Fit optimisation of a distal medial tibia plate

An iterative method for the fit optimisation of a pre-contoured fracture fixation plate for a given bone data set is presented. Both plate shape optimisation and plate fit quantification are conducted in a virtual environment utilising computer graphical methods and 3D bone and plate models. Two optimised shapes of the undersurface of an existing distal medial tibia plate were generated based on a dataset of 45 3D bone models reconstructed from computed tomography image data of Japanese tibiae. The existing plate shape achieved an anatomical fit on 13% of tibiae from the dataset. Modified plate 1 achieved an anatomical fit for 42% and modified plate 2 a fit for 67% of the bones. If either modified plate 1 or plate 2 is used, then the anatomical fit can be increased to 82% for the same dataset. Issues pertaining to any further improvement in plate fit/shape are discussed.

Reliability analysis with suspended items

Reliability analysis has several important engineering applications. Designers and operators of equipment are often interested in the probability of the equipment operating successfully to a given age - this probability is known as the equipment's reliability at that age. Reliability information is also important to those charged with maintaining an item of equipment, as it enables them to model and evaluate alternative maintenance policies for the equipment. In each case, information on failures and survivals of a typical sample of items is used to estimate the required probabilities as a function of the item's age, this process being one of many applications of the statistical techniques known as distribution fitting. In most engineering applications, the estimation procedure must deal with samples containing survivors (suspensions or censorings); this thesis focuses on several graphical estimation methods that are widely used for analysing such samples. Although these methods have been current for many years, they share a common shortcoming: none of them is continuously sensitive to changes in the ages of the suspensions, and we show that the resulting reliability estimates are therefore more pessimistic than necessary. We use a simple example to show that the existing graphical methods take no account of any service recorded by suspensions beyond their respective previous failures, and that this behaviour is inconsistent with one's intuitive expectations. In the course of this thesis, we demonstrate that the existing methods are only justified under restricted conditions. We present several improved methods and demonstrate that each of them overcomes the problem described above, while reducing to one of the existing methods where this is justified. Each of the improved methods thus provides a realistic set of reliability estimates for general (unrestricted) censored samples. Several related variations on these improved methods are also presented and justified. - i

Visual assessment of pedestrian crashes

Of the numerous factors that play a role in fatal pedestrian collisions, the time of day, day of the week, and time of year can be significant determinants. More than 60% of all pedestrian collisions in 2007 occurred at night, despite the presumed decrease in both pedestrian and automobile exposure during the night. Although this trend is partially explained by factors such as fatigue and alcohol consumption, prior analysis of the Fatality Analysis Reporting System database suggests that pedestrian fatalities increase as light decreases after controlling for other factors. This study applies graphical cross-tabulation, a novel visual assessment approach, to explore the relationships among collision variables. The results reveal that twilight and the first hour of darkness typically observe the greatest frequency of pedestrian fatal collisions. These hours are not necessarily the most risky on a per mile travelled basis, however, because pedestrian volumes are often still high. Additional analysis is needed to quantify the extent to which pedestrian exposure (walking/crossing activity) in these time periods plays a role in pedestrian crash involvement. Weekly patterns of pedestrian fatal collisions vary by time of year due to the seasonal changes in sunset time. In December, collisions are concentrated around twilight and the first hour of darkness throughout the week while, in June, collisions are most heavily concentrated around twilight and the first hours of darkness on Friday and Saturday. Friday and Saturday nights in June may be the most dangerous times for pedestrians. Knowing when pedestrian risk is highest is critically important for formulating effective mitigation strategies and for efficiently investing safety funds. This applied visual approach is a helpful tool for researchers intending to communicate with policy-makers and to identify relationships that can then be tested with more sophisticated statistical tools.

Removal of toxic metals in a multi metal system using sorbents for potential application to urban stormwater treatment

