their

implications, affecting the all important bottom line.

2319

0.012

0.011

0.010

0.009

0.008

0.007

0.006

0.005

1.20.9

Temperature/°C

Mean

Speed/mm/s

(a)

1.20.9

0.012

0.011

0.010

0.009

0.008

0.007

0.006

0.005

Speed/mm/s

Mean

19

23

T/°C

(b)

0.030.020.010.00-0.01

99

90

50

10

1

Data

Perc

ent

19 °C_0.9 mm/s

19 °C_1.2 mm/s

23 °C_0.9 mm/s

23 °C_1.2 mm/s

(c)

Figure 1. Main effects of quantitative factors (temperature and speed) on measurement

variability (a), and relevant interaction (b); contrasts shown on a normal probability plot

according to Johnson’s method (c).

Bibliography

Aggogeri, F., Barbato, G., Barini, E. M., Genta, G., Levi, R., 2008. Uncertainty assessment of

CMM measurements: design of experiment vs. simulation. Proceedings of 6th CIRP

International Conference on Intelligent Computation in Manufacturing Engineering, pp. 461-

465.

ISO 10360-2:2001, Geometrical Product Specifications (GPS) -- Acceptance and reverification

tests for coordinate measuring machines (CMM) -- Part 2: CMMs Used for Measuring Size,

International Organization for Standardization, Genève.

Johnson, L. G., 1964. Theory and technique of variation research. Elsevier.

Tukey, J. W., 1977. Exploratory data analysis. Addison-Wesley.

8

Model-based experimental designs for Ordinary and

Universal Kriging emulators. A. Baldi Antognini

1 and M. Zagoraiou

1

1

Department of Statistical Sciences, University of Bologna, Via Belle Arti, 41 – 40126 Bologna, Italy

Keywords: Computer experiments, space filling designs, mean squared prediction error, entropy,

optimal designs.

Abstract

The use of computer models to simulate the behavior of real systems is very popular in several

fields of science where simulations are used to replace physical experiments aimed at

investigating the way in which a given output depends on some inputs. However, the

requirement for the input-output model to be accurate in describing the real problem under

investigation means that the simulator may be rather complex. Therefore, the pioneers of

computer experiments (see Sacks et al.) suggested that in some cases it may be convenient to

approximate the deterministic simulator by a suitable emulator (metamodel), simpler and faster

to run. A wide variety of different metamodeling techniques are available in the literature and

one of the most popular is the Kriging methodology.

In general, designing a computer experiment differs in several aspects from designing a

physical one. The choice of an appropriate experimental plan for Kriging is a non-trivial

problem, since this type of model is non-linear. Indeed, because of the deterministic nature of

the outputs and since the observations are assumed to be correlated, the classical tools of the

optimal design theory cannot be applied directly.

The purpose of this paper is to illustrate the results obtained in Zagoraiou and Baldi Antognini

(2009), Baldi Antognini and Zagoraiou (2010a,b). In particular, we discuss model-based

experimental designs for two types of emulators, i.e. Ordinary and Universal Kriging, with

respect to different approaches, related to prediction, information gain and estimation.

Furthermore, we provide justifications and some criticism about the adoption of the space filling

designs, based on theoretical results, numerical and graphical evidence, showing also that only

in some circumstances several properties related to the uncorrelated setup hold for correlated

observations.

Bibliography

Baldi Antognini, A., Zagoraiou, M., 2010a. Space filling and locally optimal designs for

Gaussian Universal Kriging. In: P. Mantovan, P. Secchi (Eds.), Complex data modeling and

computationally intensive statistical methods. Springer, pp. 27-39.

Baldi Antognini, A., Zagoraiou, M., 2010b. Exact optimal designs for computer experiments via

Kriging metamodeling. Journal of Statistical Planning and Inference 140, 2607-2617.

Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P., 1989. Design and analysis of computer

experiments. Statistical Science 4, 409–423.

Zagoraiou, M., Baldi Antognini, A., 2009. Optimal designs for parameter estimation of the

Ornstein-Uhlenbeck process. Applied Stochastic Models in Business and Industry 25, 583-

600.

9

Form tolerance verification using the Kriging method

G. Barbato1, G. D. Panciani

1, F. Ricci1, S. Ruffa

1, G. Vicario

2

1

Politecnico di Torino, DISPEA, Corso Duca degli Abruzzi, 24 – 10129 Torino, Italy 2

Politecnico di Torino, Dep. of Mathematics, Corso Duca degli Abruzzi, 24 – 10129 Torino, Italy

Keywords: Tolerance Inspection, Sequential Designs, Kriging Predictions, CMM.

1 Introduction Manufactured parts are necessarily affected by form and size errors, assessed against

dimensional and geometrical tolerances. Such errors have to be estimated in order to test

and verify compliance with tolerances.

Different methods and devices may be used to inspect manufactured parts. Coordinate

Measuring Machines (CMM) are among the most widely used devices because of their

flexibility and versatility, catering for verification of a broad range of characteristics.

Currently, the ISO Technical Committee (ISO/TC) 213 is working on standards

concerning Geometrical Product Specification and Verification (GPS) in modern

industry, aimed at providing a comprehensive set of operations to control most

characteristics..

In the paper, we deal with a flatness tolerance problem, one of the simplest and among

the most widely used form tolerances, quite representative of other types of tolerances

for the task of analyzing verification methods. It defines a zone between two parallel

planes within which a surface must lie [ISO 1101]. As a consequence, only few points,

outer and inner ones, are relevant in verifying flatness. In order to detect the relevant

points, an inspection of the whole surface is virtually required, therefore ISO/TS 12781

prescribes, in addition to the traditional flatness symbol, the clear statement of cut-off

wavelength, in order to define the amount of information theoretically needed.

Nevertheless sampling density required in ISO standards is quite high, ways too

expensive to be applied in industrial practice.

To overcome these difficulties, development of intelligent algorithms is aimed at

obtaining a fairly “good” inspection plane, that links a reasonable number of points to

be probed together with an efficient estimate of the flatness tolerance value.

2 Experimental analysis Several experimental plans may be applied to select the points of the surface to be

measured, and several approaches to data analysis may accordingly be resorted to.

The algorithm we suggest in the paper is based upon the use of Kriging models, and on

a sequential selection of the points to be probed by the CMM. Kriging models were

extensively used to predict spatial data in geostatistics (Krige D.G., 1951); recently,

their use is strongly suggested to approximate the output of Computer Experiments

(Sachs et al., 1989a; 1989b). Once more, Kriging models have been adopted in

industrial metrology to drive the online construction of sequential designs for inspecting

industrial parts on CMM (Pedone et al., 2009). Following this approach, the Kriging

modelisation is adopted in the experimental estimation of a feature flatness error.

3 Results and discussion The uncertainty of Kriging predictions is considered in the choice both of the initial

inspection design (Pistone G., Vicario G., 2010), and of the selection of the subsequent

points to inspect. Comparison of operating characteristics of Kriging using different

10

correlation functions and different criteria for selecting the successive inspection points

is possible. Correlation functions are selected taking into account the technological

signature of the surface analyzed: Gaussian, exponential, and general exponential

functions have been considered. Criteria for selecting the successive inspection point

can be based on least squares or minimum zone methods, two methods mainly used, for

tolerance estimation. This allows to evaluate tolerances predicted on a set of candidate

points. Thereafter, the next point to be probed can be selected where the maximum

increment of tolerance value is expected, rather than where the prediction error is

maximum. The paper discusses, on the basis of experiments performed, different

approaches to use of Kriging models.

Bibliography

Krige, D. G., 1951. A statistical approach to some mine valuations and allied problems

at the Witwatersrand, Master’s Thesis, University of Witwatersrand.

Pistone G., Vicario G., 2010. Comparing and generating Latin Hypercube designs in

Kriging models,. AStA Advances in Statistical Analysis, Volume 94, Issue 4: 353–366;

DOI 10.1007/s10182-010-0142-1.

Pedone, P., Vicario, G., Romano, D., 2009. Kriging-based sequential inspection plans for

coordinate measuring machines. Appl. Stochastic Models Bus. Ind. 2009; 25:133–149.

Sacks, J., Schiller, S. B. and Welch, W. J., 1989a. Design for Computer Experiments.

Technometrics, 31, 41-47.

Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P., 1989b. Design and Analysis of

Computer Experiments. Statistical Science, 4, 409-423.

11

Strengths and limitations of Variation Mode and Effect

Analysis S. Barone

University of Palermo, Italy & Chalmers University of Technology, Sweden

Keywords: Variation Mode and Effect Analysis; FMEA; Variation Management; Robust Design.

Abstract

Variation Mode and Effect Analysis (VMEA) is a statistical engineering tool initially thought to

support product development with high focus on variation reduction. The method was initially

inspired by the wide use of Failure Mode and Effect Analysis (FMEA) in business and industry

and an increased attention on robust design. The main difference is that FMEA is based on the

concept of failure, while VMEA is developed around the concept of variation, i.e. it implies a

further step towards the awareness of variation and its implications in terms of risks and

failures.

