本文主要討論組可分處理集區設計當同一集區內漏失ｔ個對照處理時之連接穩健性，以及當漏失整個集區時之連接穩健性並且（１）令屬於同組別之試驗處理於同集區內一起出現之次數於零的條件下，分別將組可分處裡集區設計當同一集區內漏失ｔ個對照處理以及當漏失整個集區時之效率值確實解出。（２）令屬於不同組別之試驗處理於同集區內一起出現之次數為零的條件下，分別將組可分處裡集區設計當同一集區內漏失ｔ個對照處理以及當漏失整個集區時之效率值確實解出。

<p>This thesis describes the application of multivariate methods in a novel approach to the formulation of tablets for direct compression. It begins with a brief historical review, followed by a basic introduction to key aspects of tablet formulation and multivariate data analysis. The bulk of the thesis is concerned with the novel approach, in which excipients were characterised in terms of multiple physical or (in most cases) spectral variables. By applying Principal Component Analysis (PCA) the descriptive variables are summarized into a few latent variables, usually termed scores or principal properties (PP’s). In this way the number of descriptive variables is dramatically reduced and the excipients are described by orthogonal continuous variables. This means that the PP’s can be used as ordinary variables in a statistical experimental design. The combination of latent variables and experimental design is termed multivariate design or experimental design in PP’s. Using multivariate design many excipients can be included in screening experiments with relatively few experiments.</p><p>The outcome of experiments designed to evaluate the effects of differences in excipient composition of formulations for direct compression is, of course, tablets with various properties. Once these properties, e.g. disintegration time and tensile strength, have been determined with standardised tests, quantitative relationships between descriptive variables and tablet properties can be established using Partial Least Squares Projections to Latent Structures (PLS) analysis. The obtained models can then be used for different purposes, depending on the objective of the research, such as evaluating the influence of the constituents of the formulation or optimisation of a certain tablet property.</p><p>Several examples of applications of the described methods are presented. Except in the first study, in which the feasibility of this approach was first tested, the disintegration time of the tablets has been studied more carefully than other responses. Additional experiments have been performed in order to obtain a specific disintegration time. Studies of mixtures of excipients with the same primary function have also been performed to obtain certain PP’s. Such mixture experiments also provide a straightforward approach to additional experiments where an interesting area of the PP space can be studied in more detail. The robustness of a formulation with respect to normal batch-to-batch variability has also been studied.</p><p>The presented approach to tablet formulation offers several interesting alternatives, for both planning and evaluating experiments.</p>

=RESUME= Trois approches différentes ont été comparées pour lestimation de lincertitude de mesure, à savoir celles basées sur des études inter-laboratoire, sur la robustesse et sur la validation. Pour ce faire, deux techniques analytiques séparatives, la chromatographie liquide haute performance (CLHP) et lélectrophorèse capillaire (EC), ont été utilisées pour la détermination de lénantiomère R-timolol dans des échantillons de maléate de S-timolol. Loptimisation de la méthode de CLHP a été effectuée sur une phase chirale à base de cellulose modifiée selon une approche multivariée. En ce qui concerne lEC, une séparation chirale convenable a été obtenue en milieu non aqueux en utilisant de lheptakis(2,3-di-O-méthyl-6-O-sulfo)-β-cyclodextrine comme sélecteur chiral en combinaison avec le camphosulfonate. Les deux méthodes ont été validées pour lusage prédéfini en appliquant la stratégie du profil dexactitude, ce qui a permis également destimer lincertitude de mesure. Par la suite, un test de robustesse a été effectué pour les deux méthodes. Linfluence des paramètres opératoires a été évaluée en considérant non seulement les réponses qualitatives mais surtout les réponses quantitatives. Les résultats de ces dernières (teneurs en R-timolol) ont servi à lestimation de lincertitude de mesure, selon le guide ISO 5725-2. Ce même guide a été utilisé pour évaluer la reproductibilité des résultats obtenus lors des études inter-laboratoire menées avec les deux méthodes. Lincertitude estimée à partir de la reproductibilité, a été trouvée dépendante de la concentration, comme observé également lors des études de validation et de robustesse. Il apparaît que lincertitude obtenue en robustesse prédit très bien celle obtenue en inter-laboratoire et constitue donc une alternative intéressante à cette dernière. Par contre, lincertitude associée à