The dynamic properties of Leighton Buzzard sand have been investigated using a resonant column test apparatus. These data are compared with very low frequency cyclic tests on identical specimens. The comparison indicates that the properties of dry sand are independent of frequency, while those of fluid saturated sand are sensitive to the viscosity of the fluid and therefore to the frequency of oscillations. A one-dimensional model of kinematic hardening plasticity is used to predict the dynamic behaviour of the sand. The input parameters for this model are based on the results of static tests. These may be conducted on standard laboratory equipment with only minor modifications. The predictions are in good agreement with the measured data. In particular, the frequency response close to resonance is correctly shown to be asymmetric and the reduction in the resonant frequency with increasing strain amplitude is also correctly represented. The model has been used to generate a series of design curves that allow the dynamic behaviour of foundations to be predicted. Two design examples are given; an offshore gravity structure and a radar installation. The input parameters are based on a hyperbolic shear stress-shear strain equation for the soil. The practical consequences of these findings are assessed with regard to soil testing procedures and dynamic analyses of foundations.

The problem of this study was to develop a curriculum based on present destructive testing procedures used in industry dealing with the mechanical properties of ferrous and non-ferrous metals, and to organize the curriculum at the university level.

Multiplicity issues arise prevalently in a variety of situations in clinical trials and statistical methods for multiple testing have gradually gained importance with the increasing number of complex clinical trial designs. In general, two types of multiple testing can be performed (Dmitrienko et al., 2009): union-intersection testing (UIT) and intersection-union testing (IUT). The UIT is of the interest in this dissertation. Thus, the familywise error rate (FWER) is required to be controlled in the strong sense. A number of methods have been developed for controlling the FWER, including single-step and stepwise procedures. In single-step approaches, such as the simple Bonferroni method, the rejection decision of a hypothesis does not depend on the decision of any other hypotheses. Single-step approaches can be improved in terms of power through stepwise approaches, while also controlling for the desired error rate. Besides, it is also possible to improve those procedures by a parametric approach. In the first project, we developed a new and powerful single-step progressive parametric multiple (SPPM) testing procedure for correlated normal test statistics. Through simulation studies, we demonstrate that SPPM improves power substantially when the correlation is moderate and/or the magnitude of eect sizes are similar. Group sequential designs (GSD) are clinical trials allowing interim looks with the possibility of early terminations due to ecacy, harm or futility, which can reduce the overall costs and timelines for the development of a new drug. However, repeated looks of data also have multiplicity issues and could inflate the type I error rate. The proper treatments to the error inflation have been discussed widely (Pocock, 1977), (O'Brien and Fleming, 1979), (Wang and Tsiatis, 1987), (Lan and DeMets, 1983). Most literature about GSD focuses on a single endpoint. GSD with multiple endpoints however, has also received considerable attention. The main focus of our second project is a GSD with multiple primary endpoints, in which the trial is to evaluate whether at least one of the endpoints is statistically signicant. In this study design, multiplicity issues arise from repeated interims and multiple endpoints. Therefore, the appropriate adjustments must be made to control the Type I error rate. Our second purpose here is to show that the combination of multiple endpoint and repeated interim analyses can lead to a more powerful design. Via the multivariate normal distribution, a method that allows for simultaneously consideration of interim analyses and all clinical endpoints was proposed. The new approach is derived from the closure principle, thus it can control type I error rate strongly. We evaluate the power under dierent scenarios and show that it compares favorably to other methods when correlation among endpoints is non-zero. In the group sequential design framework, another interesting topic is multiple arm multiple stage design (MAMS), where multiple arms are involved in the trial at the beginning with the flexibility about treatment selection or stopping decisions during the interim analyses. One of major hurdles of MAMS is the computational cost with the increasing number of arms and interim looks. Various designs were implemented to overcome this diculty (Thall et al., 1988; Schaid et al., 1990; Follmann et al., 1994; Stallard and Todd, 2003; Stallard and Friede, 2008; Magirr et al., 2012; Wason et al., 2017), but also control the FWER with the potential inflation from the multiple arm comparisons and multiple interim tests. Here, we consider a more flexible drop-the-loser design allowing the safety information in the treatment selection without a pre-specied dropping-arms mechanism and it still retains reasonable high power. The two dierent types of stopping boundaries are proposed for such a design. A sample size is also adjustable if the winner arm is dropped due to the safety considerations.