VMEA helps identifying, scrutinizing and measuring the sources of variation and the way they

channel through the system under study and impact on important characteristics. Applied

systematically, VMEA provides a solid basis for achieving system robustness. Three VMEA

procedures have been defined to be used at different maturity levels of the development process.

Several applications have been made over the last years showing the usefulness of the tool for

both product and process (including also service) improvement.

However the method has strengths and limitations which are necessary to keep in mind.

This presentation is aimed at giving an overview of the VMEA method and its possible

ways/areas of use in the entire product/process development. Furthermore a look into the

strengths and limitations will be a specific focus of this work.

12

Sensoring Design via Rough Set Theory and Error Correcting

Codes

Irad Ben-Gal

1, Dana Kedem

1 and Gonen Singer

2

1 University of Tel Aviv, Dep. of Industrial Engineering, Ramat Aviv, Tel-Aviv 69978, Israel 2 Afeka College of Engineering, AFEKA, Tel Aviv, Israel

Key words: Rough Set Theory, Error Correcting Codes, Automatic Fault Identification, Predictive

Maintainance.

Abstract We propose a predictive maintenance approach where an Automatic Fault Identification (AFI)

mechanism is executed by a set of sensors. The sensors monitor a product or a system, and are

exposed to observation noise. The goal is to design or select the sensors such that the AFI is possible

in presence of noise. Our approach is based on combining concept of Rough Set Theory (RST) and

Error Correcting Codes (ECC). Rough Set Theory is a new mathematical approach which uses

algebraic definitions in order to deal with cases where some notions in the data set are not uniquely

defined. This approach is highly useful in data mining applications, where the data is not correct or

incomplete. Error Correcting Codes is a technique which ensures that data which is exposed to noise

can be transmitted as correctly as possible.

The related research problem can be posed in several directions. The first is analyzing the influence of

noise on RST measures. The second is suggesting a design solution to a set of noisy sensors. And the

third is finding out how sensors can be added to the sensors set in order to minimize the probability of

having errors in the data. Practical examples will be given.

13

Agricultural multi-functional vehicles and environment:choice experiments and random utility models forinvestigating renewable energies

R. Berni1, G. V. Lombardi2

1 University of Florence, Dep. of Statistics, Viale Morgagni, 59 - 50134 Florence, Italy2 University of Florence, Dep. of Urban & Regional Planning, Via Micheli, 2 - 50121 Florence, Italy

Keywords: Choice Experiments (CE), Random Utility Model (RUM), Heteroschedastic Extreme Value(HEV) model

1 Introduction

In the literature, a large number of researchers are dealing with preference measurements andchoice experiments, which are considered as one of the main general methods in order to study andimprove the consumer’s decision at improving his/her utility in changing a service or a product. Itmust be noted that the main feature of a CE is the monetary evaluation, namely the willingnessto pay, which is the quantitative expression of the respondents about their willingness to accept achange in the product concerned or in a single attribute. Furthermore, when considering a CE, therespondent is asked to give his/her preference related to a set of alternatives, called choice-set, whichis selected from an experimental design; the respondent is asked to give his/her preference withineach supplied choice-set. This paper focuses on the application of Choice Experiments and RUMmodels in the agricultural field. More precisely, preference measurements are analyzed in orderto improve the use of electrical multi-functional vehicles in farms. The statistical models appliedare the conditional logit model for a preliminary analysis and the Heteroschedastic Extreme Valuemodel, here reported. The organization of the paper is the following: in section 2 the fundamentaltheory of the HEV model is briefly outlined; in Section 3, case-study and preliminary results arereported.

2 Theory

As first step, the class of Random Utility Models (RUM) is defined. In general, every alternative isindicated by j (j = 1, ..., J), while i denotes the consumer/user (i = 1, ..., I). Each alternative willbe characterized by a vector of characteristics; in what follows, fuel, price, farm’s characteristics.Thus, the following expression is characterized by a stochastic utility index Uij , which may beexpressed, for each unit i, as:

Uij = Vij + εij (1)

where Vij is the deterministic part of utility, while εij is the random component. The randomcomponent is in general supposed independent and Gumbel or type I extreme value distributed. Inthe following formula (2), the probability density function of the Gumbel distributions is defined:

λ( εijθj

)= exp−{

εijθj} exp−

{exp

−(εijθj

) }(2)

where θj is the scale parameter related to the j-th alternative.In the RUM, the individual is assumed to choose the alternative j that gives the highest level ofutility, where the alternative j belongs to the choice-set C.The Heteroschedastic Extreme Value (HEV) model (Bhat, 1995) belongs to the RUM class, formula(1). The main feature of this model concerns the modified assumptions on the random component,which is supposed distributed as a type I extreme value distribution, formula (2), independentlybut not identically distributed. This different hypothesis on the random component allows to treatdifferently the relaxation on the IIA property (Train, 1998) because, in the HEV model, differentscale parameters across alternatives are estimated. The main evident advantage is that the scale

parameters may be defined as the weights in order to measure the uncertainty related to thealternatives and to the attributed there involved. Furthermore, the presence of large variances forthe error terms influences the effects of changing of systematic utility for the generical alternativej. Therefore, the probability for a respondent i to choose the alternative j from a choice-set Ci is:

P (yi = j) = Pi(j) =∫

ε

∏

k∈Ci;k 6=jΛ{x′ijβ − x′ikβ + εij

θk

} 1θjλ( εijθj

)dεij (3)

where θj is the scale parameter for the j alternative and λ(·) is the probability density function ofthe Gumbel distribution, as in formula (2); the term x′(·)β denotes the deterministic part of utilityof formula (1). Note that the integral function is defined on the domain [−∞,+∞] of the randomcomponent ε related to the unit i and the alternative j.In this case, preferences of respondent i are evaluated by considering a scaling term θj for thealternative j in the choice-set Ci, i.e. the heteroschedasticity of the error term.It’s not straightforward matter to say that the HEV and the Mixed Logit models (McFaddenand Train, 2000) could be considered as competitive models in order to identify and to measurethe presence of an overdispersion when modelling the consumer preferences, with respect to theconditional logit model.

3 Preliminary results

The case-study is related to 411 farmers asked to give their preferences to three choice-sets, eachformed by three alternatives, related to three multi-functional vehicles (A electrical; B bio-gas; Cdiesel). It must be noted that the response variable is defined as the choice of one alternative onthree ones. A questionnaire is supplied together with choice-sets. Some attributes involved in theexperiment are: initial price (PR), monthly cost (MC), fuel (F), power (P; KW), emissions (E;Kg/h).

TABLE 1. HEV model: estimated preferences by electrical vehicles in farm (EV-F) and price (PR)

variable coefficient s.e. p-valueconst-B 7.4884 1.5006 0.0001const-C -1.5345 1.0514 0.1444EV-F-B 1.1209 0.5967 0.0603EV-F-C 0.4452 0.5693 0.4342PR -0.43e-3 0.92e-4 0.0001scale2 1.1438 1.0225 0.2633scale3 1.3382 1.2043 0.2665

In Table 1, constants are related to vehicles B and C, respectively. Two dummies are defined forthe presence of electrical vehicles in farm (EV-F). Respondents prefer the vehicle B to A (const-B positive), while vehicle A is preferred to C (even though this coefficient is not significant).The estimated coefficient for price shows a decreasing utility for the alternative when price ishigher. Utility for the respondent who prefers vehicle B (bio-gas) is significantly influenced bythe presence of electrical vehicles in farm (EV-F), with p-value=0.06. Scale parameters are notsignificant; however, the correlation matrix of estimates shows interesting results when consideringcorrelation between scale parameters and price (positive values) or between price and constants.In this case, correlations are −0.91 and 0.60 between price and const1 or const2, respectively.

Bibliography

Bhat, C., 1995. A heteroschedstic extreme value model of intercity travel mode choice. Transporta-tion Research: part B: Methodological 29, 471–483.

McFadden, D., Train, K., 2000. Mixed mnl for discrete response. Journal of Applied Econometrics15, 447–470.

Train, K. E., 1998. Recreation demand models with taste differences over people. Land Economics74, 230–239.

Roller bench urban cycles identification for light commercial vehicles fuel consumption L.Borgarello1, E. Galliera2, A. Avanzo3, A. Fagiano3

1 Centro Ricerche Fiat, Interiors & Thermal Systems, Strada Torino, 50 – 10043 Orbassano (TO), Italy 2 Centro Ricerche Fiat, Vehicle dynamics & fuel economy, Strada Torino, 50 – 10043 Orbassano (TO),

Italy 3 IVECO, Quality evaluation, Lungo Stura Lazio, 49 – 10156 Turin, Italy Keywords: Cycle identification, Fuel consumption, Simulation, Roller bench, Multivariate approach. 1 Abstract This article describes the aim, the general approach and some statistical details regarding a part of program in collaboration between Centro Ricerche Fiat and IVECO. Aim of the projects is the evaluation of fuel consumption of commercial vehicles in real conditions on roller bench through a set of different cycles representative of different contexts. In particular on this article it will be described the approach used to identify cycle representative of light commercial vehicles in typical urban environment conditions. A similar approach is in use for medium commercial vehicles in urban contest. Starting point of the activity is a set of experimental tests done in real conditions on 2 different routes in Turin (just used from IVECO for on road consumption measurements) with 2 light commercial vehicles equipped with an on-board system that allows the data acquisition of time history of engine and vehicle variables. The experimental campaign has been planned with a simple Experimental Design using some external condition (routes, vehicle, driver, time of experimentation starting). Core part of the article will be the statistical approach used to find out synthetic cycles departing from the database of the measures obtained during the experimentation on the road. This methodology, in part original and in part derived from literature, is composed of the following phases:

• subdivision of each trip into ‘cinematic sequences’ (speed vs. time curves between subsequent stops)

• characterisation of sequences in term of statistical parameters, classification of sequences into well-differentiate classes and selection of representative sequences for each cluster

• creation of a ‘synthetic cycle’ as a succession of representative sequences for each cluster in order to measure the consumption for each class of sequences

• analysis of the road acquisition, identification of significant external parameters and grouping of road acquisitions

• identification of a weighting method to estimate consumption for group of real missions starting from measurements on synthetic cycle (partial measurements).