la validation est quant à elle différente de celle des autres approches. Cependant, elle reste parfaitement valable pour autant que le protocole de validation soit en accord avec la routine et que la méthode ne quitte pas le laboratoire qui la validée. Lors de la comparaison des deux méthodes, lincertitude obtenue en CLHP a été trouvée plus faible que celle obtenue en EC. =SUMMARY= Three different approaches (inter-laboratory, robustness and validation) have been applied to the estimation of uncertainty and compared. For that purpose, two analytical separation techniques, namely high performance chromatography liquid (HPLC) and capillary electrophoresis (CE), have been used for the determination of R-timolol enantiomer in S-timolol maleate samples. The optimisation of the HPLC method was carried out on a chiral stationary phase containing modified cellulose, by applying a multivariate approach. Concerning the CE method, a suitable chiral separation was obtained in a nonaqueous medium using heptakis(2,3-di-O-méthyl-6-O-sulfo)-β-cyclodextrin as chiral selector in combination with camphorsulfonate. The two methods were validated for the intended use by applying the strategy of the accuracy profile, which could be used additionally to estimate the uncertainty of measurement. Then, a robustness test was performed for the two methods. The influence of the operating parameters was assessed considering not only the qualitative responses but mainly the quantitative ones (the R-timolol content). The latter were used to estimate the uncertainty of measurement according to the ISO 5725-2 guide. The same guide was applied to evaluate the reproducibility of results obtained in inter-laboratory studies carried out with the two methods. The uncertainty was found to be concentration dependent, as also observed in validation and in robustness studies. The uncertainty obtained by robustness studies predicts well that obtained in inter-laboratory studies and can be proposed as an alternative to the latter. On the other hand, the estimation of uncertainty obtained with the validation studies leads to lower values than those obtained with the two other approaches but is still acceptable as long as the analytical method is used in a single laboratory. When comparing the two analytical methods, the uncertainty obtained in LC was found to be lower than that obtained in CE.

The present thesis is dedicated to the study of the behaviour of steel and composite steel-concrete building frames with a particular attention paid to the beam-to-column joint behaviour. Two main topics are investigated herein: the behaviour of sway building frames subjected to conventional loadings and the development of the membrane forces in structural beams further to the loss of a column. Regarding the first topic, the main objective is to propose a simplified analytical method to predict the ultimate load factor of composite sway building frames, a case not yet covered by the actual codes and standards. To achieve this goal, the behaviour of composite joints subjected to bending moments is first studied through experimental and analytical investigations; indeed, the joints are key elements influencing the response of sway frames. Through these investigations, a new collapse mode is identified for single-sided composite joints subjected to hogging moments and an analytical method is proposed and validated to introduce this new collapse mode in the joint design. In addition, an analytical method is also proposed and validated to predict the response of composite joints subjected to sagging moment, a situation which can occur in composite sway frames subjected to horizontal loads but not yet covered by the actual codes. Afterwards, the numerical tool used to predict the response of composite sway frames is validated through a benchmark study and through comparisons with experimental test results coming from two tests performed in European laboratories. With the so-validated software, the behaviour of actual sway building frames (i.e. frames extracted from existing buildings) is investigated, highlighting their particularities. The applicability to composite sway frames of two simplified analytical method initially developed for steel sway frames (an elastic one called the amplified sway moment method and a plastic one called the Merchant-Rankine approach) is then studied. From these investigations, it is demonstrated that the elastic method can be applied with good confidence to composite sway frames while the plastic one illustrates the same problems of accuracy already observed in previous studies on steel sway frames; in particular, the plastic method may prove to be very unsafe if the collapse mode associated to the