Statistical Quality Control Charts Based on Hyper-Geometrically Distributed Data

In some production and administrative processes, the occurrence of certain events is best described by a hyper-geometric distribution, which in turn should be pictorially depicted by what should be called a “hyper-geometric chart (Hg-chart)” in the field of Statistical Quality Control (SQC). However, this has never been the practice, since the existence of such a chart is absent; as such, prompting administrators and process engineers to make use of already existing charts for approximately depicting hyper-geometric processes. In this article, an SQC chart for any hyper-geometric process has been developed for the total number of events in a fixed number of units. This chart has been referred to as the Hg-chart. The center line (CC), lower control limit (LCL) and the upper control limit (UCL) have been obtained for the proposed chart with a sketch of how the proposed chart should be if used for simulation. It has been recommended that simulation should be used to test the proposed chart as this could prove to be more efficient and appropriate for describing hyper-geometric data rather than using an inappropriate chart to be an approximation for solving the problem.

Weakening mechanisms and the role of easy slip horizons in thrust belt development: a microstructural approach

<p>The Late Silurian Moine Thrust Zone (MTZ) of the NW Highlands of Scotland has long been fundamental to the understanding of the nature and processes that occur during thrust tectonics in the upper continental crust. This complex imbrication zone formed during final Scandian stages of the Caledonian orogeny when collision of Baltica and Laurentia led to WNW-ESE tectonic foreshortening of >100km. The MTZ juxtaposed greenschist to amphibolite facies Neoproterozoic metamorphic rocks of the Moine Supergroup over sequences of little metamorphosed Cambro-Ordovician and Neoproterozoic sedimentary rocks and their Neoarchean to Paleoproterozoic gneissic basement in a zone ranging from <1km to >20km wide.</p><p>The mechanical problems represented by thrust wedges being transported over such great distances without losing their internal cohesion has highlighted the role played by detachment structures and the need for mechanisms that create significant weakening along basal detachments that allow overthrusts to accommodate major horizontal displacements in the shallow crust. Field studies and use of section balancing techniques have highlighted that a substantial proportion of the displacement seems to be accommodated along detachments that follow specific stratigraphic levels.</p><p>Other than the Moine Thrust Mylonites and the mylonitised parts of the Cambrian Quartzites, relatively little is known about the grain scale deformation and potential weakening processes that have occurred in other parts of the MTZ. New lithological descriptions of the fault rocks and sedimentary protoliths observed in the Assynt, Durness and Eriboll areas are presented here and provide detailed microstructural evidence for the long-term weakening mechanisms that were operating at the time. These mechanisms are consistently related to the onset of grain size reduction, triggered by both chemical enhanced and geometric processes. These include feldspar alteration to fine phyllosilicates associated with cataclasis and dynamic recrystallization of quartz.</p><p>Pressure solution, evidenced by changes in the shape of minerals along cleavage surfaces and the presence of dissolution seams and caps, is widespread throughout the studied rock sequences. The profuse occurrence of this grain-scale mechanism makes it very likely that syn-deformational fluid-influx lead to the destruction of load bearing microstructural frameworks and the development of interconnected weak layers due to alteration, explaining the occurrence of detachments within impure layers of the predominantly quartzose Pipe Rock and Salterella Grit members. The progressive development of these interconnecting fine-grained weak layers resulting from incongruent diffusive mass transfer is enhanced in the more mineralogically heterogeneous units of the Cambro-Ordovician sedimentary sequence (in particular, Fucoid Beds dolomitic siltstones and Durness limestones) explaining the consistently observed slip localization in these horizons.</p>

Hybrid-dynamic objects: DGS environments and conceptual transformations

A few theoretical perspectives have been taken under consideration the meaning of an object as the result of a process in mathematical thinking. Building on their work, I shall investigate the meaning of ‘object’ in a dynamic geometry environment. Using the recently introduced notions of dynamic-hybrid objects, diagrams and sections which complement our understanding of geometric processes and concepts as we perform actions in the dynamic software, I shall explain what could be considered to be a ‘procept-in-action’. Finally, a few examples will be analyzed through the lenses of hybrid and dynamic objects in terms of how I designed them. A few snapshots of the research process will be presented to reinforce the theoretical considerations. My aim is to contribute to the field of the Didactics of Mathematics using ICT in relation to students’ cognitive development

A bivariate replacement policy for an imperfect repair system based on geometric processes

A repair replacement model for a deteriorating system with delayed repair is studied, in which the successive working times after repair and the consecutive repair times of the system are described by geometric processes. The instantaneous availability is studied in the case of general distributions for the working time, repair time and delayed repair time. A bivariate replacement policy is considered, that is, the system is replaced whenever the working age of the system reaches T or at the first hitting time of the working time after repair with respect to the working time threshold τ, whichever occurs first. The explicit expression of the long-run average cost rate under the replacement policies is derived. The corresponding optimal replacement policy can be determined numerically, and numerical examples are presented to demonstrate the application of the developed model and approach. It is shown that the optimal solution and optimal value are sensitive to the tiny change in the ratios of the Geometric processes and the expectation of the delayed repair time.

Combining Geometry and Image in Biomedical Systems

Patient anatomy, biochemical response, as well functional evaluation at organ level, are key fields that produce a significant amount of multi modal information during medical diagnosis. Visualization, processing, and storage of the acquired data sets are essential tasks in everyday medical practice. In order to perform complex processing that involves or rely on image data a robust as well versatile data structure was used as extension of the Visualization Toolkit (VTK). The proposed structure serves as a universal registration container for acquired information and post processed resulted data. The structure is a dynamic multidimensional data holder to host several modalities and/or Meta data like fused image sets, extracted features (volumetric, surfaces, edges) providing a universal coordinate system used for calculations and geometric processes. A case study of Treatment Planning System (TPS) in the stereotactic radiotherapy (RT) based on the proposed structure is discussed as an efficient medical application.

Aspects of Visualization and the Grid in a Biomedical Context

This chapter introduces some aspects of visualization and the grid. Visualization --the art and science of representing data visually-- is now recognized as an equal partner in the conduct of science via the simulation and modeling paradigm. Although not usually associated with Grid-scale problems, there are a number of Grid-dominant issues which subtend visualization. Evidently, certain data grooming issues (e.g., image preprocessing/analysis, certain computational geometric processes, certain computational topological processes) are amenable to deployment over compute Grids, but there has been equal focus on the collaborative aspect of Grid computing which is driving collaboration-based visualization systems. Here we survey some of the roles of visualization as they relate to the role of Grid computing within a biomedical context. We conclude by examining certain scheduling strategies we believe to have value in terms of the distribution of visualization tasks over Grid fabrics.