Numeric simulation of fuel consumption has been used all along the process to help statistical decisions and in order to validate results before test the cycle on roller bench. The final validation has been done testing on roller bench one of the vehicles used in road experimentation. Moreover, starting from these and other real acquisitions a tool for estimation of gearshift usage has been developed in order to define the correct gear to use when the cycle is executed on roller bench.

16

Bibliography Andrè M, “Driving Cycles Development: Characterization of the Methods, Rif 961112 SAE M. Andrè, A.J. Hickman, D. Hassel, R. Joumard, Driving Cycles for Emission Measurements

Under European Conditions”, Rif 950926 SAE J.D. Jobson, Applied Multivariate Data Analsisys, Springer-Verlag New York W.R. Dillon, M.Goldstein, Multivariate Analysis, John Wiley & Sons L. Della Ragione, A. Buonocore, M. Rapone, Metodi multivariati per l’analisi e la

visualizzazione di dati sperimentali rappresentativi dell’utilizzo reale di un’autovettura sulla tangenziale di Napoli”, SUGItalia ‘98: Atti del Convegno

M.Rapone, L.Della Ragione, F. D’Aniello, V. Luzar, Experimental Evaluation of Fuel

Consumption and Emissions in Congested Urban Traffic, Rif 952401 SAE L. Borgarello, R. Fontana, A. Fortunato, L. Mina, Identification of driving cycles and emission

in the traffic of Bologna, Rif. 01A1012 Florence ATA 2001 L. Borgarello, R. Fontana, A. Fortunato, L. Mina, Determinazione sperimentale delle emissioni

provenienti da autoveicoli circolanti in ambiente urbano, Bologna, 1999

17

On the reduction of a spatial monitoring grid: proposals and

applications to semiconductor processes Riccardo Borgoni

1, Luigi Radaelli

2, Valeria Tritto

3, Diego Zappa

4

1

Department of Statistics, University of Milano-Bicocca; Italy riccardo.borgoni@unimib.it 2

SPC & Robustness Group, Numonyx Italy; luigi.radaelli@numonyx.com 3

IRER Istituto regionale di ricerca della Lombardia, Milano, Italy, valesky85@msn.com 4

Department of Statistical Sciences, Catholic University of Milan, Italy; diego.zappa@unicatt.it

Keywords: kriging predictor, Simulated Annealing

Summary

To focus on the issue we are going to present, start considering the fabrication of integrated

circuits (IC). The process consists of a sequence of several different physical and chemical steps

performed on a thin silicon slice, called wafer. In some production processes it is necessary to

grow a silicon oxide (SiO2 ) layer over the wafer surface. The thickness of this layer has, in

general, a target value. However the actual value one gets in practice is not constant over the

wafer surface but it can randomly deviate from the target due to structural causes. In order to

control the deposition process and ensure optimal IC performances, the SiO2 layer thickness

across the wafer and across the boat must be carefully evaluated. For this reason, maps

containing wafer coordinates, where thickness must be measured, are available. Assessing

whether the deposited film thickness is uniform (or almost uniform) over the wafer surface is

essential to further steps in chip manufacturing. Data collection procedures are time consuming

and expensive: for this reason it is often worthy trying to reduce the number of points that are

necessary to accurately reproduce the film thickness over the wafer surface.

The issue previously addressed may be found in all those production processes where the

quality of a surface/volume must be kept under control.

Reducing a spatial monitoring grid requires to select a subset of the original measurement points

in such a way that the “best possible” estimate of the variable of interest is returned. In

collaboration with Numonyx, a worldwide semiconductor manufacturing company, we have

applied the simulated annealing (SA) method and compared its performance with a new

alternative method, we called ZBR (Borgoni R. et al, 2009). SA was firstly employed in spatial

sampling by Sacks and Schiller (1988) and extended by Van Groenigen and Stein (1998). ZBR

starts from assigning to the surface an optimal map, according to some criterion, and then it

searches for that subset from the original map nearest too the optimal.

In both cases the optimal solution and the maximum reduction factor of the original map go

through the computation of a prediction error which has not a unique solution and mostly

depends on what the experimenter wants to keep under control. SA has been used within a

kriging predictor paradigm in order to exploit the spatial correlation that may be consistently

estimated if data are available. ZBR has been thought for both/either those contexts where only

the map is available and/or a parametric response surface over the wafer is a priori

known/expected because of technological reasons.

Bibliography

Borgoni R, Radaelli L., Tritto V., Zappa D., 2009. Statistical Method to extract form spatial

monitoring grid an optimal subset, Numonyx, Internal report.

18

Sacks, J., Schiller, S., 1988. Spatial designs. In: Gupta, S.S., Berger, J.O. (Eds.), Statistical

Decision Theory and Related Topics IV, 2, pp. 385–399. Springer-Verlag, New York

van Groenigen, J.W., Stein A. (1998) Constrained optimization using continuous simulated

annealing, Journal of Environmental Quality, 27, 1078-1086.

19

Adaptive design of experiments:application to environmental safety studies

L. Buslig1, J. Baccou1, V. Picheny2 and J. Liandrat3

1 IRSN, CE Cadarache, 13115 Saint Paul Les Durance, France2 ECP, Grande Voie des Vignes, F-92295 Chatenay-Malabry Cedex, France3 ECM, Technopole de Chateau-Gombert, 38 rue F. Joliot Curie, 13451 Marseille Cedex 20, France

Keywords: Design of experiments, kriging, computational cost reduction, nuclear safety.

This work is devoted to the development of a new method for the construction of adaptive designof experiments and its application in the nuclear safety studies conducted by the French Institutde Radioprotection et de Surete Nucleaire (IRSN). It is based on an extension of the previouswork of Picheny et al. (2010) and therefore couples kriging theory (Cressie (1993)) with design ofexperiments optimization techniques. The originality of our approach stands in two points; firstlyin the introduction of a cost reduction strategy for the optimization step that makes easier its usein industrial applications, secondly in the definition of a more general criterion for the selectionof a new design point that allows to integrate external variables such as population density whichwill be our concern in environmental studies.

In kriging interpolation, the available data (such as measurements provided by sensors) denoted{y(xk)}k=1,...,N are considered as realizations of a subset of random variables {Y(xk), k = 1, ..., N}coming from a random process {Y(x), x ∈ D} (with D a bounded domain of IRp) that reads Y(x) =m(x)+ δ(x), x ∈ D, where m(x) is the deterministic mean structure of Y(x) and {δ(x), x ∈ D} is azero-mean random process. Kriging theory assumes that the random variables δ(x), are spatiallycorrelated. Under stationarity assumptions and constant deterministic mean structure of the ran-dom process, the spatial correlation structure of {δ(x), x ∈ D} is identified to the spatial correlationof the data and is exhibited by computing the semi-variogram, γ(h) = 1

2E((Y(x + h) − Y(x))2)(where E denotes the mathematical expectation). In practice, this quantity is approximated bya least square fit of the discrete experimental semi-variogram. The kriging estimator P (Y, x?)at a new location x? is then the linear, unbiased predictor minimizing the estimation varianceσ2

k = var(Y (x?)− P (Y, x?)).

The construction of a design of experiments (DoE) plays a key role in the prediction by kriging.It provides the information on the phenomenon under study that is then used in the estimation ofthe spatial structure. It is therefore of prime importance, especially for the decision-making processin nuclear safety studies, to have a large enough amount of information to accurately interpolate.However, considering a very rich design of experiments is not technically or economically affordablein practice, and our goal is here to find a compromise between the number of points in the designand the quality of the prediction. In this work, we focus on an iterative extension of an initial DoE.More precisely, starting from a DoE of k points, a new point is added by optimizing a criteriontranslating the quality in the prediction. There exists many ways to select this criterion. The mostnatural idea is to use the estimation variance provided by the kriging interpolation. In this case, theprocedure is based on the maximization of the so called MSE (Mean Square Error) criterion or theminimization of the so called IMSE (Integrated Mean Square Error) criterion (Sacks et al. (1989)).The MSE allows a local optimizaton since its maximum corresponds to the point where the modeluncertainty is the largest. On the contrary, the IMSE minimization leads to a global optimization(decrease of the global uncertainty). Therefore, working with IMSE is more efficient but morecostly. In practice, this kind of strategy is not fully satisfactory since we are often interested inincreasing the accuracy of the prediction in some target region such as a region where the dataexceed a given threshold (detection of a radioactive release) or where the population density is high(radioactivity mapping). Therefore, we work with an extension of the weighted MSE, resp. IMSE,denoted ∀x ∈ D, MSEw(x) = MSE(x)W (x) , resp. IMSEw =

∫D MSE(x)W (x)dx, introduced

in Picheny et al. (2010). Their advantage is to reduce the uncertainty (“MSE” term) while allowingto explore target regions (“W” term).

