Usualmente a análise de sobrevivência considera a modelagem da função da taxa de falha ou função de risco. Uma alternativa a essa visão é estudar a vida residual, que em alguns casos é mais intuitiva do que a função de risco. A vida residual é o tempo de sobrevida adicional de um indivíduo que sobreviveu até um dado instante t0. Este trabalho descreve técnicas semiparamétricas e não paramétricas para estimar a média e a mediana de vida residual em uma população, testes para igualdade dessas medidas em duas populações e também modelos de regressão. Tais técnicas já foram testadas anteriormente em dados com baixa presença de censura; aqui elas são aplicadas a um conjunto de dados de pacientes com insuficiência cardíaca que possui uma alta quantidade de observações censuradas. / Usually, survival analysis is based on the modeling of the hazard function. One alternative approach is to consider the residual life, which would be more intuitive than the hazard function. Residual lifetime is the remaining survival time of a person given he or she survived a given time point t0. We describe semiparametric and non-parametric techniques for mean and median residual life estimation in a one-sample population, as well as tests for two-sample cases and regression models. Such techniques were previously tested for moderate censored data; here we apply them to heart-failure patients data with a high rate of censoring.

The condition monitoring of multi-component systems utilizes multiple sensors to capture the functional condition of the systems and allows the sensor information to be used to reason about the health information of the systems or components. Chapter 3 considers the situation when sensor signals capture unknown mixtures of component signals and proposes a two-stage vibration-based methodology to identify component degradation signals from mixed sensor signals in order to predict component-level residual lives. Specifically, we are interested in modeling the degradation of systems that consist of two or more identical components operating under similar conditions. Chapter 4 focuses on the interactive relationship between tool wear (component degradation) and product quality degradation (sensor information) that widely exists in multistage manufacturing processes and proposes a high-dimensional stochastic differential equation model to capture the interaction relationship. Then, real-time quality measurements are incorporated to online predict the residual life of the system. Chapter 5 develops a strategy of dynamic workload adjustment for parallel multi-component systems in order to control the degradation processes and failure times of individual components, for the purpose of preventing the overlap of component failures. This chapter opens a new research direction that focuses on the active control of degradation rather than only the modeling part.

HIV/Aids Relative Survival and Mean Residual Life Analysis BY XINJIAN ZHANG Under the Direction of Gengsheng (Jeff) Qin and Ruiguang (Rick) Song ABSTRACT Generalized linear models with Poisson error were applied to investigate HIV/AIDS relative survival. Relative excess risk for death within 3 years after HIV/AIDS diagnosis was significantly higher for non-Hispanic blacks, American Indians and Hispanics compared with Whites. Excess hazard for death was also higher in men injection drug users compared with men who have sex with men (MSM). The relative excess hazard of old HIV/AIDS patients is significantly higher compared with younger patients. When CD4 increased, the relative excess hazard decreased; while with the increase of HIV viral load, the relative excess hazard decreased. This is the first study to use national wide data to examine the significance of HIV viral load as a determinant risk factor of disease progression after HIV infection; The mean residual lie needs to be further analyzed. INDEX WORDS: Human Immunodeficiency Virus (HIV), Acquired Immunodeficiency Syndrome (AIDS), Survival, Mean residual life (MRL).

Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Most industries are being forced to operate at lower costs while delivering more outputs and ensuring a safe working environment. An opportunity to achieve this for asset intensive industries lies within the complex and integrated field of Physical Asset Management (PAM). This study is specifically concerned with the maintenance subset of PAM, more specifically, the proactive maintenance strategy. A field known as prognostics emerges when combining two maintenance tactics, namely predictive and preventative maintenance. Prognostics uses historical failure data from preventative maintenance and variable readings used in predictive maintenance to estimate asset reliability. Reliability is estimated using statistical models commonly known as reliability models or survival models. Variable readings used must describe or portray the health of the assets considered and are called covariates. A problem that exists in the maintenance subset of PAM is concerned with the data needed for the survival models. The historical failure data is difficult to come by or non-existent in industry and the covariate data is often noisy and inaccurate. This poses a problem when wanting to make important maintenance decisions because the prognostics survival models require both the historical failure data and the covariate data. The covariate data is generally acquired by applying Condition Monitoring (CM) to assets, monitoring characteristics reflecting the asset’s health. Prognostics can aid with maintenance decisions because once the equipment reliability has been estimated, it is possible to predict the time that an asset can still operate at its prescribed level of performance. This time of operation, which the asset can still operate, is more commonly known as its residual life (RL). To overcome this problem, six of the most popular survival models found in literature, namely the Accelerated Failure Time Model (AFTM), Additive Hazards Model (AHM), Proportional Covariate Model (PCM), Proportional Hazards Model (PHM), Proportional Odds Model (POM) and the Prentice, Williams and Peterson (PWP), are considered and populated with historical failure data and the covariate data elicited from people. The people whom the data is obtained from are considered as experts in the field this study is conducted in. Also, the data is subjective because each expert has their own opinions and judgement concerning the assets in this study. The purpose of this study is, thus, to investigate whether subjective data can be used to populate survival models, therefore, allowing RL predictions of the assets considered. A guideline consisting of five steps that aid with what system variables to consider as covariates, which people can be selected as experts and selecting the most appropriate survival model, is created and presented. Following the guideline, a case study is conducted on power transformers at an organization in South Africa. Results from the case study reveal that the PCM is the most appropriate survival model reviewed. Using the PCM, RL predictions are made after the models are populated with subjective data and objective industry standard data. The results indicate that the subjective data yielded the same general trends but less conservative estimates when compared to industry standard data. Subjective data can, therefore, be used to populate survival models but this is inherently risky because of the less conservative results noted from this study. This study is based on a single case study, it does prove that it is possible to use the subjective data as an alternative to objective data. It is possible, however, that this characteristic does not apply for other asset types. / AFRIKAANSE OPSOMMING: Die meerderheid nywerhede word onder geweldige druk geplaas om laer bedryfskostes te handhaaf en ter selfde tyd word dit van hulle verwag om hul uitsette te vermeerder en ´n veilige werksomgewing te bied. Bate intensiewenywerhede het ´n geleentheid om hierdie druk te verlig deur gebruik te maak van ´n komplekse en geïntegreerde veld bekend as Fisiese Batebestuur (FB). Hierdie studie is gefokus op die instandhouding onderafdeling van FB, spesifiek die proaktiewe instandhoudingsstrategie. Twee proaktiewe instandhoudingstaktieke, naamlik voorspellende en voorkomende instandhoudingtaktieke, word saamgesmelt en vorm ´n veld bekend as prognostiek. Prognostiek gebruik historiese falingdata van voorkomende instandhouding en veranderlike aflesings vanaf toestandmoniteering toeristing gebruik in voorspellende instandhouding om bate batroubarheid te bereken. Hierdie betroubaarheid word bereken deur gebruik te maak van statistiese modelle bekend as oorlewingsmodelle. Een van die probleme wat voorkom in die instandhouding onderafdeling van FB het te doen met die beskikbaarheid van die data wat benodig word vir die oorlewingsmodelle. Historiese falingdata is selde beskikbaar of bestaan glad nie en die toestandsmoniteering data is dikwels onakuraat. Prognostiek word gebruik om belangrikke instandhoudingsbesluite te motiveer, dus is die beskikbaarheid en betroubaarheid van die nodige data van belange. Om hierdie struikelblok te oorkom bestudeer hierdie studie die gebruik van subjektiewe data bekom vanaf deskundiges in prognostieke oorlewingsmodelle. Die doel van hierdie studie is dus om vas te stel of subjektiewe data gebruik kan word in prognostieke oorlewingsmodelle. Ses oorlewingsmodelle wat gereeld voorkom in literatuur word nagesien in hierdie studie, die modelle sluit in die “Accelerated Failure Time Model” (AFTM), “ Additive Hazards Model” (AHM), “Proportional Covariate Model” (PCM) , “Proportional Hazards Model” (PHM), “Proportional Odds Model” (POM) en die “Prentice Williams and Peterson” (PWP) model. Hierdie modelle word aangevul deur die subjektiewe data wat onttrek is van deskundiges in ´n sekere gebied, vir hierdie studie is die gebied krag transformators. Met gebruik van hierdie modelle kan die betroubaarheid van die betrokke toerusting bereken word. Sodra die betroubaarheid bereken is kan die oorblywende lewe van die toerusting voorspel word. Die oorblywendelewe is die tyd wat ´n stuk toerusting nog moontlik kan werk sonder om te faal. Dit is belangrik omdat nodige instandhoudingsbesluite geneem moet word. Hierdie studie stel ´n metode voor vir die uitvoer van die navorsing en soortgelyke studies. Die metode dui vyf stappe aan wat voorstel watter veranderlikes om te gebruik as kovariate in die oorlewingsmodelle, watter mense as deskundiges gekies kan word, en hoe om die mees toepasslikke oorlewingsmodelle te kies. Nadat hierdie metode voorgestel is word dit toegepas op krag transformators in ´n gevallestudie wat plaasgevind het in Suid Afrika. Vir die gevallestudie is die PCM die meestoepaslikke oorlewingsmodel. Die oorblywende lewe voorspellings wat die metode opgelewer het is met die voorspellings gebaseer op die industriestandaard data vergelyk. Die resultate dui aan dat deskundiges minder konserwatiewe beramings lewer. Dus kan die subjektiewe data gebruik word in oorlewingsmodelle maar die beramings is minder konserwatief en daarom van natuur meer riskant. Hierdie studie se gevolgtrekkings is gebaseer op ´n enkele gevallestudie. Dit is dus moontlik dat die subjektiewe data dalk nie as ´n alternatief gebruik kan word met ander tipes toerusting nie.