ultimate limit state is a panel plastic mechanism. Finally, according to these results, a simplified analytical method is developed for the prediction of the ultimate load factor of steel and composite sway frames. The proposed method is founded on the Ayrton-Perry formulation and is validated through comparison to results obtained with full non-linear numerical analyses performed on more than 300 steel and composite frames. The so-validated method is easy to apply and permits to predict with a very good accuracy the ultimate load factor of a sway frame and the collapse mode appearing at the ultimate limit state. Founded on the knowledge gained from the previous topic on the structural behaviour of steel and composite structures, the behaviour of such structures subjected to an exceptional event is investigated within the second topic. The main objective is to propose a simplified analytical procedure to predict the development of the membrane forces within a structure further to the loss of a column and their effects on the structural response. In a first step, a general procedure allowing the prediction of the response of a structure further to the loss of a column is first defined, with a particular attention paid to the influence of the development of the catenary action on this response. Then, an experimental test performed at Liège University and simulating the loss of a column in a composite frame is described. The objective of this test is to observe the development of the catenary action within the tested structure and its effect on the joint behaviour. The described test constitutes a European first in this domain. Also, as for the previous topic, the behaviour of joints is investigated in details. Here, the particularity is the fact that the joints are subjected to combined bending moments and axial loads when the membrane effects developed in the structure. In a previous PhD thesis presented at Liège University, an analytical procedure founded on the component method was developed to predict the response of steel joints subjected to such loading. Within the present thesis, this method is extended to composite joints and validated through comparisons to experimental tests. Afterwards, the numerical tool used for the numerical investigations is validated through a benchmark study and through comparisons with the results of the experimental test performed at Liège University. In particular, the difficulty of simulating the actual behaviour of beam-to-column joints subjected to combined bending moments and axial loads is illustrated. With the so-validated software, a simplified substructure modelling, on which the developed analytical method is founded, is then validated. In addition, parametric numerical studies are performed on the substructure modelling in order to identify the parameters to be considered within the developed method. Finally, the developed simplified analytical method is described and validated through comparisons between the experimental results and the analytical prediction. With this easy-to-apply method, a very good accuracy is achieved; in particular, it is possible to predict the requested deformation capacity in the structural elements where plastic hinges are developed and the membrane forces which have to be supported by the structure./ La présente thèse est dédiée à létude du comportement des portiques de bâtiments en acier et mixte acier-béton avec une attention particulière portée sur le comportement des assemblages poutre-colonne. Deux sujets principaux sont abordés : létude du comportement des portiques à nuds transversalement déplaçables soumis à un chargement classique et létude du développement des efforts membranaires dans les poutres dun portique suite à la perte dune colonne. Concernant le premier sujet, lobjectif principal est de proposer une méthode analytique simplifiée permettant de prédire le multiplicateur de charge ultime de portiques mixtes à nuds transversalement déplaçables, cas non encore couvert par les codes actuels. Pour atteindre cet objectif, le comportement des assemblages mixtes soumis à des moments de flexion est étudié dans un premier temps aux travers détudes expérimentales et analytiques, les assemblages étant des éléments clés dans létude du comportement des portiques à nuds transversalement déplaçables. Via ces études, un nouveau mode de ruine est mis en évidence pour les assemblages mixtes externes et une méthode analytique est proposée et validée pour la prise en compte de ce nouveau mode de ruine dans le dimensionnement de ces assemblages. De plus, une méthode analytique est également proposée et validée pour prédire la réponse des assemblages mixtes soumis à moment positif, situation pouvant