20

Since the point that maximizes the MSE is usually located near the one that minimizes the IMSE,we propose to combine these two criteria to avoid a computationaly costly numerical treatment.More precisely, we replace the direct minimization of IMSEw over the whole domain D by atwo-step procedure described in the next proposition for bivariate DoEs.

Proposition 1 Let Xk be the DoE with k points and {xi, i = 1, ...L} (L >> k) a uniform dis-cretization grid of D ⊂ IR2. If D(x, r) stands for the disk centered on x and of radius r, the DoEXk+1 is obtained as follows:

1) Find x = maxx∈{xi,i=1,...L}MSEw and choose rx such that D(x, rx) defines a neighbourhoodof x containing the candidates for the new point to add,

2) Construct Xk+1 = Xk ∪ {x?} such that x? = minx∈D(x,rx)IMSEXk∪{x}w where

IMSEXk∪{x}w = 1

L

∑Li=1 MSE

Xk∪{x}w (xi) and MSE

Xk∪{x}w is the weighted MSE computed

from the DoE Xk ∪ {x}.Step 2 requires a numerical integration over the whole domain D (and therefore L kriging evalua-tions for every candidate x) which can be computationaly costly in practice (L ∼ 30000). However,for classical semi-variogram models such as exponential, gaussian or spherical, it is possible to re-strict the integration to a neighbourhood of x by slightly modifying the criterion to optimize. Moreprecisely, noticing that ∀x ∈ D, MSE

Xk∪{x}w −MSEXk

w is locally non-zero in the disk D(x, 2a) (adenotes the range or the practical range depending on the semi-variogram model), we substituteto the optimization problem of Step 2) the following problem:

x? = maxx∈D(x,rx)1

|D(x, 2a)|∑

xi∈D(x,2a)

(MSEXk∪{x}

w (xi)−MSEXk

w (xi))

,

where |D(x, 2a)| is the number of grid points belonging to the disk D(x, 2a).

This methodology has been successfully applied in the frame of IRSN environmental studies. Ithas been used for the extension of the radioactivity sensor network over France. Starting from thecurrent network of 158 sensors (Figure 1, left), 20 have been iteratively added in the target regionwhere the population density is high (Figure 1, right). This has been performed with an affordablecomputational cost, which was not the case when working with the direct minimization of IMSEw

on the whole domain.

(a) (b)

FIGURE 1. The radioactivity sensor network over France. (a) The current network of 158 sensors. (b) Thecurrent network of 158 sensors (black points) and the 20 added sensors (blue points).

Bibliography

Cressie, N. A., 1993. Statistics for spatial data. Wiley Series in Probability and MathematicalStatistics.

Picheny, V., Ginsbourger, D., Roustant, O., Haftka, R. T., 2010. Adaptive designs of experimentsfor accurate approximation of a target region. Journal of Mechanical Design 132(7).

Sacks, J., Welch, W. J., Mitchell, T. J., Wynn, P., 1989. Design and analysis of computer experi-ments. Statistical Science 4(4), 409–423.

21

Multivariate Permutation Methods for Improving the Quality of Industrial Processes L. Corain1, F. Mattiello2 and L. Salmaso1

1 University of Padova, Department of Management and Engineering, Str. S. Nicola, 3 – 36100

Vicenza, Italy 2 University of Bologna, Department of Statistics, Via delle Belle Arti, 41 – 40126 Bologna, Italy Keywords: nonparametric combination, permutation tests. Abstract Statistical control methods for monitoring industrial processes are nowadays widely recognized as essential tools in order to obtain high quality processes at the base of any successful business activity. For example, when developing new products the research aim is often focused on evaluating the product/process performances from a multivariate point of view, i.e. with respect to more than one aspect and/or under several conditions. From the statistical point of view, when the response variable of interest is multivariate in nature, the problem may become quite difficult to cope with, due to the high dimensionality of the parametric space. In such a case, the parametric approach presents a number of drawbacks: the assumption of normality may be not realistic for many real problems and for small sample sizes (such as that of the most real applications) the parametric approximation for finite samples may be often inappropriate. Moreover, when increasing the dimensionality (no. of parameters), the parametric approach is affected by the problem of the loss of degree of freedom hence the estimation procedure may become at least not accurate (or sometimes even not feasible). Conversely, the combination-based permutation approach (Pesarin and Salmaso, 2010) offers several advantages: it is a robust solution, with respect to the true underlying random error distribution; it may take into account for the dependence structure of response variables; it can be applied to a variety of different complex settings/designs thanks to its ability to break down the problem into a set of simpler sub-problems, providing each one with its own solution to be combined into a final global solution. Bibliography Pesarin, F., Salmaso, L., 2010. Permutation Tests for Complex Data: Theory, Applications and

Software. Wiley: Chichester.

22

Mercury dosing solutions based on innovative Hg compounds for efficientlamps: mixture optimization using a DOE approach

A. Corazza1, M. P. D’Ambrosio2 and V. Massaro1

1 SAES Getters S.p.A., Viale Italia, 77 – 20200 Lainate (MI), Italy2 SixSigmaIn Team s.n.c., Via Stradivari 7 – 20200 Lainate (MI), Italy

Keywords: Design of Experiment, Mixture Optimization, Mercury, Lamps.

Abstract: Fluorescent lamps are very efficient light sources, but for the generation of radiation they exploitmercury that has a strong negative effect on the environment. Worldwide regulations are pushing to reduce themercury content in fluorescent lamps, both compact and linear lamps, and to minimize their environmentalimpact during production without emission of undesired mercury vapours. New advanced technologicalsolutions are required for a safe and precise Hg dosing in lamp down to the low level of few milligrams in eachlamp. One of the most effective technologies is the dosing through solid mercury dispensers based on stable Hgcompounds: this solution is very reliable for a safe and controlled delivery of small amounts of mercury, justwhen the lamps are sealed to avoid pollution issues.A suitable Hg alloy is used to release mercury when heated at high temperatures for a relatively short time(activation process at about 900°C for 30 seconds). In order to maximize the mercury yield from the dispensersspecial promoting powders are mixed together with the Hg containing powder to favour a massive and quick Hgrelease. An important improvement to simplify lamp manufacturing is related to the development of dispensingmixtures able to deliver all the present mercury at temperatures lower than 900°C in a reduced activation time.As known, when two or more components are combined together, mixture DOE is ideal to study the responsesas a function of proportions rather than amounts: therefore mixture-design experiments were carried out, onlaboratory scale, to identify the best combinations of mercury compounds and promoters to maximize mercuryyield at relatively low temperatures. Once selected the two most promising reagents to be mixed with themercury alloy, DOE was used to create a three-component model and to determine the proper ratios needed forthe improvement of the mercury release.

The paper will present main results of a mixture design built to generate a map of the Hg yield over a specifiedregion of formulation for the three components mixture. The positive outcomes of the work will be exploited forfurther optimization studies.

Bibliography

Anderson, Mark, and Patrick Whitcomb, 2007. DOE Simplified: Practical Tools for Effective Experimentation,Second Edition. New York: Productivity Press.

Anderson, Mark, and Patrick Whitcomb, 2005. RSM Simplified: Optimizing Processes Using ResponseMethods for Design of Experiments. New York: Productivity Press.

Cornell, John, 2002. Experiments with Mixtures. Third Edition. New York: John Wiley and Sons.

23

Algebraic generation of orthogonal fractional factorial

designs: some results based on integer linear programming

R. Fontana1 and A. Braunstein

2

1

Politecnico of Turin, Dep. of Mathematics, Corso Duca degli Abruzzi, 24 – 10129 Turin, Italy 2

Human Genetics Foundation, via Nizza 52 - 10126 Turin, Italy and Politecnico of Turin, Dep. of

Physics, Corso Duca degli Abruzzi, 24 – 10129 Turin, Italy

Keywords: Design of experiments, Algebraic Statistics, Integer Linear Programming

Abstract

Generation of orthogonal fractional factorial designs (OFFD) is a relevant and extensively

studied subject in applied statistics.

In this paper we show how searching for an OFFD that satisfies a set of constraints, expressed

in terms of orthogonality between simple and interaction effects, is, in many applications,

equivalent to solving an integer linear programming problem.

We use a recent methodology (Fontana and Pistone, 2010), based on polynomial counting

functions and strata, that represents OFFDs as the positive integer solutions of a system of linear

equations Γ. Then we set up an optimization problem where the cost function to be minimized

is, for example, the size of the OFFD and the constraints are represented by the system Γ.

Finally we search for a solution using standard integer programming techniques. Some

applications are presented.