Usualmente a análise de sobrevivência considera a modelagem da função da taxa de falha ou função de risco. Uma alternativa a essa visão é estudar a vida residual, que em alguns casos é mais intuitiva do que a função de risco. A vida residual é o tempo de sobrevida adicional de um indivíduo que sobreviveu até um dado instante t0. Este trabalho descreve técnicas semiparamétricas e não paramétricas para estimar a média e a mediana de vida residual em uma população, testes para igualdade dessas medidas em duas populações e também modelos de regressão. Tais técnicas já foram testadas anteriormente em dados com baixa presença de censura; aqui elas são aplicadas a um conjunto de dados de pacientes com insuficiência cardíaca que possui uma alta quantidade de observações censuradas. / Usually, survival analysis is based on the modeling of the hazard function. One alternative approach is to consider the residual life, which would be more intuitive than the hazard function. Residual lifetime is the remaining survival time of a person given he or she survived a given time point t0. We describe semiparametric and non-parametric techniques for mean and median residual life estimation in a one-sample population, as well as tests for two-sample cases and regression models. Such techniques were previously tested for moderate censored data; here we apply them to heart-failure patients data with a high rate of censoring.

Analysis of reliability data plays an important role in the maintenance decision making process. The accurate estimation of residual life in components and systems can be a great asset when planning the preventive replacement of components on machines. Artificial intelligence is a field that has rapidly developed over the last twenty years and practical applications have been found in many diverse areas. The use of such methods in the maintenance field have however not yet been fully explored. With the common availability of condition monitoring data, another dimension has been added to the analysis of reliability data. Neural networks allow for explanatory variables to be incorporated into the analysis process. This is expected to improve the quality of predictions when compared to the results achieved through the use of methods that rely solely on failure time data. Neural networks can therefore be seen as an alternative to the various regression models, such as the proportional hazards model, which also incorporate such covariates into the analysis. For the purpose of investigating their applicability to the problem of predicting the residual life of machines and components, neural networks were trained and tested with the data of two different reliability related datasets. The first dataset represents the renewal case where repair leads to complete restoration of the system. A typical maintenance situation was simulated in the laboratory by subjecting a series of similar test pieces to different loading conditions. Measurements were taken at regular intervals during testing with a number of sensors which provided an indication of the test piece’s condition at the time of measurement. The dataset was split into a training set and a test set and a number of neural network variations were trained using the first set. The networks’ ability to generalize was then tested by presenting the data from the test set to each of these networks. The second dataset contained data collected from a group of pumps working in a coal mining environment. This dataset therefore represented an example of the situation encountered with a repaired system. The performance of different neural network variations was subsequently compared through the use of cross-validation. It was proved that in most cases the use of condition monitoring data as network inputs improved the accuracy of the neural networks’ predictions. The average prediction error of the various neural networks under comparison varied between 431 and 841 seconds on the renewal dataset, where test pieces had a characteristic life of 8971 seconds. When optimized the multi-layer perceptron neural networks trained with the Levenberg-Marquardt algorithm and the general regression neural network produced a sum of squares error within 11.1% of each other for the data of the repaired system. This result emphasizes the importance of adjusting parameters, network architecture and training targets for optimal performance The advantage of using neural networks for predicting residual life was clearly illustrated when comparing their performance to the results achieved through the use of the traditional statistical methods. The potential of using neural networks for residual life prediction was therefore illustrated in both cases. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2007. / Mechanical and Aeronautical Engineering / MEng / unrestricted

In this thesis we investigate thinning of the renewal process. After multinomial thinning from a renewal process A, we obtain the k thinned processes, A_i , i =1,¡K, k. Based on some characterizations of the Poisson process as a renewal process, we give another characterizations of the Poisson process from some relations of expectation, variance, covariance, residual life of the k thinned processes. Secondly, we consider that at each arrival time we allow the number of arrivals to be i.i.d. random variables, also the mass of each unit atom can be split into k new atoms with the i-th new atom assigned to the process D_i , i =1,¡K, k. We also have characterizations of the Poisson process from some relations of expectation, variance of the process D_i , i =1,¡K, k.

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The first part of this master's thesis deals with the high cycle fatigue of materials, especially on growing cracks using linear elastic fracture mechanics. Much of this work is focused on the concept of stress intensity factor. This concept is nowadays one of the most widely used concepts for describing a body with crack. The first part ends with theoretical approaches to determine the residual fatigue life of the body with a crack. The second part of this master's thesis is focused on the determination of residual fatigue life of a specified railway wheelset. An existence of crack-like defect is assumed at the railway wheelset. The goal of this master's thesis is to estimate how long it will take to grow from initial defect to a critical crack length. The last part of this master's thesis is devoted to addiction order load cycles on crack growth rate.