apparaître dans les portiques mixtes à nuds transversalement déplaçables soumis à un chargement horizontal mais non encore couverte par les codes actuels. Ensuite, loutil numérique utilisé pour prédire la réponse des portiques est validé par une étude comparative réalisée avec différents logiciels et par une comparaison à des résultats expérimentaux provenant de deux essais réalisés dans des laboratoires européens. Avec cet outil ainsi validé, le comportement de portiques mixtes réels (cest-à-dire extraits de bâtiments existants) est étudié en mettant en évidence leurs particularités. Lapplicabilité à des structures mixtes de deux méthodes simplifiées initialement développées pour des portiques en acier à nuds transversalement déplaçables (une élastique intitulée amplified sway moment method et une plastique intitulée approche de Merchant-Rankine) est alors étudiée. Suite à cette étude, il est démontré que la méthode élastique peut être assurément appliquée aux portiques mixtes tandis que la méthode plastique démontre les mêmes problèmes de précision que ceux déjà observés dans des études précédentes réalisées sur des portiques en acier ; en particulier, la méthode peut se révéler être très insécuritaire si le mécanisme de ruine associé à létat limite ultime est un mécanisme plastique de panneau. Finalement, suite à cette dernière observation, une méthode analytique simplifiée est développée pour la prédiction du multiplicateur de charge ultime de portiques mixtes et en acier à nuds transversalement déplaçables. La méthode proposée est fondée sur la formulation dAyrton-Perry et est validée par des comparaisons à des résultats obtenus via des analyses non-linéaires réalisées sur plus de 300 portiques en acier et mixtes. La méthode ainsi validée est facile à utiliser et permet dobtenir le multiplicateur de ruine dun portique avec une très bonne précision ainsi que le mode de ruine apparaissant à létat limite ultime. Suite à lexpérience acquise sur le comportement des structures en acier et mixtes soumises à un chargement « classique », le comportement de celles-ci soumises à une action exceptionnelle a alors été étudié. Lobjectif principal est la proposition dune méthode analytique simplifiée permettant de prédire le développement des forces membranaires dans une structure suite à la perte dune colonne et leurs effets sur la réponse structurale. Dans un premier temps, une procédure générale permettant de prédire la réponse dune structure lors de la perte dune colonne est définie, mettant en évidence linfluence du développement des efforts membranaire sur cette réponse. Un essai expérimental réalisé à lUniversité de Liège et simulant la perte dune colonne dans un portique mixte est ensuite présenté. Lobjectif de cet essai est dobserver le développement des efforts membranaires dans la structure testée et leurs effets sur le comportement des assemblages. Lessai présenté constitue une première européenne dans ce domaine. Comme pour le sujet précédent, le comportement des assemblages est aussi étudié en détail. Ici, la particularité est le fait que les assemblages sont soumis à la fois à des moments de flexion et à des efforts axiaux lorsque les effets membranaires se développent dans la structure. Dans une thèse de doctorat précédente présentée à lUniversité de Liège, une procédure analytique fondée sur la méthode des composantes a été développée pour prédire la réponse dassemblages en acier soumis à un tel chargement. Dans la présente thèse, cette méthode est étendue au cas des assemblages mixtes et validées via des comparaisons à des résultats expérimentaux. Ensuite, loutil numérique utilisé est validé par une étude comparative réalisée avec différents logiciels et par des comparaisons aux résultats de lessai réalisé à lUniversité de Liège. En particulier, la difficulté de simuler le comportement réel dassemblages soumis à une action combinée defforts de flexion et defforts axiaux est illustrée. Avec le logiciel ainsi validé, un modèle simplifié de sous-structure permettant de développer la méthode analytique simplifiée est défini et validé via des études numériques. De plus, des études paramétriques sont réalisées sur ce modèle afin didentifier les paramètres à prendre en compte dans la méthode développée. Finalement, la méthode simplifiée développée est décrite et validée via des comparaisons entre les résultats expérimentaux et les prédictions analytiques. Avec cette méthode facile à utiliser, une très bonne précision est obtenue ; en particulier, il est possible de prédire la demande en terme de capacité de déformation au niveau des éléments structuraux où se forment des rotules plastiques et de déterminer les efforts membranaires devant être supportés par la structure.

