A multivariate frailty model for disease recurrences and survival

A multivariate frailty hazard model is developed for joint-modeling of three correlated time-to-event outcomes: (1) local recurrence, (2) distant recurrence, and (3) overall survival. The term frailty is introduced to model population heterogeneity. The dependence is modeled by conditioning on a shared frailty that is included in the three hazard functions. Independent variables can be included in the model as covariates. The Markov chain Monte Carlo methods are used to estimate the posterior distributions of model parameters. The algorithm used in present application is the hybrid Metropolis-Hastings algorithm, which simultaneously updates all parameters with evaluations of gradient of log posterior density. The performance of this approach is examined based on simulation studies using Exponential and Weibull distributions. We apply the proposed methods to a study of patients with soft tissue sarcoma, which motivated this research. Our results indicate that patients with chemotherapy had better overall survival with hazard ratio of 0.242 (95% CI: 0.094 - 0.564) and lower risk of distant recurrence with hazard ratio of 0.636 (95% CI: 0.487 - 0.860), but not significantly better in local recurrence with hazard ratio of 0.799 (95% CI: 0.575 - 1.054). The advantages and limitations of the proposed models, and future research directions are discussed. ^

Prognosis of amyotrophic lateral sclerosis

Two cohorts of amyotrophic lateral sclerosis (ALS) patients were identified. One incidence-based cohort from Harris County, Texas with 97 cases, and the other a clinic referral series from an ALS clinic in Houston, Texas with 439 cases were followed-up to evaluate the prognosis of ALS. The overall Kaplan-Meier 3-year survival after diagnosis was similar, 0.287 for the incidence cohort and 0.313 for the referral cohort. However, the 5-year survival was much lower for the incidence cohort than the referral cohort (0.037 vs. 0.206). The large difference in 5-year survival was thought to be the results of a stronger unfavorable effect of the prognostic factors in the incidence cohort than in the referral cohort.^ Cohort-specific Weibull regression models were derived to evaluate the cohort-specific prognostic factors and survival probability with adjustment of certain prognostic factors.^ The major prognostic factors were: age at diagnosis, bulbar onset, black ethnicity, and positive family history of ALS in both cohorts. Female gender, simultaneous upper and lower extremities onset were specifically unfavorable factors in the incidence cohort. In the incidence cohort the prognosis was relatively favorable for cases with duration from onset to diagnosis longer than 4 months, however in the referral cohort the relatively favorable prognosis only occurred in cases with duration from onset to diagnosis 1 year or longer and was strongest in cases with duration 5 years and longer. Age at diagnosis modified the effect of bulbar onset in the incidence cohort but not in the referral cohort. The estimated survival with presence of an unfavorable prognostic factor identified in the incidence cohort was higher for the referral cohort than for the incidence cohort. Future studies are indicated to investigate the disease heterogeneity issue of ALS based on survival distribution of ALS. ^

A SIMULATION STUDY OF THE SIZE AND POWER OF SOME TWO-SAMPLE TESTS FOR UNEQUALLY CENSORED SURVIVAL DATA (RANK TESTS, LOGRANK, PROPORTIONAL HAZARDS, WILCOXON TESTS, EXPONENTIAL DISTRIBUTION)

Sizes and power of selected two-sample tests of the equality of survival distributions are compared by simulation for small samples from unequally, randomly-censored exponential distributions. The tests investigated include parametric tests (F, Score, Likelihood, Asymptotic), logrank tests (Mantel, Peto-Peto), and Wilcoxon-Type tests (Gehan, Prentice). Equal sized samples, n = 18, 16, 32 with 1000 (size) and 500 (power) simulation trials, are compared for 16 combinations of the censoring proportions 0%, 20%, 40%, and 60%. For n = 8 and 16, the Asymptotic, Peto-Peto, and Wilcoxon tests perform at nominal 5% size expectations, but the F, Score and Mantel tests exceeded 5% size confidence limits for 1/3 of the censoring combinations. For n = 32, all tests showed proper size, with the Peto-Peto test most conservative in the presence of unequal censoring. Powers of all tests are compared for exponential hazard ratios of 1.4 and 2.0. There is little difference in power characteristics of the tests within the classes of tests considered. The Mantel test showed 90% to 95% power efficiency relative to parametric tests. Wilcoxon-type tests have the lowest relative power but are robust to differential censoring patterns. A modified Peto-Peto test shows power comparable to the Mantel test. For n = 32, a specific Weibull-exponential comparison of crossing survival curves suggests that the relative powers of logrank and Wilcoxon-type tests are dependent on the scale parameter of the Weibull distribution. Wilcoxon-type tests appear more powerful than logrank tests in the case of late-crossing and less powerful for early-crossing survival curves. Guidelines for the appropriate selection of two-sample tests are given. ^

