Bayesian accelerated life tests: exponential and Weibull models
- Authors: Izally, Sharkay Ruwade
- Date: 2016
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/3003 , vital:20351
- Description: Reliability life testing is used for life data analysis in which samples are tested under normal conditions to obtain failure time data for reliability assessment. It can be costly and time consuming to obtain failure time data under normal operating conditions if the mean time to failure of a product is long. An alternative is to use failure time data from an accelerated life test (ALT) to extrapolate the reliability under normal conditions. In accelerated life testing, the units are placed under a higher than normal stress condition such as voltage, current, pressure, temperature, to make the items fail in a shorter period of time. The failure information is then transformed through an accelerated model commonly known as the time transformation function, to predict the reliability under normal operating conditions. The power law will be used as the time transformation function in this thesis. We will first consider a Bayesian inference model under the assumption that the underlying life distribution in the accelerated life test is exponentially distributed. The maximal data information (MDI) prior, the Ghosh Mergel and Liu (GML) prior and the Jeffreys prior will be derived for the exponential distribution. The propriety of the posterior distributions will be investigated. Results will be compared when using these non-informative priors in a simulation study by looking at the posterior variances. The Weibull distribution as the underlying life distribution in the accelerated life test will also be investigated. The maximal data information prior will be derived for the Weibull distribution using the power law. The uniform prior and a mixture of Gamma and uniform priors will be considered. The propriety of these posteriors will also be investigated. The predictive reliability at the use-stress will be computed for these models. The deviance information criterion will be used to compare these priors. As a result of using a time transformation function, Bayesian inference becomes analytically intractable and Markov Chain Monte Carlo (MCMC) methods will be used to alleviate this problem. The Metropolis-Hastings algorithm will be used to sample from the posteriors for the exponential model in the accelerated life test. The adaptive rejection sampling method will be used to sample from the posterior distributions when the Weibull model is considered.
- Full Text:
- Date Issued: 2016
- Authors: Izally, Sharkay Ruwade
- Date: 2016
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/3003 , vital:20351
- Description: Reliability life testing is used for life data analysis in which samples are tested under normal conditions to obtain failure time data for reliability assessment. It can be costly and time consuming to obtain failure time data under normal operating conditions if the mean time to failure of a product is long. An alternative is to use failure time data from an accelerated life test (ALT) to extrapolate the reliability under normal conditions. In accelerated life testing, the units are placed under a higher than normal stress condition such as voltage, current, pressure, temperature, to make the items fail in a shorter period of time. The failure information is then transformed through an accelerated model commonly known as the time transformation function, to predict the reliability under normal operating conditions. The power law will be used as the time transformation function in this thesis. We will first consider a Bayesian inference model under the assumption that the underlying life distribution in the accelerated life test is exponentially distributed. The maximal data information (MDI) prior, the Ghosh Mergel and Liu (GML) prior and the Jeffreys prior will be derived for the exponential distribution. The propriety of the posterior distributions will be investigated. Results will be compared when using these non-informative priors in a simulation study by looking at the posterior variances. The Weibull distribution as the underlying life distribution in the accelerated life test will also be investigated. The maximal data information prior will be derived for the Weibull distribution using the power law. The uniform prior and a mixture of Gamma and uniform priors will be considered. The propriety of these posteriors will also be investigated. The predictive reliability at the use-stress will be computed for these models. The deviance information criterion will be used to compare these priors. As a result of using a time transformation function, Bayesian inference becomes analytically intractable and Markov Chain Monte Carlo (MCMC) methods will be used to alleviate this problem. The Metropolis-Hastings algorithm will be used to sample from the posteriors for the exponential model in the accelerated life test. The adaptive rejection sampling method will be used to sample from the posterior distributions when the Weibull model is considered.
- Full Text:
- Date Issued: 2016
Single station TEC modelling during storm conditions
- Authors: Uwamahoro, Jean Claude
- Date: 2016
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/3812 , vital:20545
- Description: It has been shown in ionospheric research that modelling total electron content (TEC) during storm conditions is a big challenge. In this study, mathematical equations were developed to estimate TEC over Sutherland (32.38oS, 20.81oE), during storm conditions, using the Empirical Orthogonal Function (EOF) analysis, combined with regression analysis. TEC was derived from GPS observations and a geomagnetic storm was defined for Dst ≤ -50 nT. The inputs for the model were chosen based on the factors that influence TEC variation, such as diurnal, seasonal, solar and geomagnetic activity variation, and these were represented by hour of the day, day number of the year, F10.7 and A index respectively. The EOF model was developed using GPS TEC data from 1999 to 2013 and tested on different storms. For the model validation (interpolation), three storms were chosen in 2000 (solar maximum period) and three others in 2006 (solar minimum period), while for extrapolation six storms including three in 2014 and three in 2015 were chosen. Before building the model, TEC values for the selected 2000 and 2006 storms were removed from the dataset used to construct the model in order to make the model validation independent on data. A comparison of the observed and modelled TEC showed that the EOF model works well for storms with non-significant ionospheric TEC response and storms that occurred during periods of low solar activity. High correlation coefficients between the observed and modelled TEC were obtained showing that the model covers most of the information contained in the observed TEC. Furthermore, it has been shown that the EOF model developed for a specific station may be used to estimate TEC over other locations within a latitudinal and longitudinal coverage of 8.7o and 10.6o respectively. This is an important result as it reduces the data dimensionality problem for computational purposes. It may therefore not be necessary for regional storm-time TEC modelling to compute TEC data for all the closest GPS receiver stations since most of the needed information can be extracted from measurements at one location.