This thesis is divided into two parts. The first part deals with theNevanlinna-Pick interpolation problem, a problem which occursnaturally in several applications such as robust control, signalprocessing and circuit theory. We consider the problem of shaping andapproximating solutions to the Nevanlinna-Pick problem in a systematicway. In the second part, we study distance measures between powerspectra for spectral estimation. We postulate a situation where wewant to quantify robustness based on a finite set of covariances, andthis leads naturally to considering the weak*-topology. Severalweak*-continuous metrics are proposed and studied in this context.In the first paper we consider the correspondence between weighted entropyfunctionals and minimizing interpolants in order to find appropriateinterpolants for, e.g., control synthesis. There are two basic issues that weaddress: we first characterize admissible shapes of minimizers bystudying the corresponding inverse problem, and then we developeffective ways of shaping minimizers via suitable choices of weights.These results are used in order to systematize feedback controlsynthesis to obtain frequency dependent robustness bounds with aconstraint on the controller degree.The second paper studies contractive interpolants obtained as minimizersof a weighted entropy functional and analyzes the role of weights andinterpolation conditions as design parameters for shaping theinterpolants. We first show that, if, for a sequence of interpolants,the values of the corresponding entropy gains converge to theoptimum, then the interpolants converge in H_2, but not necessarily inH-infinity. This result is then used to describe the asymptoticbehaviour of the interpolant as an interpolation point approaches theboundary of the domain of analyticity.A quite comprehensive theory of analytic interpolation with degreeconstraint, dealing with rational analytic interpolants with an apriori bound, has been developed in recent years. In the third paper,we consider the limit case when this bound is removed, and only stableinterpolants with a prescribed maximum degree are sought. This leadsto weighted H_2 minimization, where the interpolants areparameterized by the weights. The inverse problem of determining theweight given a desired interpolant profile is considered, and arational approximation procedure based on the theory is proposed. Thisprovides a tool for tuning the solution for attaining designspecifications. The purpose of the fourth paper is to study the topology and develop metricsthat allow for localization of power spectra, based on second-orderstatistics. We show that the appropriate topology is theweak*-topology and give several examples on how to construct suchmetrics. This allows us to quantify uncertainty of spectra in anatural way and to calculate a priori bounds on spectral uncertainty,based on second-order statistics. Finally, we study identification ofspectral densities and relate this to the trade-off between resolutionand variance of spectral estimates.In the fifth paper, we present an axiomatic framework for seekingdistances between power spectra. The axioms requirethat the sought metric respects the effects of additive andmultiplicative noise in reducing our ability to discriminate spectra.They also require continuity of statistical quantities withrespect to perturbations measured in the metric. We then present aparticular metric which abides by these requirements. The metric isbased on the Monge-Kantorovich transportation problem and iscontrasted to an earlier Riemannian metric based on theminimum-variance prediction geometry of the underlying time-series. Itis also being compared with the more traditional Itakura-Saitodistance measure, as well as the aforementioned prediction metric, ontwo representative examples. / QC 20100817

When two or more chaotic systems are coupled, they may exhibit synchronized chaotic oscillations. The synchronization of chaos is usually understood as the regime of chaotic oscillations in which the corresponding variables or coupled systems are equal to each other. This kind of synchronized chaos is most frequently observed in systems specifically designed to be able to produce this behaviour. In this thesis, one particular type of synchronization, called impulsive synchronization, is investigated and applied to low dimensional chaotic, hyperchaotic and spatiotemporal chaotic systems. This synchronization technique requires driving one chaotic system, called response system, by samples of the state variables of the other chaotic system, called drive