Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

‘Reliability Concepts in Quantile-based Analysis of Lifetime Data

Reliability analysis is a well established branch of statistics that deals with the statistical study of different aspects of lifetimes of a system of components. As we pointed out earlier that major part of the theory and applications in connection with reliability analysis were discussed based on the measures in terms of distribution function. In the beginning chapters of the thesis, we have described some attractive features of quantile functions and the relevance of its use in reliability analysis. Motivated by the works of Parzen (1979), Freimer et al. (1988) and Gilchrist (2000), who indicated the scope of quantile functions in reliability analysis and as a follow up of the systematic study in this connection by Nair and Sankaran (2009), in the present work we tried to extend their ideas to develop necessary theoretical framework for lifetime data analysis. In Chapter 1, we have given the relevance and scope of the study and a brief outline of the work we have carried out. Chapter 2 of this thesis is devoted to the presentation of various concepts and their brief reviews, which were useful for the discussions in the subsequent chapters .In the introduction of Chapter 4, we have pointed out the role of ageing concepts in reliability analysis and in identifying life distributions .In Chapter 6, we have studied the first two L-moments of residual life and their relevance in various applications of reliability analysis. We have shown that the first L-moment of residual function is equivalent to the vitality function, which have been widely discussed in the literature .In Chapter 7, we have defined percentile residual life in reversed time (RPRL) and derived its relationship with reversed hazard rate (RHR). We have discussed the characterization problem of RPRL and demonstrated with an example that the RPRL for given does not determine the distribution uniquely

Characterizations of some continuous distributions using partial moments

Inthis paper,we define partial moments for a univariate continuous random variable. A recurrence relationship for the Pearson curve using the partial moments is established. The interrelationship between the partial moments and other reliability measures such as failure rate, mean residual life function are proved. We also prove some characterization theorems using the partial moments in the context of length biased models and equilibrium distributions

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

Efeitos da variação da carga por eixo, pressão de inflação e tipo de pneu na resposta elástica de um pavimento

O presente trabalho é uma análise experimental que procura investigar os efeitos dos fatores carga por eixo, pressão de inflação e tipo de pneu sobre o desempenho de pavimentos. Os dados e informações existentes sobre o quadro de cargas por eixo praticada pela frota de veículos pesados é razoável. A ação conjunta dos referidos fatores é ainda uma questão pouco explorada. Assim, para compensar a escassez de dados sobre pressão de inflação e tipo de construção de pneus utilizados na frota de carga, programou-se uma pesquisa de campo na rodovia estadual RS/240. As informações oriundas da pesquisa demonstram que há um acréscimo generalizado no valor da pressão dos pneus e um aumento de uso dos pneus de fabricação radial em relação aos pneus convencionais. Os dados de campo subsidiaram a programação de um experimento fatorial cruzado executado na Área de Pesquisas e Testes de Pavimentos da UFRGS/DAER. A variação dos níveis dos fatores deu-se através de um simulador linear de tráfego atuando sobre uma pista experimental com 20 m de comprimento por 3,5 m de largura. Tendo como resposta estrutural do pavimento a máxima deflexão superficial recuperável medida com uma viga Benkelmam, determinou-se como significantes os efeitos dos fatores carga por eixo e pressão de enchimento dos pneus. Os cálculos estatísticos indicam também que não há diferenças significativas entre os pneus tipo 9.00R20 e 9.00x20 e que todas interações não exercem efeitos significativos sobre a variável de resposta. Em seqüência, determinaram-se as áreas de contato do rodado duplo do simulador de tráfego com a superfície do pavimento ensaiado para as combinações dos níveis dos fatores. Pode-se, então, comparar área de contato medida com área circular calculada, considerada em muitos modelos de dimensionamento de pavimentos. Relacionou-se a variação da pressão de contato com a deflexão recuperável e procedeu-se uma comparação da mesma com a pressão de inflação nominal dos pneus. Apresenta-se um modelo de análise do desempenho do pavimento em função da carga por eixo e da pressão de inflação, nos limites do experimento. Os dados decorrentes do experimento viabilizaram a determinação dos Fatores de Equivalência de Cargas para os níveis dos fatores, considerando-se o pavimento ensaiado. Avaliou-se, via evolução das deflexões e dos Fatores de Equivalência de Cargas, a redução da vida do pavimento, obtendo-se, para a combinação de níveis mais críticos de carregamento, resultados significativos de até 88 % de redução. Propõe-se, por último, uma formulação para o Fator de Equivalência de Cargas que considere também a ação da pressão de inflação.