- Full Text:
- Date Issued: 2016
- Authors: Uwamahoro, Jean Claude
- Date: 2016
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/3812 , vital:20545
- Description: It has been shown in ionospheric research that modelling total electron content (TEC) during storm conditions is a big challenge. In this study, mathematical equations were developed to estimate TEC over Sutherland (32.38oS, 20.81oE), during storm conditions, using the Empirical Orthogonal Function (EOF) analysis, combined with regression analysis. TEC was derived from GPS observations and a geomagnetic storm was defined for Dst ≤ -50 nT. The inputs for the model were chosen based on the factors that influence TEC variation, such as diurnal, seasonal, solar and geomagnetic activity variation, and these were represented by hour of the day, day number of the year, F10.7 and A index respectively. The EOF model was developed using GPS TEC data from 1999 to 2013 and tested on different storms. For the model validation (interpolation), three storms were chosen in 2000 (solar maximum period) and three others in 2006 (solar minimum period), while for extrapolation six storms including three in 2014 and three in 2015 were chosen. Before building the model, TEC values for the selected 2000 and 2006 storms were removed from the dataset used to construct the model in order to make the model validation independent on data. A comparison of the observed and modelled TEC showed that the EOF model works well for storms with non-significant ionospheric TEC response and storms that occurred during periods of low solar activity. High correlation coefficients between the observed and modelled TEC were obtained showing that the model covers most of the information contained in the observed TEC. Furthermore, it has been shown that the EOF model developed for a specific station may be used to estimate TEC over other locations within a latitudinal and longitudinal coverage of 8.7o and 10.6o respectively. This is an important result as it reduces the data dimensionality problem for computational purposes. It may therefore not be necessary for regional storm-time TEC modelling to compute TEC data for all the closest GPS receiver stations since most of the needed information can be extracted from measurements at one location.
- Full Text:
- Date Issued: 2016
The impact of three different footwear conditions on individual biomechanical, physiological and perceptual responses during running.
- Authors: McDougall, Justin John
- Date: 2016
- Subjects: Running -- Physiological aspects , Running shoes -- Physiological aspects , Running -- Health aspects
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5177 , http://hdl.handle.net/10962/d1019988
- Description: Background: Despite the introduction of running footwear in the 1970’s, running injury rates continue to be unacceptably high. The subsequent revival of barefoot running and the introduction of minimalist footwear occurred, in an attempt to reduce injury rates and increase performance. There is much contention in the literature around the effectiveness of these footwear conditions. Furthermore individual responses have recently been proposed to provide more accurate and reflective conclusions than the use of mean data. Objectives: Twofold: a) to compare the biomechanical, physiological and perceptual responses between the shod, minimalist and barefoot footwear conditions and b) to assess and compare individual responses under these footwear conditions. Methods: 26 well-trained, male, habitually shod endurance runners, aged between 18 - 30 years completed three experimental sessions on an indoor runway and motorized treadmill. Each session was completed in either the shod, minimalist or barefoot condition, running at 15km.h-1. Variables assessed included stride rate, stride length, impact peak, vertical impact and average loading rate and strike time (biomechanical); heart rate, oxygen consumption and electromyography (physiological); and rating of perceived exertion and body discomfort (perceptual). Results: Biomechanics – Stride rate and stride length showed a significant (p<0.001) increase and decrease respectively when running in the minimalist or barefoot conditions versus shod. Running barefoot versus the minimalist and shod conditions resulted in a significantly (p<0.001) greater vertical impact loading rate. Strike time was significantly (p=0.008) reduced running in the minimalist and barefoot conditions versus shod. Physiology – Running barefoot versus shod resulted in a significantly (p=0.02) reduced heart rate and Tibialis Anterior activity (p=0.005). There was a large variability in individual responses for many variables, with responders and non-responders seen. Conclusion: The study suggests that there are significant differences between all three forms of running for some variables. It was further noted that there is support for the proposal that individual responses are highly variable and should be analysed accordingly
- Full Text:
- Date Issued: 2016
- Authors: McDougall, Justin John
- Date: 2016
- Subjects: Running -- Physiological aspects , Running shoes -- Physiological aspects , Running -- Health aspects
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5177 , http://hdl.handle.net/10962/d1019988