system, at discrete moments. Equi-Lagrange stability and equi-attractivity in the large property of the synchronization error become our major concerns when discussing the dynamics of synchronization to guarantee the convergence of the error dynamics to zero. Sufficient conditions for equi-Lagrange stability and equi-attractivity in the large are obtained for the different types of chaos-generating systems used. The issue of robustness of synchronized chaotic oscillations with respect to parameter variations and time delay, is also addressed and investigated when dealing with impulsive synchronization of low dimensional chaotic and hyperchaotic systems. Due to the fact that it is impossible to design two identical chaotic systems and that transmission and sampling delays in impulsive synchronization are inevitable, robustness becomes a fundamental issue in the models considered. Therefore it is established, in this thesis, that under relatively large parameter perturbations and bounded delay, impulsive synchronization still shows very desired behaviour. In fact, criteria for robustness of this particular type of synchronization are derived for both cases, especially in the case of time delay, where sufficient conditions for the synchronization error to be equi-attractivity in the large, are derived and an upper bound on the delay terms is also obtained in terms of the other parameters of the systems involved. The theoretical results, described above, regarding impulsive synchronization, are reconfirmed numerically. This is done by analyzing the Lyapunov exponents of the error dynamics and by showing the simulations of the different models discussed in each case. The application of the theory of synchronization, in general, and impulsive synchronization, in particular, to communication security, is also presented in this thesis. A new impulsive cryptosystem, called induced-message cryptosystem, is proposed and its properties are investigated. It was established that this cryptosystem does not require the transmission of the encrypted signal but instead the impulses will carry the information needed for synchronization and for retrieving the message signal. Thus the security of transmission is increased and the time-frame congestion problem, discussed in the literature, is also solved. Several other impulsive cryptosystems are also proposed to accommodate more solutions to several security issues and to illustrate the different properties of impulsive synchronization. Finally, extending the applications of impulsive synchronization to employ spatiotemporal chaotic systems, generated by partial differential equations, is addressed. Several possible models implementing this approach are suggested in this thesis and few questions are raised towards possible future research work in this area.

ABSTRACT ROBUST CONTROL CHARTS &Ccedil / etiny&uuml / rek, Aysun M. Sc., Department of Statistics Supervisor: Dr. BariS S&uuml / r&uuml / c&uuml / Co-Supervisor: Assoc. Prof. Dr. Birdal Senoglu December 2006, 82 pages Control charts are one of the most commonly used tools in statistical process control. A prominent feature of the statistical process control is the Shewhart control chart that depends on the assumption of normality. However, violations of underlying normality assumption are common in practice. For this reason, control charts for symmetric distributions for both long- and short-tailed distributions are constructed by using least squares estimators and the robust estimators -modified maximum likelihood, trim, MAD and wave. In order to evaluate the performance of the charts under the assumed distribution and investigate robustness properties, the probability of plotting outside the control limits is calculated via Monte Carlo simulation technique.

This paper explores the problem of electrical sports equipment includes 2D-animation, storage media and the safety-protection over out of control of speed and the supporting supervisory control apparatus. This paper succeeded in developing a highly efficient DSP-based motor driver system in the form of a jogging machine which employs IVSC and RISC control law. The simulation and experimental results show that the proposed system meets the requirements of servo tracking with excellent transient, steady state responses and robustness. This paper design a multi-functional FPGA uses in control system of sports equipment to provide the designing flexibility for different scales, solutions to the difficulties of production and maintenance, and the extension for future development of sports equipment.