It is worth noting that the methodology does not put any restriction on the number of levels of

each factor and so it can be applied to a really wide range of designs, including mixed

orthogonal arrays.

Bibliography

Fontana, R., Pistone, G.: Algebraic generation of Orthogonal Fractional Factorial Designs,

Paper presented at 45th Scientific Meeting of the Italian Statistical Society, 16-18 June 2010.

Available at http://homes.stat.unipd.it/mgri/SIS2010/Program/contributedpaper/654-1297-3-

DR.pdf

Hedayat, A. S., Sloane, N. J. A., Stufken, J., 1999. Orthogonal arrays. Theory and applications.

Springer Series in Statistics. Springer-Verlag, New York.

24

Bayesian efficient capital at risk estimation L. Gao1, P. Giudici2 and S. Figini2

1 Management School, Shandong University, China 2 University of Pavia, Department of Statistics and Applied Economics Keywords: Extreme Value Theory, Bayesian Models, Markov Chain Monte Carlo, Risk Measures. 1 Summary According to the last proposals by the Basel Committee, banks are allowed to use the Advanced Measurement Approaches (AMA) option for the computation of their capital charge covering operational risks (see e.g. Figini et al. 2010 and Salini et al. 2010). In this contribution we focus on operational risk data. We propose a Bayesian extension for extreme value models (EVT) using Markov Chain Monte Carlo algorithms. Bayesian techniques offer an alternative to parameter estimation methods, such as maximum likelihood estimation, for EVT models (see e.g. De Haan et al. 2006). These techniques treat the parameters to be estimated as random variables, instead of some fixed, possibly unknown, constants. We investigate, with real examples, how Bayesian analysis can be used to estimate the parameters of EVT models, for the case where we have no prior knowledge at all and the case where we have prior knowledge in the form of expert opinion. In addition, Bayesian analysis provides a framework for the incorporation of information from external data into a loss model based on internal data; this is again illustrated using the data at hand. The proposed method is appealing and it allows us to incorporate additional information in the form of expert opinions about the unknown parameters into the estimation process. This plays a crucial role in reducing the statistical uncertainty around both parameter and capital estimates when observed data is insufficient to accurately estimate the tail behaviour of loss distribution. However, we have to emphasize that choosing priors should be done carefully because if they are concentrated far away from true values there is a danger of obtaining biased parameter and capital estimates. The results achieved underline that our proposal performs better with respect to classical EVT models in terms of value at risk and, consequently, capital at risk required to cover expected and unexpected losses. Bibliography De Haan L., Ferreira, A. 2006. Extreme Value Theory: An Introduction, Springer Verlag. Figini, S., Giudici, P. and Uberti P., 2010. A threshold based approach to merge data in fiancial

risk management. Journal of Applied Statistics 11, 1815 - 1824. Salini, S., Kenett, R. and Figini S., 2010. Optimal scaling for risk assessment: merging of

operational and financial data. Quality and Reliability Engineering International 26, {887–897.

25

Weld quality improvements using parameter design approach P. Hammersberg1 and H. Olsson2

1 Chalmers University of Technology, Dep. of Materials and Manufacturing Technology, SE-412 96

Göteborg, Sweden (peter.hammersberg@chalmers.se) 2 Volvo Construction Equipment, Operations, Quality Department, Box 303,SE-671 27 Arvika, Sweden

(Hasse.Olsson@volvo.com) Keywords: Robot MIG welding, Design of experiments, Multi-responses surface optimisation 1 Abstract In this study the change in pre-conditions for quality/inspection are studied when the performance of an existing robotised welding process is improved using parameter design from robust design methodology. The findings are several. First, it was found that it is possible to build empirical response surface models of the key performance indicators that serve to improve the chances to find settings in the welding geometry that fulfil all requirements without increasing production cost. Secondly, modelling of welding processes, in contrast to most processes, requires high resolution experimental plans since many multi parameters interactions are active. Indicating very complex response surfaces. Thirdly, it was also found that basic industrial standard gauges and procedures for weld quality inspection easily are out-dated if not care is taken to investigate and improve all measurement systems used relative the actual variations occurring in the production. Fourthly, improved welding performance in production will change pre-conditions for both product development and quality surveillance facilitating evolution of interdisciplinary co-operation.

26

Fast calculation of the Sobol’s indices using complex linear models A. Jourdan1

1 Department of mathematics, E.I.S.T.I, 26 avenue des Lilas, 64062 Pau cedex 9, France Keywords: Sensitivity analysis, trigonometric regression, Latin hypercube, orthogonal design. 1 Introduction The global sensitivity analysis is used to study the effect of random input variables, x1,…,xd, on the response variability of a computer code, y. The Sobol’ indices (Saltelli et al., 2000)) are commonly used to quantify the contribution of each input variable in the response variance decomposition. The Sobol’ indices are estimated using Monte-Carlo methods and require a large number of simulations. When the simulations are time-consuming, a well-known method consists of replacing the computer model by a metamodel, such as a Gaussian process model or a neural network (Santner et al., 2003), Fang et al., 2006)), with a fast computation time. This technique cumulates the error of the modeling and the error of the Monte Carlo estimation. 2 An analytical expression of the Sobol’ indices The idea of this work is to avoid the Monte-carlo estimation. For this, we assume that the experimental domain is discrete and we use the expansion of the computer response on an orthogonal basis of complex functions (Yates’s basis) (Kobilinsky, 1990) to build the complex linear model (also called trigonometric regression or Fourier model, Bates et al., 1998), ∀x∈[0,1]d

ε+β+β+β= ∑+∈

><π−><π

Ah

h,x2h

h,x2h0 ee)x(y ii

where <..> is the usual scalar product of Rd, ε~N(0,σ²) and the set of frequencies A+ is a set of

integer d-dimensional vectors such that 0∉A+, h∈A+ ⇒ -h∉A+. Assuming a discrete domain is not restrictive, since a wide variety of computer experimental designs (Latin hypercubes, orthogonal arrays, nets,…) supposes a discretization of the experimental domain. This metamodel allows one to derive an analytical estimation of Sobol’ indices. In particular, the first and second order indices are given by

∑

≠=≠

∈ +

ββ=

ij,0h0h

Ah

hhi

j

i

2)Y(Var

1S ∑

≠=≠≠

∈ +

ββ=

j,ik,0h0h,0h

Ah

hhij

k

ji

2)Y(Var

1S .

with ∑+∈

ββ=Ah

hh2)Y(Var .

The computational cost of the sensitivity indices is reduced to the estimation of the coefficients of the complex linear model. This method does not require Monte-Carlo estimation and the error depends only on the accuracy of the metamodel. The coefficients are estimated from the computer responses at the experimental design points D={x 1,…,xn}, using an ordinary least square regression,

( ) YZZZˆ *1* −=β ,

27

where { } { }[ ]++ ∈∈ βββ=β AhhAhh0

t,, and { } { }[ ]++ ∈

><π∈

><π= Ahhx2

Ahhx2j jj

e,e,1)x(Z i-i is

the jth row of the design matrix Z. 3 The experimental design The experimental design is a Latin hypercube whose entries are in {0,…,n}, where n is a prime number, such that

• the n rows of the Latin hypercube are the linear combinations (modulo n) of the d-dimensional vector

(-q1,-q2,…,-qd-1|1), qi∈{0,…,n} • and

)(modsqs d

1d

1i

ii n≠∑−

=

where s=(s1,…,sd) is either h∈A+ or h+k with h∈A+ and k∈A+ or h-k with h∈A+ and k∈A+ and h≠k.

In this way the experimental design is orthogonal (Bailey, 1985)

YZ1ˆ *

n=β

4 Application This method is successfully applied on two analytical functions commonly used to compare sensitivity analysis methods: The Ishigami function and the Sobol’ function. We compare this new method with two existing methods : a Monte Carlo estimation with a Gaussian process as metamodel (Santner et al. (2003)) and an analytical expression of the Sobol’s indices defined by Sudret (2008).

Bibliography Bailey, R.A., 1985. Factorial designs and abelian groups, Linear Algebra Appl. 70, 349-363. Bates, R.A., Riccomagno, E., Schwabe, R. and Wynn, H.P., 1998. Lattices and dual lattices in

optimal experimental design for Fourier models, Computational Statistics and Data Analysis 28, 283-296.

Fang K.T., Li R., Sudjianto A., 2006. Design and modeling for computer experiments. Chapman&Hall, London.

Kobilinsky, A., 1990. Complex linear models and cyclic designs, Linear Algebra Appl. 127, 227-282.

Saltelli A., Chan K., Scott M., Eds., 2000. Sensitivity Analysis. Wiley Series in probability and statistics.

Santner T.J.. Williams B.J.. Notz W. I., 2003. The Design and Analysis of Computer Experiments. Springer Series in Statistics. Springer-Verlag New York.

Sudret B., 2008. Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering & System Safety, 93, 964-979.