Análise topológica experimental por perfilometria cíclica indutiva de superficies de paredes estruturais

To enhance the maintenance practices, Oil and Gas Pipelines are inspected from the inside by automated systems called PIG (Pipeline Inspection Gauge). The inspection and mapping of defects, as dents and holes, in the internal wall of these pipelines are increasingly put into service toward an overall Structural Integrity Policy. The residual life of these structures must be determined such that minimize its probability of failure. For this reason, the investigation on the detection limits of some basic topological features constituted by peaks or valleys disposed along a smooth surface is of great value for determining the sensitivity of the measurements of defects from some combinations of circumferential, axial and radial extent. In this investigation, it was analyzed an inductive profilometric sensor to scan three races, radius r1, r2, r3, in a circular surface of low carbon steel, equipped with eight consecutive defects simulated by bulges and holes by orbit, equally spaced at p/4 rad. A test rig and a methodology for testing in laboratory were developed to evaluate the sensor response and identify their dead zones and jumps due to fluctuations as a function of topological features and scanning velocity, four speeds different. The results are presented, analyzed and suggestions are made toward a new conception of sensor topologies, more sensible to detect these type of damage morphologies

Avaliação dos danos por fluência da serpentina da caldeira da REVAP

The determination of the remaining life of equipment operating at high temperatures has been a great challenge for their owners. The use of safety factors, often conservative, makes the replacement of equipment or of its components at the end of the life of design gets financially unviable. This study aimed to estimate the remaining life of the serpentine of the secondary superheater of one of REVAP’s boilers (Henrique Lage Refinery), through accelerated creep tests and comparison of the results with the techniques based on microstructure and hardness. When conducting a proper assessment it’s possible to increase the equipment reliability, ensuring operational continuity and physical integrity. The tests showed a minimal residual life of 12.7 years (111,252 hours), longer than the design life (100,000 hours), even after a period of operation of approximately 250,000 hours, confirming the conservatism of the project. The techniques based on microstructure and hardness did not show good correlation with the creep test, decreasing the reliability of these techniques in determining the residual life

Reliability studies of the skew normal distribution

It has been observed in various practical applications that data do not conform to the normal distribution, which is symmetric with no skewness. The skew normal distribution proposed by Azzalini(1985) is appropriate for the analysis of data which is unimodal but exhibits some skewness. The skew normal distribution includes the normal distribution as a special case where the skewness parameter is zero. In this thesis, we study the structural properties of the skew normal distribution, with an emphasis on the reliability properties of the model. More specifically, we obtain the failure rate, the mean residual life function, and the reliability function of a skew normal random variable. We also compare it with the normal distribution with respect to certain stochastic orderings. Appropriate machinery is developed to obtain the reliability of a component when the strength and stress follow the skew normal distribution. Finally, IQ score data from Roberts (1988) is analyzed to illustrate the procedure.