Vulnerability of buildings to disproportionate (or progressive) collapse has become an increasingly important performance issue following the collapses of the Alfred P. Murrah Federal Building in Oklahoma City in 1995 and the World Trade Center in 2001. Although considerable research has been conducted on this topic, there are still numerous unresolved research issues. This dissertation is aimed at developing structural models and analysis procedures for robustness assessment of steel building structures typical of construction practices in the United States, and assessing the performance of these typical structures. Beam-column connections are usually the most vulnerable elements in steel buildings structures suffering local damage. Models of three typical frame connections for use in robustness assessment have been developed with different techniques, depending on the experimental data available to support such models. A probabilistic model of a pre-Northridge moment-resisting connection was developed through finite element simulations, in which the uncertainties in the initial flaw size, beam yield strength and fracture toughness of the weld were considered. A macro-model for a bolted T-stub connections was developed by considering the behavior of each connection element individually (i.e. T-stub, shear tab and panel zone) and assembling the elements to form a complete connection model, which was subsequently calibrated to experimental data. For modeling riveted connections in older steel buildings that might be candidates for rehabilitation, a new method was proposed to take advantage of available experimental data from tests of earthquake-resistant connections and to take into account the effects of the unequal compressive and tensile stiffnesses of top and bottom parts in a connection and catenary action. These connection models were integrated into nonlinear finite element models of structural systems to allow the effect of catenary and other large-deformation action on the behavior of the frames and their connections following initial local structural damage to be assessed. The performance of pre-Northridge moment-resisting frames was assessed with both mean-centered deterministic and probabilistic assessment procedures; the significance of uncertainties in collapse assessment was examined by comparing the results from both procedures. A deterministic assessment of frames with full and partial-strength bolted T-stub connections was conducted considering three typical beam spans in both directions. The vulnerability of an older steel building with riveted connections was also analyzed deterministically. The contributions from unreinforced masonry infill panels and reinforced concrete slabs on the behavior of the building were investigated. To meet the need for a relatively simple procedure for preliminary vulnerability assessment, an energy-based nonlinear static pushdown analysis procedure was developed. This procedure provides an alternative method of static analysis of disproportionate collapse vulnerability that can be used as an assessment tool for regular building frames subjected to local damage. Through modal analysis, dominant vibration modes of a damaged frame were first identified. The structure was divided into two parts, each of which had different vibration characteristics and was modeled by a single degree-of-freedom (SDOF) system separately. The predictions were found to be sufficiently close to the results of a nonlinear dynamic time history analysis (NTHA) that the method would be useful for collapse-resistant design of buildings with regular steel framing systems.

This thesis describes the application of multivariate methods in a novel approach to the formulation of tablets for direct compression. It begins with a brief historical review, followed by a basic introduction to key aspects of tablet formulation and multivariate data analysis. The bulk of the thesis is concerned with the novel approach, in which excipients were characterised in terms of multiple physical or (in most cases) spectral variables. By applying Principal Component Analysis (PCA) the descriptive variables are summarized into a few latent variables, usually termed scores or principal properties (PP’s). In this way the number of descriptive variables is dramatically reduced and the excipients are described by orthogonal continuous variables. This means that the PP’s can be used as ordinary variables in a statistical experimental design. The combination of latent variables and experimental design is termed multivariate design or experimental design in PP’s. Using multivariate design many excipients can be included in screening experiments with relatively few experiments. The outcome of experiments designed to evaluate the effects of differences in excipient composition of formulations for direct compression is, of course, tablets with various properties. Once these properties, e.g. disintegration time and tensile strength, have been determined with standardised tests, quantitative relationships between descriptive variables and tablet properties can be established using Partial Least Squares Projections to Latent Structures (PLS) analysis. The obtained models can then be used for different purposes, depending on the objective of the research, such as evaluating the influence of the constituents of the formulation or optimisation of a certain tablet property. Several examples of applications of the described methods are presented. Except in the first study, in which the feasibility of this approach was first tested, the disintegration time of the tablets has been studied more carefully than other responses. Additional experiments have been performed in order to obtain a specific disintegration time. Studies of mixtures of excipients with the same primary function have also been performed to obtain certain PP’s. Such mixture experiments also provide a straightforward approach to additional experiments where an interesting area of the PP space can be studied in more detail. The robustness of a formulation with respect to normal batch-to-batch variability has also been studied. The presented approach to tablet formulation offers several interesting alternatives, for both planning and evaluating experiments.