Effect of patient accrual patterns on power and size of log-rank test for time-to-event outcome in clinical trials

The determination of size as well as power of a test is a vital part of a Clinical Trial Design. This research focuses on the simulation of clinical trial data with time-to-event as the primary outcome. It investigates the impact of different recruitment patterns, and time dependent hazard structures on size and power of the log-rank test. A non-homogeneous Poisson process is used to simulate entry times according to the different accrual patterns. A Weibull distribution is employed to simulate survival times according to the different hazard structures. The current study utilizes simulation methods to evaluate the effect of different recruitment patterns on size and power estimates of the log-rank test. The size of the log-rank test is estimated by simulating survival times with identical hazard rates between the treatment and the control arm of the study resulting in a hazard ratio of one. Powers of the log-rank test at specific values of hazard ratio (≠1) are estimated by simulating survival times with different, but proportional hazard rates for the two arms of the study. Different shapes (constant, decreasing, or increasing) of the hazard function of the Weibull distribution are also considered to assess the effect of hazard structure on the size and power of the log-rank test. ^

The assumptions and effects of conservative procedures in low -dose risk assessment for setting safety standards

Conservative procedures in low-dose risk assessment are used to set safety standards for known or suspected carcinogens. However, the assumptions upon which the methods are based and the effects of these methods are not well understood.^ To minimize the number of false-negatives and to reduce the cost of bioassays, animals are given very high doses of potential carcinogens. Results must then be extrapolated to much smaller doses to set safety standards for risks such as one per million. There are a number of competing methods that add a conservative safety factor into these calculations.^ A method of quantifying the conservatism of these methods was described and tested on eight procedures used in setting low-dose safety standards. The results using these procedures were compared by computer simulation and by the use of data from a large scale animal study.^ The method consisted of determining a "true safe dose" (tsd) according to an assumed underlying model. If one assumed that Y = the probability of cancer = P(d), a known mathematical function of the dose, then by setting Y to some predetermined acceptable risk, one can solve for d, the model's "true safe dose".^ Simulations were generated, assuming a binomial distribution, for an artificial bioassay. The eight procedures were then used to determine a "virtual safe dose" (vsd) that estimates the tsd, assuming a risk of one per million. A ratio R = ((tsd-vsd)/vsd) was calculated for each "experiment" (simulation). The mean R of 500 simulations and the probability R $<$ 0 was used to measure the over and under conservatism of each procedure.^ The eight procedures included Weil's method, Hoel's method, the Mantel-Byran method, the improved Mantel-Byran, Gross's method, fitting a one-hit model, Crump's procedure, and applying Rai and Van Ryzin's method to a Weibull model.^ None of the procedures performed uniformly well for all types of dose-response curves. When the data were linear, the one-hit model, Hoel's method, or the Gross-Mantel method worked reasonably well. However, when the data were non-linear, these same methods were overly conservative. Crump's procedure and the Weibull model performed better in these situations. ^