Title: Multidimensional statistics and applications to study genes Author: Mgr. Peter Bubelíny Department: Department of probability and mathematical statistics Supervisor: prof. Lev Klebanov, DrSc., KPMS MFF UK Abstract: Microarray data of gene expressions consist of thousands of genes and just some tens of observations. Moreover, genes are highly correlated between themselves and contain systematic errors. Hence the magnitude of these data does not afford us to estimate their correlation structure. In many statistical problems with microarray data, we have to test some thousands of hypotheses simultaneously. Due to dependence between genes, p-values of these hypotheses are dependent as well. In this work, we compared conve- nient multiple testing procedures reasonable for dependent hypotheses. The common manner to make microarray data more uncorrelated and partially eliminate systematic errors is normalizing them. We proposed some new normalizations and studied how different normalizations influence hypothe- ses testing. Moreover, we compared tests for finding differentially expressed genes or gene sets and identified some interesting properties of some tests such as bias of two-sample Kolmogorov-Smirnov test and interesting behav- ior of Hotelling's test for dependent components of observations. In the end of...

In this dissertation, we propose a computational approach using a resampling based permutation test as an alternative to MCP-Mod (a hybrid framework integrating the multiple comparison procedure and the modeling technique) and gMCP-Mod (generalized MCP-Mod) [11], [29] in the step of identifying significant dose-response signals via model selection. We name our proposed approach RMCP-Mod or gRMCP-Mod correspondingly. The RMCP-Mod/gRMCP-Mod transforms the drug dose comparisons into a dose-response model selection issue via multiple hypotheses testing, an area where not much extended researches have been done, and solve it using resampling based multiple testing procedures [38]. The proposed approach avoids the inclusion of the prior dose-response knowledge known as "guesstimates" used in the model selection step of the MCP-Mod/gMCP-Mod framework, and therefore reduces the uncertainty in the significant model identification. When a new drug is being developed to treat patients with a specified disease, one of the key steps is to discover an optimal drug dose or doses that would produce the desired clinical effect with an acceptable level of toxicity. In order to nd such a dose or doses (different doses may be able to produce the same or better clinical effect with similar acceptable toxicity), the underlying dose-response signals need to be identified and thoroughly examined through statistical analyses. A dose-response signal refers to the fact that a drug has different clinical effects at many quantitative dose levels. Statistically speaking, the dose-response signal is a numeric relationship curve (shape) between drug doses and the clinical effects in quantitative measures. It's often been a challenge to nd correct and accurate efficacy and/or safety dose-response signals that would best describe the dose-effect relationship in the drug development process via conventional statistical methods because the conventional methods tend to either focus on a fixed, small number of quantitative dosages or evaluate multiple pre-denied dose-response models without Type I error control. In searching for more efficient methods, a framework of combining both multiple comparisons procedure (MCP) and model-based (Mod) techniques acronymed MCP-Mod was developed by F. Bretz, J. C. Pinheiro, and M. Branson [11] to handle normally distributed, homoscedastic dose response observations. Subsequently, a generalized version of the MCP- Mod named gMCP-Mod which can additionally deal with binary, counts, or time-to-event dose-response data as well as repeated measurements over time was developed by J. C. Pinheiro, B. Bornkamp, E. Glimm and F. Bretz [29]. The MCP-Mod/gMCP-Mod uses the guesstimates" in the MCP step to pre-specify parameters of the candidate models; however, in situations where the prior knowledge of the dose-response information is difficult to obtain, the uncertainties could be introduced into the model selection process, impacting on the correctness of the model identification. Throughout the evaluation of its application to the hypothetical and real study examples as well as simulation comparisons to the MCP-Mod/gMCP-Mod, our proposed approach, RMCP-Mod/gRMCP-Mod seems a viable method that can be used in the practice with some further improvements and researches that are still needed in applications to broader dose-response data types. / Statistics