28

Managing Risks with Data R.S. Kenett

The KPA Group, Israel and University of Turin, Turin, Italy Keywords: Risk Management, Data Integration, Semantic Analysis, Bayesian Networks, Association Rules

Risk events can have significant impact on business activities, consumers and the environment. Toyota, British Petroleum and GlaxoSmithKline recently provided striking examples of this. Toyota announced a recall of 2.3 million U.S. vehicles on January 21st, 2010 and its shares dropped 21 percent, wiping out $33 billion of the company’s market capitalization. British Petroleum’s oil spill in the Gulf of Mexico on April 20th, 2010, which killed 11 workers, is another example. GlaxcoSmithKline PLC, announced on July 10th, 2010 that it would charge $2.4 billion to offset the estimated $6 billion liability exposure after the FDA panel returned mixed recommendations that kept the Avandia diabetes treatment drug on the market with new warning statements. Assessing exposure to potential risk events and initiating proactive risk mitigation actions is currently a clear priority of businesses, organizations and governments world-wide. Managing risks with data is a growing discipline that involves data acquisition and data merging, risk analytics and risk management decisions support systems. The presentation will provide an overview of modern integrated risk management, including examples of how qualitative unstructured data, like text and voice recordings, can be combined with quantitative data like balance sheets and technical performance, to generate integrated risk scores. We suggest that data based risk analysis is an essential competency complementing and reinforcing the more traditional subjective scoring methods used in classical risk management. The examples we will use consist of applications of risk scoring models, Bayesian Networks to map cause and effect, Ontologies to interpret automated text annotation, ETL to merge various data bases and a follow up integrated risk management approach.

Bibliography Figini, S., Kenett, R.S. and Salini, S., 2010. Integrating Operational and Financial Risk

Assessments. Quality and Reliability Engineering International, Vol. 26, No. 8, pp. 887-897.

Kenett, R.S. and Zacks, S., 1998. Modern Industrial Statistics: Design and Control of Quality

and Reliability, Duxbury Press, San Francisco, Spanish edition, 2000, 2nd edition 2003, Chinese edition, 2004.

Kenett, R.S. and Salini, S., 2008. Relative Linkage Disequilibrium Applications to Aircraft Accidents and Operational Risks. Transactions on Machine Learning and Data Mining, Vol.1, No 2, pp. 83-96.

Kenett, R.S. and Baker, E.M., 2010. Process Improvement and CMMI for Systems and

Software, Taylor and Francis, Auerbach CRC Publications.

Kenett, R.S. and Raanan, Y., 2010. Operational Risk Management: a practical approach to

intelligent data analysis, Wiley and Sons.

MUSING, 2006. MUlti-industry, Semantic-based next generation business INtelliGence (IST- FP6 27097).

29

How to choose a simulation model for computerexperiments: A local approach

S. Kuhnt1, T. Muhlenstadt1

1 TU Dortmund University, Faculty of Statistics, 44221 Dortmund, Germany

Keywords: Computer experiments, Computer code validation

Abstract

In many scientific areas non-stochastic simulation models such as finite element simulations replacereal experiments. A common approach is to fit a meta model, e.g. a Gaussian process model (Sant-ner et al., 2003), a radial basis function interpolation (Buhmann, 2000) or a Kernel interpolation(Muhlenstadt and Kuhnt, 2009), to computer experiments conducted with the simulation model.We deal with situations where more than one simulation model is available for the same real exper-iment, with none being the best over all possible input combinations (Muhlenstadt et al., 2011).Based on fitted models for a real experiment as well as for computer experiments using the differentsimulation models a criterion is derived to identify the locally best one. Applying this criterionto a number of design points allows for splitting the design space into areas where the individualsimulation models are locally superior. An example from sheet metal forming is analyzed, wherethree different simulation models are available. In this application and many similar problems thenew approach provides valuable assistance with the choice of the simulation model to be used.

Bibliography

Buhmann, M. D., 2000. Radial basis functions. In: Iserles, A. (Ed.), Acta Numerica. CambridgeUniversity Press, pp. 1 – 38.

Muhlenstadt, T., Gosling, M., Kuhnt, S., 2011. How to choose the simulations model for computerexperiments: A local approach. Submitted for publication.

Muhlenstadt, T., Kuhnt, S., 2009. Kernel interpolation. Technical report, Faculty of Statistics,Technische Universitt Dortmund, Dortmund, Germany.

Santner, T., Williams, B., Notz, W., 2003. The Design and Analysis of Computer Experiments.Springer Series in Statistics. Springer Verlag, New York.

30

Multicriterial Optimization of Several Responses based onLoss Functions

S. Kuhnt1, N. Rudak1

1 TU Dortmund University, Fac. of Statistics, Vogelpothsweg 87 - 44221 Dortmund, Germany

Keywords: Multiple responses, Robust parameter design, Simultaneous optimization.

Abstract

In technical applications, often a set of response variables with corresponding target values dependson some control variables. In these cases an off-line quality control prior to the actual manufacturingfrequently implies optimizing the mean as well as minimizing the variance of the responses.Most of the existing methods for the analysis and optimization of multiple responses require somekind of weighting of these responses, for instance in terms of costs or desirabilities. Particularlyat the design stage, such information is hardly available or will rather be subjective. Kuhnt andErdbruegge (2004) present an alternative strategy using loss functions and a penalty matrix whichcan be decomposed into a standardizing and a weight matrix. The effect of different weight matricesis displayed in Joint Optimization Plots in terms of predicted response means and variances.Furthermore Erdbruegge et al. (2011) show that every point that minimizes the conditional meanof the loss function is Pareto optimal.The new R package JOP (Kuhnt and Rudak, 2011) is an implementation of the Joint OptimizationPlot and is available on CRAN in the version 2.0.1. We demonstrate the use of the Joint Optimiza-tion Plot in various applications from mechanical engineering, e.g. sheet metal forming processes(Kleiner et al., 2006) and thermal spraying processes.

Bibliography

Erdbruegge, M., Kuhnt, S., Rudak, N., 2011. Joint optimization of several responses based on lossfunctions. submitted.

Kleiner, M., Kuhnt, S., Goesling, M., Busch, A., Homberg, W., Gather, U., 2006. Parameter designfor high pressure sheet metal hydroforming of sculptured surfaces. Production Engineering Re-search and Development, Annals of the German Academic Society for Production EngineeringWGP 8, 153–158.

Kuhnt, S., Erdbruegge, M., 2004. A strategy of robust paramater design for multiple responses.Statistical Modelling 4, 249–264.

Kuhnt, S., Rudak, N., 2011. JOP: Joint optimization plot. R Package version 2.0.1.

31

Integrated models in healthcare

Yifat Lavi1

1 University of Turin, Business and management, Corso U. Sovietica 218 bis, Turin, Italy

Keywords: Integrated models, Healthcare, Six Sigma, Lean Manufacturing, DEA

Abstract Achieving excellence can be a hard task. Many companies and organizations have the ambition of becoming

exceptional for the benefit of their customers, investors and employees. In order to achieve such goals, one needs a

robust methodology, management support and hard work.

When referring to a healthcare system, being exceptional is an ethical obligation not only an ambition.

Healthcare processes are a key determinant of the quality of care. Delays in test results, mistakes in administering

medicine, lack of information about a patient health history and radiology retakes are only a few such examples. Lack

of consistent procedures and incorrect treatments are a major health hazard in a hospital.

Healthcare workers in all departments are expected to continuously improve the quality, timeliness, and cost of their

services to the community. Six Sigma is a management methodology which combines the reduction of waste and

complexity of lean manufacturing with quality improvement and statistical data analysis. Six Sigma and the related

methodology of Lean Six Sigma allow healthcare workers to get more for their patients and increase the effectiveness

of the services they provide.

Employees in hospitals play a large role in total service outcome. All employees provide service, whether to internal

or external customers. It is essential to make sure they give the best possible service, whether it's administrative or

physiological. For this purpose, there is a need to learn what drives employees and what will ensure their satisfaction

at work which will then result in good service.

Our research combines mathematical (Six Sigma), economic (DEA) and practical (Lean) methods with human

resources methodologies (human sigma) in order to achieve the level of excellence needed by healthcare providers all

over the world.

Bibliography John H. Flaming, Curt Coffman and James K. Harter, 2005. On "Manage your human sigma". In: Harvard Business

Review p.1-10.

Anthony J. Rucci, Steven P. Kim and Richard T. Quinn, 1998. On "The employee–customer–profit chain at Sears". In:

Harvard Business Review p.83–97.

Peter J. Sherman, 2010. On "Strengthening the Employee-customer Interaction", In: http://www.isixsigma.com/

A. Blanton Godfrey and Ron S. Kenett, 2007. On "Joseph M.Juran, a Perspective on Past Contributions and Future

Impact". In Quality Reliability Engineering International Vol.23 p.653–663.

Ron S. Kenett, 2009. On "Managing Integrated Models: A challenge for Top Management and the Quality Manager".

In Gallille Annual Quality conference, Ort Braude College, Carmiel, Israel.

Silvia Salini and Ron S. Kenett, 2009. On “Bayesian Networks of Customer Satisfaction Survey Data”. In: Journal of

Applied Statistics, Vol. 36, No. 11, pp. 1177-1189.

Ron S. Kenett, 2004. On "The Integrated Model, Customer Satisfaction Surveys and Six Sigma". In: The First

International Six Sigma Conference, CAMT, Wroclaw, Poland.