Estimadores bayesianos de la fiabilidad con muestreo censurado

El estudio de la fiabilidad de componentes y sistemas tiene gran importancia en diversos campos de la ingenieria, y muy concretamente en el de la informatica. Al analizar la duracion de los elementos de la muestra hay que tener en cuenta los elementos que no fallan en el tiempo que dure el experimento, o bien los que fallen por causas distintas a la que es objeto de estudio. Por ello surgen nuevos tipos de muestreo que contemplan estos casos. El mas general de ellos, el muestreo censurado, es el que consideramos en nuestro trabajo. En este muestreo tanto el tiempo hasta que falla el componente como el tiempo de censura son variables aleatorias. Con la hipotesis de que ambos tiempos se distribuyen exponencialmente, el profesor Hurt estudio el comportamiento asintotico del estimador de maxima verosimilitud de la funcion de fiabilidad. En principio parece interesante utilizar metodos Bayesianos en el estudio de la fiabilidad porque incorporan al analisis la informacion a priori de la que se dispone normalmente en problemas reales. Por ello hemos considerado dos estimadores Bayesianos de la fiabilidad de una distribucion exponencial que son la media y la moda de la distribucion a posteriori. Hemos calculado la expansion asint6tica de la media, varianza y error cuadratico medio de ambos estimadores cuando la distribuci6n de censura es exponencial. Hemos obtenido tambien la distribucion asintotica de los estimadores para el caso m3s general de que la distribucion de censura sea de Weibull. Dos tipos de intervalos de confianza para muestras grandes se han propuesto para cada estimador. Los resultados se han comparado con los del estimador de maxima verosimilitud, y con los de dos estimadores no parametricos: limite producto y Bayesiano, resultando un comportamiento superior por parte de uno de nuestros estimadores. Finalmente nemos comprobado mediante simulacion que nuestros estimadores son robustos frente a la supuesta distribuci6n de censura, y que uno de los intervalos de confianza propuestos es valido con muestras pequenas. Este estudio ha servido tambien para confirmar el mejor comportamiento de uno de nuestros estimadores. SETTING OUT AND SUMMARY OF THE THESIS When we study the lifetime of components it's necessary to take into account the elements that don't fail during the experiment, or those that fail by reasons which are desirable to exclude from consideration. The model of random censorship is very usefull for analysing these data. In this model the time to failure and the time censor are random variables. We obtain two Bayes estimators of the reliability function of an exponential distribution based on randomly censored data. We have calculated the asymptotic expansion of the mean, variance and mean square error of both estimators, when the censor's distribution is exponential. We have obtained also the asymptotic distribution of the estimators for the more general case of censor's Weibull distribution. Two large-sample confidence bands have been proposed for each estimator. The results have been compared with those of the maximum likelihood estimator, and with those of two non parametric estimators: Product-limit and Bayesian. One of our estimators has the best behaviour. Finally we have shown by simulation, that our estimators are robust against the assumed censor's distribution, and that one of our intervals does well in small sample situation.

Analysis of the Mechanical Properties of Multicrystalline and Monocrystalline Silicon Wafers Manufactured by Casting Methods

Quasi-monocrystalline silicon wafers have appeared as a critical innovation in the PV industry, joining the most favourable characteristics of the conventional substrates: the higher solar cell efficiencies of monocrystalline Czochralski-Si (Cz-Si) wafers and the lower cost and the full square-shape of the multicrystalline ones. However, the quasi-mono ingot growth can lead to a different defect structure than the typical Cz-Si process. Thus, the properties of the brand-new quasi-mono wafers, from a mechanical point of view, have been for the first time studied, comparing their strength with that of both Cz-Si mono and typical multicrystalline materials. The study has been carried out employing the four line bending test and simulating them by means of FE models. For the analysis, failure stresses were fitted to a three-parameter Weibull distribution. High mechanical strength was found in all the cases. The low quality quasi-mono wafers, interestingly, did not exhibit critical strength values for the PV industry, despite their noticeable density of extended defects.

Modelos de evolución de masas de pinus sylvestris l.

