Not available / text

published_or_final_version / Applied Statistics / Master / Master of Social Sciences

published_or_final_version / Statistics / Master / Master of Social Sciences

published_or_final_version / Statistics / Master / Master of Philosophy

Due to changes of the thermal environment, thermal stresses are produced in structures. Two approaches based on the stochastic process theory are used to describe this phenomenon. The structure is idealized as a long hollow viscoelastic cylinder. Two sites are considered: Barrow (AK) and Yuma (AZ). First passage concepts are applied to characterize the reliability of the system. Crossings are assumed to follow either the behavior of the Poisson process or Markov process. In both cases, the distribution of the time to first passage is taken to be the exponential distribution. Because the material is viscoelastic, statistically and time varying barriers (strengths) with Normal, Log-Normal, or Neibull distributions are considered. Degradation of the barriers by aging and cumulative damage are incorporated in the analysis. / Ph. D. / incomplete_metadata

Therapeutic horseback riding (THR) uses the horse as a therapeutic apparatus in physical and psychological therapy. This dissertation suggests a more appropriate technique for measuring the effect of THR. A research survey of the statistical methods used to determine the effect of THR was undertaken. Although researchers observed clinically meaningful change in several of the studies, this was not supported by statistical tests. A logistic regression approach is proposed as a solution to many of the problems experienced by researchers on THR. Since large THR related data sets are not available, data were simulated. Logistic regression and t-tests were used to analyse the same simulated data sets, and the results were compared. The advantages of the logistic regression approach are discussed. This statistical technique can be applied in any field where the therapeutic value of an intervention has to be proven scientifically. / Mathematical Sciences / M. Sc. (Statistics)

Therapeutic horseback riding (THR) uses the horse as a therapeutic apparatus in physical and psychological therapy. This dissertation suggests a more appropriate technique for measuring the effect of THR. A research survey of the statistical methods used to determine the effect of THR was undertaken. Although researchers observed clinically meaningful change in several of the studies, this was not supported by statistical tests. A logistic regression approach is proposed as a solution to many of the problems experienced by researchers on THR. Since large THR related data sets are not available, data were simulated. Logistic regression and t-tests were used to analyse the same simulated data sets, and the results were compared. The advantages of the logistic regression approach are discussed. This statistical technique can be applied in any field where the therapeutic value of an intervention has to be proven scientifically. / Mathematical Sciences / M. Sc. (Statistics)

Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2007. / The aim of this study is to assess the welfare of South Africa in terms of poverty and inequality. This is done using the Income and Expenditure Survey (IES) of 2000, released by Statistics South Africa, and reviewing the distribution of income in the country. A brief literature review of similar studies is given along with a broad de nition of poverty and inequality. A detailed description of the dataset used is given together with aspects of concern surrounding the dataset. An analysis of poverty and income inequality is made using datasets containing the continuous income variable, as well as a created grouped income variable. Results from these datasets are compared and conclusions made on the use of continuous or grouped income variables. Covariate analysis is also applied in the form of biplots. A brief overview of biplots is given and it is then used to obtain a graphical description of the data and identify any patterns. Lastly, the conclusions made in this study are put forward and some future research is mentioned.