Apichat Sopadang, 2009. On "Desirability Function", In: Faculty of engineering Chiang Mai University.

Mary Jean Ryan and William Paul Thompson, 2007. On Cqi and the Renovation of an American Health Care System:

A Culture Under Construction. In: ASQC Quality Press.

Thomas G. Zidel, 2006. On A lean guide to transforming healthcare, In ASQ quality press.

A New Approach to the Optimal Design of Blocked andSplit-Plot Experiments

K. Mylona1 and P. Goos1,2

1 Universiteit Antwerpen, Faculty of Applied Economics, City Campus - Prinsstraat 13 - 2000 Antwerpen,Belgium

2 Erasmus Universiteit Rotterdam, Erasmus School of Economics, Postbus 1738, DR Rotterdam 3000,Netherlands

Keywords: Split-plot experiments, Blocked experiments, Optimal designs, Gaussian quadrature, Re-stricted maximum likelihood.

Abstract

Many industrial experiments, such as block experiments and split-plot experiments, involve oneor more restrictions on the randomization. In these experiments the observations are obtained ingroups. A key difference between blocked and split-plot experiments is that there are two sortsof factors in split-plot experiments. Some factors are held constant for all the observations withina group or whole plot, whereas others are reset independently for each individual observation.The former factors are called whole-plot factors, whereas the latter are referred to as sub-plotfactors. Often, the levels of the whole-plot factors are, in some sense, hard to change, while thelevels of the sub-plot factors are easy to change. D-optimal designs, which guarantee efficientestimation of the fixed effects of the statistical model that is appropriate given the random blockor split-plot structure, have been constructed in the literature by various authors. However, ingeneral, model estimation for block and split-plot designs requires the use of generalized leastsquares and the estimation of two variance components. We propose a new Bayesian optimal designcriterion which does not just focus on fixed-effects estimation but also on variance-componentestimation. A novel feature of the criterion is that it incorporates prior information about thevariance components through log-normal or beta prior distributions. Finally, we also present analgorithm for generating efficient designs based on the new criterion. We implement several lesser-known quadrature approaches for the numerical approximation of the new optimal design criterion.

33

Computer Experiments for Large Logistic Systems

M. Neblik1, S. Kuhnt1 and L. Mest2

1 TU Dortmund University, Fac. of Statistics, Vogelpothsweg 87 - 44221 Dortmund, Germany2 TU Dortmund University, Fac. of Mechanical Engineering, Leonhard–Euler–Straße 2 - 44221 Dortmund,

Germany

Keywords: Computer experiments, logistic systems, operating strategies.

Abstract

In complex logistic systems there are several factors that influence the efficiency of a system. Inmany cases these factors are operational decisions, for example using FiFo or LiFo for incomingtrucks waiting for service. We treat the special case of forwarding agencies, where trucks deliverpiece goods, which are handled and finally loaded onto other trucks. For an optimal choice of theoperating strategies, information is needed concerning their impact on the efficiency of the agency.This information cannot be obtained from varying the real system.

We therefore develop methods using computer experiments to analyse the effect of different op-erating strategies. For this purpose the simulation tool TransSim-Node (Neumann and Deymann(2008)) is especially designed. It offers the possibility to simulate forwarding agencies with all theirdetails. Any combination of operating strategies for the different parts of the process can be im-plemented and simulated. Very detailed results of a single piece good can be requested as outputas well as results about the whole system like throughput times. This makes the simulation veryaccurate but also computationally expensive, requiring an appropriate experimental design. Thequality of the results of course depends heavily on the used input data.

Real datasets as input data may contain special occurrences that favor one or another operatingstrategy. Instead of using the real datasets we suggest to generate new datasets from a statisticalmodel containing only main characteristics. This eliminates misleading incidents from the data andfurthermore some variation is introduced to the simulation. Several problems have to be solvedwhile generating this new data. For instance there is an inherent coherence between an outgoingtrucks arrival time and its destination that has to be identified. There are a lot of different restric-tions and coherences that have to be considered. Otherwise the new data would not be realisticand lead to faulty results.

The process of dealing with these restrictions, extract the characteristics from the original datasetand generate the new data will be explained in detail. A dataset from a real forwarding agency inGermany that was recorded in March 2010 will be used as an example.

Bibliography

Neumann, L., Deymann, S., 2008. TransSim-Node - a simulation tool for logistics nodes. Proceed-ings of the Industrial Simulation Conference 2008, 283–287.

34

Space-time Gaussian processes for the approximation ofpartially converged simulations

V. Picheny1

1 Ecole Centrale de Paris, Grande voie des vignes, Chatenay-Malabry, France

Keywords: Partial convergence, computer experiments, metamodeling

1 Partially converged simulations

Using computer experiments and metamodels for facilitating optimization and statistical analysisof engineering systems has become commonplace. However, despite the growth of computationalcapabilities, the complexity of the simulators drastically limit the number of available experiments.In this context, a promising solution to alleviate the computational costs consists of using partiallyconverged simulations instead of exact solutions. The gain in computational time is of course at aprice of precision in the response.This work addresses the issue of fitting a Gaussian process metamodel to partially convergedsimulation data, and using such model in optimization. The main challenge consists in the adequateapproximation of the error due to partial convergence. The simplest approach is to model such erroras pure noise (Huang et al., 2006). A more complex model, called co-kriging, has been proposedwhen both partially and completely converged simulations are available (Forrester et al., 2006).However, this type of models is usable only when a single (or very few) levels of convergence areconsidered, while in practice the levels of convergence can vary from one simulation to another.Here, we propose to fit a Gaussian process in the joint space of design parameters and computationaltime. The model is constructed by building a covariance function that reflects accurately the actualstructure of the error.

2 Gaussian process approximation

In the context of partially converged simulations, an observation zi is defined by the set of inputparameters x ∈ D ⊂ Rd and by computational time t ∈ R+∗ (typically proportional to the numberof solver iterations). In order to predict such types of responses, Gaussian processes are particularlyadapted since they allow the definition of models that can inherit the structure of the function toapproximate. Indeed, we consider that the observed function is a realization of a random processZ(x, t). We model Z as the sum of a process F independent of t, and a process G that depends onboth x and t:

Z(x, t) = F (x) +G(x, t) (1)

F is the response given by the simulator with complete convergence, and then can be modeled withthe usual assumptions: stationarity, ergodicity, etc. (as for a kriging model in a classical framework).G is the error term due to partial convergence, and has a more complex structure. In the x space,it can be observed that two runs with close sets of input parameters converge in a similar fashion,hence their partially converged response are correlated. In the t direction, except for the first fewiterations that often show large oscillations, the convergence is smooth so the responses evaluatedat successive time steps are also correlated. Moreover, G is naturally instationary in t, since theconvergence error tends to zero when the computational time increases. More generally, it can beassumed that the error variance decreases monotonically with computational time.We propose a covariance function for G of the following form (with the notation u = (x, t)):

kG(u, u′) = σ2rx(|x− x′|)rt(|t− t′|)f(t)f(t′) (2)

where rx and rt are two stationary correlations, and f is the attenuation function that monotoni-cally decreases to zero when t tends to infinity. f can be for instance a polynomial or exponentialfunction:

f(t) =(

1t

)q

or f(t) = exp (−αt) (3)

2 Space-time Gaussian processes for the approximation of partially converged simulations

Finally, the kernel of the process Z can be written as the sum of the kernels of F and G:

kZ(u, u′) = kG(u, u′) + kF (x, x′) (4)= σ2

Grx(|x− x′|)rt(|t− t′|)f(t)f(t′) + σ2F rF (|x− x′|) (5)

Using this kernel, we are able to perform simulation, conditional simulation, hence learning withGaussian processes. In the fashion of simple kriging, the prediction mean and variance of theprocess conditional on the observation can be written simply in terms of covariance matrices. Forthe estimation of covariance parameters (or hyperparameters), likelihood quantities can be derivedand used to perform optimization. Moreover, in optimization or any decision process, the value ofinterest is actual (or completely converged value), for t = +∞. With our model, the predictionfor this asymptotic value takes simple form, and can even be seen as a simple kriging models withcorrelated residuals.

3 Application to a CFD simulator

We applied our method to the fitting of data provided by the simulation of the flow in a two-dimensional pipe, which shape is defined by up to 13 parameters. The level of convergence can betuned by the user by changing the number of steps of the simulator solver. With few input param-eters, the proposed model is found to very accurately approximate the fully converged solutions.In higher dimensions, the approximation quality remains high but requires several implentationtricks for the learning of hyperparameters.

FIGURE 1. Prediction of the output of a simulator based on five observations with different convergencelevels. Upper graphs: exact response, design of experiments, and (right) : asymptotic prediction (black),exact response (red) and observations (blue). Lower graphs: mean and standard deviation of the gaussianprocess model; difference between the mean and actual response.

References

Huang, D., Allen, T., Notz, W., and Miller, R., 2006. Sequential kriging optimization using multiple-fidelity evaluations, Structural and Multidisciplinary Optimization, 32(5), 369382.

Forrester, A., Bressloff, N., and Keane, A., 2006. Optimization using surrogate models and par-tially converged computational fluid dynamics simulations, Proceedings of the Royal Society A,462(2071), 2177.

