Academic literature on the topic 'Experiments designs'

Most design of experiments assumes predetermined design regions. Design regions with uncertainty are of interest in the first chapter. This chapter proposes optimal designs under a two-part model to handle the uncertainty in the design region. In particular, the logit model in the two-part model is used to assess the uncertainty on the boundary of the design region. The second chapter proposes an efficient and effective multi-layer data collection scheme (Layers of Experiments) for building accurate statistical models to meet tight tolerance requirement commonly encountered in nano-fabrication. "Layers-of-Experiments" (LOE) obtain sub-regions of interest (layer) where the process optimum is expected to lie and collect more data in the sub-regions with concentrated focus. The third chapter contributes a new design criterion combining model-based optimal design and model-free space-filling design in a constraint manner. The proposed design is useful when the fitted statistical model is required to have both characteristics: accuracy in statistical inference and design space exploration. The fourth chapter proposes adaptive combined designs in the layers of experiments. This chapter also develops methods to improve model quality by combining information from various layers and from engineering models. Combined designs are modified to improve its efficiency by incorporate collected field data from several layers of experiments. Updated engineering models are used to build more accurate statistical models.

Problem statement: The D-optimal design is often used in clinical research. In multi-factor clinical experiments it is natural to restrict the experiment's design space so as not to give a patient the combination of several high dose treatments simultaneously. Under such design space restrictions it is unknown what designs are D-optimal. The goal of the thesis has been to find D-optimal designs for these design spaces. Approach: Two new algorithms for finding D-optimal designs with one, two or three factors with linear models has been developed and implemented in MATLAB. Two restricted design spaces were explored. In cases when the program could not find the D-optimal design an analytic approach was used. Results: Special attention was given to the two factor model with interaction. All of the D-optimal designs for this model, N less or equal to 30, and their permutations have been listed as well as their continous designs. Conclusion: In one of the restricted design regions a simple design pattern appeared for N greater than or equal to 7. In the other restricted design region no obvious pattern was found but its continuous design could be calculated through analysis. It turned out that the number of trials at the lowest dose combination did not change when moving from the full space design to the restricted design regions.<br>Frågeställning: D-optimala designer är vanliga i kliniska studier. När flera faktorer (läkemedel) prövas samtidigt kan det vara nödvändigt att begränsa försöksrummet så att patienterna undviker att få en hög dos av flera faktorer samtidigt. I sådana begränsade försöksrum är det okänt vilka designer som är D-optimala. Uppsatsens mål har varit att hitta D-optimala designer i begränsade försöksrum. Metod: Två nya algoritmer för att hitta D-optimala designer med en, två eller tre dimensioner och linjära modeller har utvecklats och implementerats i MATLAB. Två begränsade försöksrum har utforskats. I de fall då MATLAB-programmet inte kunde hitta de D-optimala designerna användes analytiska metoder. Resultat: Analys av en tvåfaktormodell med interaktion utforskades särskilt noggrant. Alla D-optimala designer och permutationer av dessa i de båda begränsade försöksrummen har listats för alla N mindre än eller lika med 30, samt även deras kontinuerliga designer. Slutsats: För det ena försöksrummet upptäcktes ett mönster i designen då N är större än eller lika med 7. I det andra försöksrummet upptäcktes inget mönster och det krävdes således analytiska metoder för att finna dess kontinuerliga design. Det visade sig att antalet försök i den lägsta doskombinationen förblev oförändrat då man bytte från det fulla designrummet till de båda begränsade designrummen.

Computer experiments facilitate, through mathematical modelling, various experiments that would otherwise be very difficult to perform, or even impossible. Computer experiments are employed to emulate situations in areas such as weather modelling, astrophysics, economics and many more. In conducting a computer experiment, we are required to select a design for the initial values x⁽¹⁾, . . . , x(n) of a process, and then emulate the output based on the process and the initial values. The quality of the emulator therefore depends partly on the process and partly on the choice of initial values. We will only consider the Gaussian Process in this thesis, and the focus of our analysis will be on the selection of initial values. We consider the effects of selecting a random versus a rational design for the initial values of computer experiments. We aim to study a broad range of possible computer models that are likely to arise in practice. Therefore, we present the analysis of eight different design choices, each of which is either random or rational, for the initial values. These initial values are applied to five different test functions that we consider to be prevalent in practice. We observe the effect of each of the designs on each of the test functions at three different sample sizes. The goal of this thesis is to present a comprehensive study of various standard design choices and make recommendations to a practitioner on a robust design for the initial values of a computer experiment on a given function. As well as ultimately recommend a universally robust design for the initial values of any computer experiment.

This thesis was motivated by the collaborative research undertaken by QMUL and Pfizer UK into improving experiments at pre-clinical drug development. In theory, the most efficient designs for these particular experiments, as well as for many other studies, are optimal designs. Since, however, their implementation poses challenges — and several emerged during the project — optimal designs are uncommon in practice. To address these challenges the thesis introduces a comprehensive design framework, which both generalizes and simplifies optimal design. At the core of this framework are optimal relaxed designs, seldom considered before. Like a standard design measure a relaxed design has non-integer replications and is mathematically tractable; unlike the former, whose replications must sum to one, it allows the replications total to be unconstrained. The methodology discussed in this thesis assumes design of experiments for parameter estimation, given a response model, but also applies to broader problems. Although the motivation and applications come from the pharmaceutical project, the ultimate goal is to develop an intuitive and versatile design toolkit for experimenters in various practical fields.