This dissertation thesis is focused on the problem of the noise measurement and construction of the noise test station what was also interest of my employer - company Kollmorgen,sr.o. This testing station should be located directly in the assembly line with target of the noise motor s identification. On base of these measured values and implemented intelligent testing procedures, we should be able to identify real root cause of the noise The noise of electrical machines is actual issue. There is a big pressure for low-noise driving system construction created by many end-customers. We can achieve these requirements with 100% quality of all parts of current product, implementation of noise testing station and also with design optimization of the current product. Basic testing procedures of induction motors were showed in first part of this work (chapter 4.1.). These procedures are able to provide good picture of the motor condition. For the motor noise measurements was constructed a workplace including noise box with acoustical absorption up to 30dB what allowed the workplace implementation directly into the motor assembly line. Testing techniques and frequency analysis procedures were implemented sequentially with the target of the test evaluation improvement. After the detailed analyze of the motor noise root causes was performed check of the current motor design with respect of the “noiselessness” motor construction principles. As next step was created the motor prototype with optimized construction with target of the motor noise reduction. This optimized motor was tested and compared with standard motor design.

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The central theme of this thesis is the construction of simultaneous confidence regions (SCR) corresponding to stepwise multiple comparison procedures (MCP). The first chapter is devoted to the theory of multiple comparisons, including the class of closed testing procedures which contains every MCP that strongly con- trols the familywise error rate. The second chapter is concerned with the gene- ral principle of construction of SCR corresponding to closed testing procedures. These general results are used in the third and the forth chapter for deriving the SCR corresponding to a subclass of closed testing procedures which are based on weighted Bonferroni tests. The SCR corresponding to the Holm, the Holm(W), the fixed-sequence and the fallback MCP are derived explicitly. The theoretical results are numerically illustrated on a bioequivalence study. In the fifth chapter we briefly discuss the SCR corresponding to the Hommel, the Hochberg and the step-down Dunnett MCP.

From the Proceedings of the 1975 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 11-12, 1975, Tempe, Arizona / Current catchment methods of measuring precipitation have several problems which affect their accuracy. The physical presence of the gage disturbs windflow patterns and reduces catch. Other errors of less significance arise from evaporation from the gage, and wetting of the gage. A method is described of measuring precipitation by scattering light from a beam by waterdrops. The sampling medium is a collimated beam from a helium-neon laser. The amount of light scattered is a function of the number and size of drops intercepting the beam.

The aim of this work is to assess the current state of risk analysis and of the critical points system HACCP (Hazard Analysis and Critical Control Point) in a food processing business of the PETA Bohemia limited company. On the basis of the latest findings the new optimal HACCP system, which is based on scientific data, systematically identifies specific risks and measures for their control so as to ensure food safety. A food business operator is obliged to create a critical points system by Regulation (EC) No 852/2004 of the European Parliament and of the Council of 29 April 2004 on the hygiene of foodstuffs, Article 5 ``Hazard analysis and critical control points``, paragraph 1: ``Food business operators shall put in place, implement and maintain a permanent procedure or procedures based on the HACCP principles.`` The introductory part contains a short literature retrieval on the development of management methods and on the control of food products by means of the HACCP system. These systems are generally considered as a useful tool for food business operators serving to control risks which can occur in food. They are science-based and systematic, they identify specific risks and measures for control in order to ensure food safety. They are a tool for risk assessment and setting up of control systems which do not depend on testing of the final product but focus mainly on prevention. All HACCP systems can be accomodated to changes such as progress in external adaptation of equipment, process of manufacturing or technological development. The practical part describes in detail the technological process of producing pastry products, especially short pastry. The production is applied into a small bakery of the PETA Bohemia limited company which was founded in Soběslav in 1991. On the base of interviews and provided background information it was possible to view the food business in a complex manner and to get an insight into the current , as well as the past situation of the company and its goals. The risk analysis of the technological process of short pastry production enabled to determine a critical control point, its attributes and values of critical limits, to define the system of managed state monitoring and to determine corrective measures. A manual of the HACCP elaborated in this manner fulfills all legislative requirements. By its implentation the Peta BOHEMIA company gains a risk management system of high quality leading in its final effect towards production of high quality healthy food. The system focused mainly on practical and expert knowledge of the staff connected with sensoric knowledge of final pastry products puts emphasis on encreasing their personal responsibility and understanding of the problem.