Multivariate process capability assessment with imprecisedata

M. Scagliarini1 and S. Evangelisti2

1 University of Bologna, Dep. of Statistics, via Belle Arti , 41 - 40126 Bologna, Italy2 University of Bologna, Dep. of Civil, Environmental and Materials Engineering, via Terracini, 28 - 40131

Bologna, Italy

Keywords: Multivariate process capability analysis, Measurement uncertainty, Coverage probability.

1 Introduction

Process capability analysis often entails characterizing or assessing processes or products based onmore than one quality characteristic. According to the comprehensive encyclopedic work by Pearnand Kotz (2006), multivariate process capability assessment can be obtained from: the probabilityof nonconforming products using the distribution of the multivariate process; the ratio of a toleranceregion to a process region; different approaches using loss functions; geometric distance approachinvolving principal components analysis. In this work the effects of multivariate gauge measurementerrors on multivariate process region are studied. The proposed method is based on the study of aquadratic form and allows to assess the decrease of coverage caused by measurement uncertainty.

2 Multivariate process region

Taam et al. (1993) proposed a multivariate capability index defined as a ratio of two volumes

MCpm =V ol.(R1)V ol.(R2)

(1)

where R1 is the modified process region and R2 is a scaled 99.73% process region. Under theassumption that the vector of the m quality characteristics of interest possesses a multivariatenormal distribution X v N(µ,Σ) the volume of R2 can be written as

V ol.(R2) = V ol.(R3)×D (2)

whereR3 = {X : (X− µ)′Σ−1(X− µ) ≤ K(m)} (3)

is the region in which 99.73% process values fall, K(m) is the 99.73th percentile of the χ2 distri-bution with m degrees of freedom,

D = [1 + (µ−T)′Σ−1(µ−T)] (4)

is a constant quadratic form and T is the vector of target values. Under the normality assumptionthe volume of R3 is

V ol.(R3) =|Σ|1/2(πK(m))m/2

Γ[(m/2) + 1](5)

3 Measurement uncertainty

In practice, the true quality characteristics that we are interested in monitoring are not easy toobserve, but we instead observe surrogates of them which are the true quality characteristics plusmeasurement errors. In the following discussion, we assume the multivariate measurement errormodel

Y = X + e (6)

where e ∼ N(0,Σe), Σe is assumed to be a positive definite matrix and X and e are independent.From the above discussion it follows that the observable quality characteristics, which is usuallyobtained from some physical measurements, is normally distributed Y ∼ N(µ,Σy) where Σy =Σ + Σe. In the presence of multivariate gauge measurement errors the region in which 99.73%process values fall the process region is

R3e = {X : (X− µ)′Σ−1y (X− µ) ≤ K(m)} (7)

Let us consider the X that, in the error free case, lies on the boundary of process region R3

B3 = {X : (X− µ)′Σ−1(X− µ) = K(m)} (8)

If we define the difference vectordX = (X− µ) (9)

then region (8) can be written as

B3 = {X : dX′Σ−1dX = K(m)} (10)

Let us examine the measurement error case, considering only the X that lie on the boundary ofR3. In this situation, we can define

Q(Xe) = {X : dX′Σ−1

y dX = K(m)} (11)

where X ∈ B3.Q(Xe) is a quadratic form and, under the normality assumption, is distributed as a χ2 with mdegrees of freedom. Q(Xe) ≤ K(m) with equality only when Σe is a matrix of zeros. This resultmeans that the X which define the boundary B3 of the ellipsoid containing the 99.73% of the processregion in the presence of measurement errors define an ellipsoid with a smaller coverage than theprocess region (3). A valuable aspect of this approach consists in the possibility of summarizingthe effects of multivariate measurement error on the process region since it is possible to determineanalytically both the minimum and the maximum values of Q(Xe). Following Mardia et al. (1979)we have that

max(Q(Xe)) = [ maximum eigenvalue of Σ(Σ−1y )]×K(m) (12)

min(Q(Xe)) = [ minimum eigenvalue of Σ(Σ−1y )]×K(m) (13)

Therefore it is possible to evaluate the loss of coverage caused by measurement errors in twoscenarios: the best-case scenario using the max(Q(Xe)); the worst-case scenario using min(Q(Xe)).This approach may be useful since it allows a probabilistic evaluation of the effects of gaugeimprecision in multivariate process capability analysis involving only the notion of process region.In the work two example are considered to demonstrate the applicability of the proposed method.

Bibliography

Mardia, K. V., Kent, J. T., Bibby, J. M., 1979. Multivariate Analysis. Academic press, San Diego.

Pearn, W., Kotz, S., 2006. Encyclopedia and Handbook of Process Capability Indices, Series onQuality, Reliability and Engineering Statistics, Vol. 12. World Scientific Publishing, Singapore.

Taam, W., Subbaiah, P., Liddy, W., 1993. A note on multivariate capability indices. Journal ofApplied Statistics 20.

Use of the Design of Experiments to Develop a Scalable Route to a

Key Chirally Pure Arylpiperazine F. Tinazzi, G. Guercio

Aptuit, Development and Manufacturing, via A. Fleming, 4 - 37135 Verona, Italy

Keywords: Design of expeiments, computer modelling, pilot plant.

The dynamic kinetic resolution (DKR) of an Arylpiperazine in the presence of 3,5-dichlorosalicyl

aldehyde as racemizing agent and (L)-mandelic acid as precipitating agent is a key step in the

synthesis of a final API selected as novel NK-1 antagonist. The reaction was optimised on a

laboratory scale and no problems were encountered. However, some problems were encountered in

the pilot plant, with a considerable amount of product adhering to the reactor walls. Moreover, a very

difficult azeotropical removal of the water to the target level led to a further decrease of the yield. In

fact while the yield achieved on a 5 L scale was about 70%, the overall yield in plant was only about

50%.

Hence, it was evident that the DKR needed further optimization. This was accomplished by means of

a full factorial Design of Experiment (DoE) study, implying 12 reactions and two center points to

evaluate the curvature, which looked into reaction conditions and stirring rates. As a result of the DoE

study, stirring rate was the most significant factor influencing the primary yield of the reaction.

Moreover, a strong interaction between water and dichlorosalicyl aldehyde was observed; thank to

this, the larger amount of water obtained in the pilot plant scale, was buffered by a larger amount of

aldehyde.

Figure 1. DoE on parameters affecting the DKR

Further to the DoE, a computer modelling study was carried out, enabling us to design an appropriate

reactor configuration to ensure efficient mixing. The initially employed round bottomed vessel with

baffles led to the tendency to form dead mixing zones, which subsequently turned into encrustation.

The computer modelling suggested using a conical vessel without baffles, as this would be ideal for

thick suspensions and would avoid the dead mixing zones issue.

39

Figure 2. Computer modelling

When the process was repeated on pilot-plant scale with the new conditions (more aldehyde and the

suggested vessel configuration) it was possible to reproduce the yield and purity achieved on the lab

scale.

Bibliography

Guercio, G.; Bacchi, S.; Goodyear, M.; Carangio, A.; Tinazzi, F. and Curti, S., 2008, Synthesis of the

NK1 Receptor Antagonist GW597599. Part 1: Development of a Scalable Route to a Key Chirally

Pure Arylpiperazine. Organic Process Research & Development, vol.12, n.6, p.1188-1194

40

Index

F. Aggogeri, 7A. Avanzo, 16J. Baccou, 20A. Baldi Antognini, 9G. Barbato, 7, 10E.M. Barini, 7S. Barone, 12I. Ben-Gal, 13R. Berni, 14L. Borgarello, 16R. Borgoni, 18A. Braunstein, 24L. Buslig, 20L. Corain, 22A. Corazza, 23M. P. D’Ambrosio, 23S. Evangelisti, 37A. Fagiano, 16S. Figini, 25R. Fontana, 24E. Galliera, 16L. Gao, 25G. Genta, 7P. Giudici, 25P. Goos, 33G. Guercio, 39P. Hammersberg, 26A. Jourdan, 27D. Kedem, 13R.S. Kennett, 29S. Kuhnt, 30, 31, 34Y. Lavi, 32R. Levi, 7J. Liandrat, 20G. V. Lombardi, 14V. Massaro, 23F. Mattiello, 22L. Mest, 34T. Muhlenstadt, 30K. Mylona, 33M. Neblik, 34

H. Olsson, 26G. D. Panciani, 10V. Picheny, 20, 35L. Radaelli, 18F. Ricci, 10N. Rudak, 31S. Ruffa, 10L. Salmaso, 22M. Scagliarini, 37G. Singer, 13F. Tinazzi, 39V. Tritto, 18G. Vicario, 10M. Zagoraiou, 9D. Zappa, 18

41

Joint ENBIS-DEINDE 2011 Spring Conference

Torino (Italy), 16-18 March 2011

ENBIS DEINDE 2011

Contact address: enbis-deinde2011@calvino.polito.itWeb site: http://calvino.polito.it/enbis deinde 2011/

c© — Copyrights 2011 —

DIMAT - Dipartimento di Matematica - Politecnico di Torino

10129 Torino, Corso Duca degli Abruzzi, 24