In the context of increasing demand for potable water and the depletion of water resources, stormwater is a logical alternative. However, stormwater contains pollutants, among which metals are of particular interest due to their toxicity and persistence in the environment. Hence, it is imperative to remove toxic metals in stormwater to the levels prescribed by drinking water guidelines for potable use. Consequently, various techniques have been proposed, among which sorption using low cost sorbents is economically viable and environmentally benign in comparison to other techniques. However, sorbents show affinity towards certain toxic metals, which results in poor removal of other toxic metals. It was hypothesised in this study that a mixture of sorbents that have different metal affinity patterns can be used for the efficient removal of a range of toxic metals commonly found in stormwater. The performance of six sorbents in the sorption of Al, Cr, Cu, Pb, Ni, Zn and Cd, which are the toxic metals commonly found in urban stormwater, was investigated to select suitable sorbents for creating the mixtures. For this purpose, a multi criteria analytical protocol was developed using the decision making methods: PROMETHEE (Preference Ranking Organisation METHod for Enrichment Evaluations) and GAIA (Graphical Analysis for Interactive Assistance). Zeolite and seaweed were selected for the creation of trial mixtures based on their metal affinity pattern and the performance on predetermined selection criteria. The metal sorption mechanisms employed by seaweed and zeolite were defined using kinetics, isotherm and thermodynamics parameters, which were determined using the batch sorption experiments. Additionally, the kinetics rate-limiting steps were identified using an innovative approach using GAIA and Spearman correlation techniques developed as part of the study, to overcome the limitation in conventional graphical methods in predicting the degree of contribution of each kinetics step in limiting the overall metal removal rate. The sorption kinetics of zeolite was found to be primarily limited by intraparticle diffusion followed by the sorption reaction steps, which were governed mainly by the hydrated ionic diameter of metals. The isotherm study indicated that the metal sorption mechanism of zeolite was primarily of a physical nature. The thermodynamics study confirmed that the energetically favourable nature of sorption increased in the order of Zn < Cu < Cd < Ni < Pb < Cr < Al, which is in agreement with metal sorption affinity of zeolite. Hence, sorption thermodynamics has an influence on the metal sorption affinity of zeolite. On the other hand, the primary kinetics rate-limiting step of seaweed was the sorption reaction process followed by intraparticle diffusion. The boundary layer diffusion was also found to limit the metal sorption kinetics at low concentration. According to the sorption isotherm study, Cd, Pb, Cr and Al were sorbed by seaweed via ion exchange, whilst sorption of Ni occurred via physisorption. Furthermore, ionic bonding is responsible for the sorption of Zn. The thermodynamics study confirmed that sorption by seaweed was energetically favourable in the order of Zn < Cu < Cd < Cr . Al < Pb < Ni. However, this did not agree with the affinity series derived for seaweed suggesting a limited influence of sorption thermodynamics on metal affinity for seaweed. The investigation of zeolite-seaweed mixtures indicated that mixing sorbents have an effect on the kinetics rates and the sorption affinity. Additionally, the theoretical relationships were derived to predict the boundary layer diffusion rate, intraparticle diffusion rate, the sorption reaction rate and the enthalpy of mixtures based on that of individual sorbents. In general, low coefficient of determination (R2) for the relationships between theoretical and experimental data indicated that the relationships were not statistically significant. This was attributed to the heterogeneity of the properties of sorbents. Nevertheless, in relative terms, the intraparticle diffusion rate, sorption reaction rate and enthalpy of sorption had higher R2 values than the boundary layer diffusion rate suggesting that there was some relationship between the former set of parameters of mixtures and that of sorbents. The mixture, which contained 80% of zeolite and 20% of seaweed, showed similar affinity for the sorption of Cu, Ni, Cd, Cr and Al, which was attributed to approximately similar sorption enthalpy of the metal ions. Therefore, it was concluded that the seaweed-zeolite mixture can be used to obtain the same affinity for various metals present in a multi metal system provided the metal ions have similar enthalpy during sorption by the mixture.

Analysing seasonal data

Many common diseases, such as the flu and cardiovascular disease, increase markedly in winter and dip in summer. These seasonal patterns have been part of life for millennia and were first noted in ancient Greece by both Hippocrates and Herodotus. Recent interest has focused on climate change, and the concern that seasons will become more extreme with harsher winter and summer weather. We describe a set of R functions designed to model seasonal patterns in disease. We illustrate some simple descriptive and graphical methods, a more complex method that is able to model non-stationary patterns, and the case–crossover for controlling for seasonal confounding.

Comparison of three expert elicitation methods for logistic regression on predicting the presence of the threatened brush-tailed rock-wallaby petrogale penicillata

Numerous expert elicitation methods have been suggested for generalised linear models (GLMs). This paper compares three relatively new approaches to eliciting expert knowledge in a form suitable for Bayesian logistic regression. These methods were trialled on two experts in order to model the habitat suitability of the threatened Australian brush-tailed rock-wallaby (Petrogale penicillata). The first elicitation approach is a geographically assisted indirect predictive method with a geographic information system (GIS) interface. The second approach is a predictive indirect method which uses an interactive graphical tool. The third method uses a questionnaire to elicit expert knowledge directly about the impact of a habitat variable on the response. Two variables (slope and aspect) are used to examine prior and posterior distributions of the three methods. The results indicate that there are some similarities and dissimilarities between the expert informed priors of the two experts formulated from the different approaches. The choice of elicitation method depends on the statistical knowledge of the expert, their mapping skills, time constraints, accessibility to experts and funding available. This trial reveals that expert knowledge can be important when modelling rare event data, such as threatened species, because experts can provide additional information that may not be represented in the dataset. However care must be taken with the way in which this information is elicited and formulated.