Dissertation (PhD)--Stellenbosch University, 2000. / ENGLISH ABSTRACT: The use of helicopters has become almost universally accepted as the method of choice in the enumeration of large ungulates in Southern Africa. In most cases decisions affecting management of these populations are made based on a single count result. In all these instances the within technique variance is ignored, often leading to decisions based on type I or type II statistical errors where the within technique variance is misconstrued as the population change. Many studies have investigated the issue of accuracy of counting methods and a few have quoted precision values for various methods. Very few have, however, investigated power and those extant have approached the problem from a prospective point of view and predicted power values. This study has made use of replicated counts from 12 sites of the original 23 in four vegetation types of the then Transvaal Province. The study sites vary in terms of size and all counts were undertaken with an experienced, trained team in which only four observers were used. A comprehensive post hoc analysis of the results of the field surveys shows precision and power to vary widely according to species and vegetation type and concludes that gamecounting results are largely site specific. A decline in observations during the course of four hours of survey is demonstrated and although the exact cause cannot be determined, correction factors have been constructed for two vegetation types. Observers are shown to differ from one another in observation profile during the course of surveys. This study demonstrates, describes and quantifies the existence of several phenomena suspected to exist by experienced game counters, biologists and wildlife managers and makes proposals in terms of improving the data returned from expensive aerial surveys. / AFRIKAANSE OPSOMMING: In Suider-Afrika word die gebruik van 'n helikopter vir die tel van hoefdiere byna algemeen aanvaar as die metode wat voorkeur geniet. In meeste gevalle word besluitnemings rakende die bestuur van hierdie populasies gebaseer op die resultate van 'n enkele telling. In al die gevalle word tegniekverwante afwykings buite rekening gelaat en dit het die gevolg dat bestuursbesluite gebaseer word op tipe I en tipe II statistiese foute, en dit lei weer op hulle beurt dat tegniekverwante afwykings verkeerdelik geïnterpreteer word as die rede vir veranderings in die bevolkings. Verskeie studies het al die feitegeskil omtrent die akkuraatheid van telmetodes ondersoek en sommige het herhaalbaarheidswaardes vir die verskillende metodes aangehaal. Baie min het egter statistiese mag ondersoek en die wat dit wel gedoen het, het prospektiewe magsanalise as uitgangspunt gebruik en statistiese magwaardes voorspelom die probleem aan te spreek. Hierdie studie het gebruik gemaak van herhaalde tellings van 12 gebiede uit die oorspronklike 23 in vier veldtipes geleë in die ou Transvaal Provinsie. Die studiegebiede verskil in groottes. Alle tellings is deur 'n bekwaamde opgeleide span gedoen wat slegs vier waarnemers ingesluit het. 'n Omvattende post hoc analise van die resultate van die veldopnames dui aan dat herhaalbaarheid en statistiese mag baie varieer met betrekking tot spesies en veldtipes en word die gevolgtrekking gemaak dat wildtellingsresultate grootliks gebiedsgebonde is. In Afname in waarnemings gedurende die verloop van In vier uuropname, is waargeneem en alhoewel die ware oorsaak nie vasgestel kan word nie, is korreksiefaktore bereken vir twee veldtipes. Dit blyk dat waarnemers van mekaar verskil het met betrekking tot hul waarnemingsprofiele gedurende die verloop van die opnames. Hierdie studie dui aan, beskryf en kwantifiseer die bestaan van verskeie verskynsels wat vermoedelik bestaan het by ervare wildtelIers, bioloë en wildlewebestuurders en maak voorstelle met betrekking tot die verbetering van data wat tydens duur lugopnames ingesamel word.

Reliability prediction of components operating in complex systems has historically been conducted in a statistically isolated manner. Current physics-based, i.e. mechanistic, component reliability approaches focus more on component-specific attributes and mathematical algorithms and not enough on the influence of the system. The result is that significant error can be introduced into the component reliability assessment process. The objective of this study is the development of a framework that infuses the influence of the system into the process of conducting mechanistic-based component reliability assessments. The formulated framework consists of six primary steps. The first three steps, identification, decomposition, and synthesis, are qualitative in nature and employ system reliability and safety engineering principles for an appropriate starting point for the component reliability assessment. The most unique steps of the framework are the steps used to quantify the system-driven local parameter space and a subsequent step using this information to guide the reduction of the component parameter space. The local statistical space quantification step is accomplished using two newly developed multivariate probability tools: Multi-Response First Order Second Moment and Taylor-Based Inverse Transformation. Where existing joint probability models require preliminary statistical information of the responses, these models combine statistical information of the input parameters with an efficient sampling of the response analyses to produce the multi-response joint probability distribution. Parameter space reduction is accomplished using Approximate Canonical Correlation Analysis (ACCA) employed as a multi-response screening technique. The novelty of this approach is that each individual local parameter and even subsets of parameters representing entire contributing analyses can now be rank ordered with respect to their contribution to not just one response, but the entire vector of component responses simultaneously. The final step of the framework is the actual probabilistic assessment of the component. Variations of this final step are given to allow for the utilization of existing probabilistic methods such as response surface Monte Carlo and Fast Probability Integration. The framework developed in this study is implemented to conduct the finite-element based reliability prediction of a gas turbine airfoil involving several failure responses. The framework, as implemented resulted in a considerable improvement to the accuracy of the part reliability assessment and an increased statistical understanding of the component failure behavior.