Fatiga en CFRP: Caracterización y Método Óptico para la Estimación del Daño

El desarrollo de nuevas estructuras aeroespaciales optimizadas, utilizan materiales compuestos, para los componentes críticos y subsistemas, principalmente polímeros reforzados con fibra de carbono (CFRP). Un conocimiento profundo del estado de daño por fatiga de estructuras de CFRP avanzado, es esencial para predecir la vida residual y optimizar los intervalos de inspección estructural, reparaciones y/o sustitución de componentes. Las técnicas actuales se basan principalmente en la medición de cargas estructurales a lo largo de la vida útil de la estructura mediante galgas extensométricas eléctricas. Con esos datos, se estima la vida a fatiga utilizando modelos de acumulación de daño. En la presente tesis, se evalúa la metodología convencional para la estimación de la vida a fatiga de un CFRP aeronáutico. Esta metodología está basada en la regla de acumulación de daño lineal de Palmgren-Miner, y es aplicada para determinar la vida a fatiga de estructuras sometidas a cargas de amplitud variable. Se ha realizado una campaña de ensayos con cargas de amplitud constante para caracterizar un CFRP aeronáutico a fatiga, obteniendo las curvas clásicas S-N, en diferentes relaciones de esfuerzo. Se determinaron los diagramas de vida constante, (CLD), también conocidos como diagramas de Goodman, utilizando redes neuronales artificiales debido a la ausencia de modelos coherentes para materiales compuestos. Se ha caracterizado la degradación de la rigidez debido al daño por fatiga. Se ha ensayado un segundo grupo de probetas con secuencias estandarizadas de cargas de amplitud variable, para obtener la vida a fatiga y la degradación de rigidez en condiciones realistas. Las cargas aplicadas son representativas de misiones de aviones de combate (Falstaff), y de aviones de transporte (Twist). La vida a fatiga de las probetas cicladas con cargas de amplitud variable, se comparó con el índice de daño teórico calculado en base a la regla de acumulación de daño lineal convencional. Los resultados obtenidos muestran predicciones no conservativas. Esta tesis también presenta el estudio y desarrollo, de una nueva técnica de no contacto para evaluar el estado de daño por fatiga de estructuras de CFRP por medio de cambios de los parámetros de rugosidad. La rugosidad superficial se puede medir fácilmente en campo con métodos sin contacto, mediante técnicas ópticas tales como speckle y perfilómetros ópticos. En el presente estudio, se han medido parámetros de rugosidad superficial, y el factor de irregularidad de la superficie, a lo largo de la vida de las probetas cicladas con cargas de amplitud constante y variable, Se ha obtenido una buena tendencia de ajuste al correlacionar la magnitud de la rugosidad y el factor de irregularidad de la superficie con la degradación de la rigidez de las probetas fatigadas. Estos resultados sugieren que los cambios en la rugosidad superficial medida en zonas estratégicas de componentes y estructuras hechas de CFRP, podrían ser indicativas del nivel de daño interno debido a cargas de fatiga. Los resultados también sugieren que el método es independiente del tipo de carga de fatiga que ha causado el daño. Esto último hace que esta técnica de medición sea aplicable como inspección para una amplia gama de estructuras de materiales compuestos, desde tanques presurizados con cargas de amplitud constante, estructuras aeronáuticas como alas y colas de aeronaves cicladas con cargas de amplitud variable, hasta aplicaciones industriales como automoción, entre otros. ABSTRACT New optimized aerospace structures use composite materials, mainly carbon fiber reinforced polymer composite (CFRP), for critical components and subsystems. A strong knowledge of the fatigue state of highly advanced (CFRP) structures is essential to predict the residual life and optimize intervals of structural inspection, repairs, and/or replacements. Current techniques are based mostly on measurement of structural loads throughout the service life by electric strain gauge sensors. These sensors are affected by extreme environmental conditions and by fatigue loads in such a way that the sensors and their systems require exhaustive maintenance throughout system life. In the present thesis, the conventional methodology based on linear damage accumulation rules, applied to determine the fatigue life of structures subjected to variable amplitude loads was evaluated for an aeronautical CFRP. A test program with constant amplitude loads has been performed to obtain the classical S-N curves at different stress ratios. Constant life diagrams, CLDs, where determined by means of Artificial Neural Networks due to the absence of consistent models for composites. The stiffness degradation due to fatigue damage has been characterized for coupons under cyclic tensile loads. A second group of coupons have been tested until failure with a standardized sequence of variable amplitude loads, representative of missions for combat aircraft (Falstaff), and representative of commercial flights (Twist), to obtain the fatigue life and the stiffness degradation under realistic conditions. The fatigue life of the coupons cycled with variable amplitude loads were compared to the theoretical damage index calculated based on the conventional linear damage accumulation rule. The obtained results show non-conservative predictions. This thesis also presents the evaluation of a new non-contact technique to evaluate the fatigue damage state of CFRP structures by means of measuring roughness parameters to evaluate changes in the surface topography. Surface roughness can be measured easily on field with non-contact methods by optical techniques such as speckle and optical perfilometers. In the present study, surface roughness parameters, and the surface irregularity factor, have been measured along the life of the coupons cycled with constant and variable amplitude loads of different magnitude. A good agreement has been obtained when correlating the magnitude of the roughness and the surface irregularity factor with the stiffness degradation. These results suggest that the changes on the surface roughness measured in strategic zones of components and structures made of CFRP, could be indicative of the level of internal damage due to fatigue loads. The results also suggest that the method is independent of the type of fatigue load that have caused the damage. It makes this measurement technique applicable for a wide range of inspections of composite materials structures, from pressurized tanks with constant amplitude loads, to variable amplitude loaded aeronautical structures like wings and empennages, up to automotive and other industrial applications.

Limiting Distributions for Lifetimes in Alternating Renewal Processes

2000 Mathematics Subject Classification: 60K05

Challenges in residual service life assessment for refurbishment

A need for an efficient life care management of building portfolio is becoming increasingly due to increase in aging building infrastructure globally. Appropriate structural engineering practices along with facility management can assist in optimising the remaining life cycle costs for existing public building portfolio. A more precise decision to either demolish, refurbish, do nothing or rebuilt option for any typical building under investigation is needed. In order to achieve this, the status of health of the building needs to be assessed considering several aspects including economic and supply-demand considerations. An investment decision for a refurbishment project competing with other capital works and/or refurbishment projects can be supported by emerging methodology residual service life assessment. This paper discusses challenges in refurbishment projects of public buildings and with a view towards development of residual service life assessment methodology

Residual strength and fatigue life assessment of composite patch repaired specimens

Design, analysis and technology for the integrity enhancement of damaged or underdesigned structures continues to be an engineering challenge. Bonded composite patch repairs to metallic structures is receiving increased attention in the recent years. It offers various advantages over rivetted doubler, particularly for airframe repairs. This paper presents an experimental investigation of residual strength and fatigue crack-growth life of an edge-cracked aluminium specimen repaired using glass epoxy composite patch. The investigation begins with the evaluation of three different surface treatments from bond strength viewpoint. A simple thumb rule formula is employed to estimate the patch size. Cracked and repaired specimens are tested under static and fatigue loading. The patch appears to restore the original strength of the undamaged specimen and enhance the fatigue crack growth life by an order of magnitude. (C) 1999 Elsevier Science Ltd. All rights reserved.