- Description: Background: Despite the introduction of running footwear in the 1970’s, running injury rates continue to be unacceptably high. The subsequent revival of barefoot running and the introduction of minimalist footwear occurred, in an attempt to reduce injury rates and increase performance. There is much contention in the literature around the effectiveness of these footwear conditions. Furthermore individual responses have recently been proposed to provide more accurate and reflective conclusions than the use of mean data. Objectives: Twofold: a) to compare the biomechanical, physiological and perceptual responses between the shod, minimalist and barefoot footwear conditions and b) to assess and compare individual responses under these footwear conditions. Methods: 26 well-trained, male, habitually shod endurance runners, aged between 18 - 30 years completed three experimental sessions on an indoor runway and motorized treadmill. Each session was completed in either the shod, minimalist or barefoot condition, running at 15km.h-1. Variables assessed included stride rate, stride length, impact peak, vertical impact and average loading rate and strike time (biomechanical); heart rate, oxygen consumption and electromyography (physiological); and rating of perceived exertion and body discomfort (perceptual). Results: Biomechanics – Stride rate and stride length showed a significant (p<0.001) increase and decrease respectively when running in the minimalist or barefoot conditions versus shod. Running barefoot versus the minimalist and shod conditions resulted in a significantly (p<0.001) greater vertical impact loading rate. Strike time was significantly (p=0.008) reduced running in the minimalist and barefoot conditions versus shod. Physiology – Running barefoot versus shod resulted in a significantly (p=0.02) reduced heart rate and Tibialis Anterior activity (p=0.005). There was a large variability in individual responses for many variables, with responders and non-responders seen. Conclusion: The study suggests that there are significant differences between all three forms of running for some variables. It was further noted that there is support for the proposal that individual responses are highly variable and should be analysed accordingly
- Full Text:
- Date Issued: 2016
Electrode surface modification using iron(II) phthalocyanine immobilized via electrografting and click chemistry and clicked onto azide-functionalized quantum dots: applications in electrocatalysis
- Authors: Nxele, Siphesihle Robin
- Date: 2016
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/3464 , vital:20501
- Description: Tetrakis(5-hexynoxy)Fe(II) phthalocyanine was used alone and in combination with quantum dots (QDs) in order to test the electrocatalytic ability with hydrazine and paraquat as the analytes of interest. This novel phthalocaynine was successfully synthesised and characterized using various characterisation techniques. The QDs used were the well-known core-shell CdSe/ZnS nanostructures. The fabrication of glassy carbon electrodes involved covalent attachment by electrochemical grafting and click chemistry for the first part of the work and the second part involved the conjugation of the synthesised QDs and the phthalocyanine by click chemistry. This approach of conjugating these nanostructures introduced another aspect of novelty to the work reported in this thesis. The immobilisation of this conjugate on a glassy carbon electrode (GCE) was achieved by adsorption. Characterisation techniques such as infrared spectroscopy, x-ray diffractometry, UV/vis spectroscopy, transmission electron microscopy and x-ray photoelectron spectroscopy were used to characterise the molecules and conjugates of interest. With respect to the electrocatalytic part of the work, electrode surface characterisation involved scanning electrochemical microscopy and cyclic voltammetry to determine changes in the nature of the surface as well as reactivity of the surface at different modification steps. Detection limits and the sensitivity determined for the electrocatalysts fabricated here proved to be an improvement compared to other reported work involving phthalocyanines and the test analytes chosen for application. With respect to the conjugate, the electrocatalytic ability was improved when the QDs and phthalocyanine were combined using click chemistry compared to using the phthalocyanine alone.
- Full Text:
- Date Issued: 2016
- Authors: Nxele, Siphesihle Robin
- Date: 2016
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/3464 , vital:20501
- Description: Tetrakis(5-hexynoxy)Fe(II) phthalocyanine was used alone and in combination with quantum dots (QDs) in order to test the electrocatalytic ability with hydrazine and paraquat as the analytes of interest. This novel phthalocaynine was successfully synthesised and characterized using various characterisation techniques. The QDs used were the well-known core-shell CdSe/ZnS nanostructures. The fabrication of glassy carbon electrodes involved covalent attachment by electrochemical grafting and click chemistry for the first part of the work and the second part involved the conjugation of the synthesised QDs and the phthalocyanine by click chemistry. This approach of conjugating these nanostructures introduced another aspect of novelty to the work reported in this thesis. The immobilisation of this conjugate on a glassy carbon electrode (GCE) was achieved by adsorption. Characterisation techniques such as infrared spectroscopy, x-ray diffractometry, UV/vis spectroscopy, transmission electron microscopy and x-ray photoelectron spectroscopy were used to characterise the molecules and conjugates of interest. With respect to the electrocatalytic part of the work, electrode surface characterisation involved scanning electrochemical microscopy and cyclic voltammetry to determine changes in the nature of the surface as well as reactivity of the surface at different modification steps. Detection limits and the sensitivity determined for the electrocatalysts fabricated here proved to be an improvement compared to other reported work involving phthalocyanines and the test analytes chosen for application. With respect to the conjugate, the electrocatalytic ability was improved when the QDs and phthalocyanine were combined using click chemistry compared to using the phthalocyanine alone.
- Full Text:
- Date Issued: 2016