An evaluation of shot peening, residual stress and stress relaxation on the fatigue life of AISI 4340 steel

Shot peening is a method widely used to improve the fatigue strength of materials. through the creation of a compressive residual stress field (CRSF) in their surface layers. In the present research the gain in fatigue life of AISI 4340 steel, Used in landing gear. is evaluated under four Shot peening conditions. Rotating bending fatigue tests were conducted and the CRSF was measured by an X-ray tensometry prior and during fatigue tests. It was observed that relaxation of the CRSF occurred due to the fatigue process. In addition, the fractured fatigue specimens were investigated using a scanning electron microscope in order to obtain information about the crack initiation points. The evaluation of fatigue life, relaxation of CRSF and crack sources are discussed. (C) 2002 Elsevier B.V. Ltd. All rights reserved.

Measurement of LSP-induced residual stresses and fatigue life on thin-walled aluminium alloys specimens

This thesis work encloses activities carried out in the Laser Center of the Polytechnic University of Madrid and the laboratories of the University of Bologna in Forlì. This thesis focuses on the superficial mechanical treatment for metallic materials called Laser Shock Peening (LSP). This process is a surface enhancement treatment which induces a significant layer of beneficial compressive residual stresses underneath the surface of metal components in order to improve the detrimental effects of the crack growth behavior rate in it. The innovation aspect of this work is the LSP application to specimens with extremely low thickness. In particular, after a bibliographic study and comparison with the main treatments used for the same purposes, this work analyzes the physics of the operation of a laser, its interaction with the surface of the material and the generation of the surface residual stresses which are fundamentals to obtain the LSP benefits. In particular this thesis work regards the application of this treatment to some Al2024-T351 specimens with low thickness. Among the improvements that can be obtained performing this operation, the most important in the aeronautic field is the fatigue life improvement of the treated components. As demonstrated in this work, a well-done LSP treatment can slow down the progress of the defects in the material that could lead to sudden failure of the structure. A part of this thesis is the simulation of this phenomenon using the program AFGROW, with which have been analyzed different geometric configurations of the treatment, verifying which was better for large panels of typical aeronautical interest. The core of the LSP process are the residual stresses that are induced on the material by the interaction with the laser light, these can be simulated with the finite elements but it is essential to verify and measure them experimentally. In the thesis are introduced the main methods for the detection of those stresses, they can be mechanical or by diffraction. In particular, will be described the principles and the detailed realization method of the Hole Drilling measure and an introduction of the X-ray Diffraction; then will be presented the results I obtained with both techniques. In addition to these two measurement techniques will also be introduced Neutron Diffraction method. The last part refers to the experimental tests of the fatigue life of the specimens, with a detailed description of the apparatus and the procedure used from the initial specimen preparation to the fatigue test with the press. Then the obtained results are exposed and discussed.

Induction of engineered residual stresses fields and enhancement of fatigue life of high reliability metallic components by laser shock processing

Laser shock processing (LSP) is being increasingly applied as an effective technology for the improvement of metallic materials mechanical and surface properties in different types of components as a means of enhancement of their corrosion and fatigue life behavior. As reported in previous contributions by the authors, a main effect resulting from the application of the LSP technique consists on the generation of relatively deep compression residual stresses field into metallic alloy pieces allowing an improved mechanical behaviour, explicitly the life improvement of the treated specimens against wear, crack growth and stress corrosion cracking. Additional results accomplished by the authors in the line of practical development of the LSP technique at an experimental level (aiming its integral assessment from an interrelated theoretical and experimental point of view) are presented in this paper. Concretely, follow-on experimental results on the residual stress profiles and associated surface properties modification successfully reached in typical materials (especially Al and Ti alloys characteristic of high reliability components in the aerospace, nuclear and biomedical sectors) under different LSP irradiation conditions are presented along with a practical correlated analysis on the protective character of the residual stress profiles obtained under different irradiation strategies. Additional remarks on the improved character of the LSP technique over the traditional “shot peening” technique in what concerns depth of induced compressive residual stresses fields are also made through the paper