En el capítulo dedicado a la calidad de la estación, como primera etapa se realiza una exhaustiva revisión bibliográfica a partir de la cual se comprueba que los métodos más precisos para determinar esta calidad, en términos generales, son aquellos basados en la relación de la altura con la edad. En base a los datos que se encuentran disponibles y como fruto de esta revisión bibliográfica, se decide probar tres métodos: uno de ellos que estudia la evolución de la altura en función del diámetro (MEYER) y los otros dos en función de la edad (BAILEY y CLUTTER y GARCÍA). Para probar estos métodos, se utilizan datos de parcelas de producción distribuidas en los tres principales sistemas montañosos de España: Ibérico, Central y Pirenaico. El modelo de MEYER implica una clasificación previa de las parcelas en función de su clase de sitio y los ajustes se realizan para cada clase, con lo que se obtienen cuatro curvas polimórficas. La ecuación que describe este modelo es: H = 1.3 + s(1-e-bD) El modelo de BAILEY y CLUTTER genera también un sistema de curvas polimórficas y se genera a partir de la relación entre el 1og de la altura y la inversa de la edad: log H = a + b¡(1/AC) Este método implica una agrupación o estratificación de las parcelas en clases de sitio. Por último, se prueba el modelo de GARCÍA que se basa en una ecuación diferencial estocástica: dHc(t) = b(ac-Hc(t)) + a(t)dw(t) y se prueba la siguiente estructura paramétrica: a b c °"0 o *o H0 global 1 oca 1 g1obal 0.00 global 0.00 0.0 Posteriormente se hace un análisis de los residuos en que se aplica la prueba de Durbin-Watson que detecta la presencia de correlación serial. Se verifica la forma aproximada a un "cometa" en los residuos, lo que es frecuente en series de tiempo cuando la magnitud analizada (en nuestro caso, la altura dominante) se acumula en el tiempo. Esta prueba no es concluyente en el sentido de que no aclara que modelo es el más apropiado. Finalmente, se validan estos modelos utilizando datos de las parcelas de clara. Para esto se utiliza información de arboles tipo sometidos a análisis de tronco. Esta validación permite concluir que el modelo de GARCÍA es el que mejor explica la evolución del crecimiento en altura. En el capítulo dedicado a las distribuciones diamétricas, se pretende modelizar dichas distribuciones a través de variables de estado. Para esto, como primera etapa, se prueban para 45 parcelas y tres inventarios, las siguientes funciones: - Normal - Gamma - Ln de dos parámetros - Ln de tres parámetros - Beta I I - Wei bul 1 Mediante el uso de chi-cuadrado como estimador de la bondad del ajuste, se determina que la función de Weibull es la que mejor responde a la distribución diamétrica de nuestras parcelas. Posteriormente, se comprueba la bondad de dicho ajuste, mediante la prueba de Kolmogorov-Smirnov, el que determina que en el 99X de los casos, el ajuste es aceptable. Luego se procede a la recuperación de 1 os*parámetros de la función de Weibull; a, b y c. En esta etapa se estratifica la información y se realizan análisis de varianza (ANOVA) y pruebas de medias de TUKEY que dan como resultado el que se continúe trabajando por tratamiento y por inventario quedando la diferencia entre sitios absorbida por la altura dominante. Para la recuperación de los parámetros, se utilizan las variables de estado que definen a nuestras parcelas; edad, densidad, altura dominante, diámetro medio cuadrático y área basimétrica. El método seguido es la obtención de ecuaciones de regresión con las variables de estado como independientes para predecir los valores de los parámetros antes mencionados. Las ecuaciones se obtienen utilizando distintas vías (STEPWISE, ENTER y RSQUARE) lo que nos proporciona abundante material para efectuar la selección de éstas. La selección de las mejores ecuaciones se hace en base a dos estadísticos conocidos: - Coeficiente de determinación ajustado: R2 a - Cp de MALLOWS Estos elementos se tratan en forma conjunta considerando, además, que el número de parámetros esté en concordancia con el número de datos. El proceso de selección implica que se obtengan 36 ecuaciones de regresión que posteriormente se validan en dos sentidos. Por una parte, se calcula el valor de cada parámetro según la ecuación que le corresponda y se compara con el valor de los parámetros calculados en el ajuste de Weibull. Lo que se puede deducir de esta etapa es que la distorsión que sufren los parámetros al efectuar ecuaciones de regresión, es relativamente baja y la diferencia se produce debido a errores que se originan al realizar los modelos. Por otra parte, con las parcelas que se encuentren disponibles, se valida el modelo en el sentido de hacer el proceso inverso al anterior, es decir a partir de sus variables de estado, fácilmente medibles, se obtienen los valores de los parámetros que definen a la función de Weibull. Con esto se reconstruye la distribución diamétrica de cada función. Los resultados que se obtienen de esto indican que los ajustes son aceptables a un nivel del 1X en el caso de tres parcelas.

Modelling the spatio-temporal pattern of primary dispersal in stone pine (Pinus pinea L.) stands in the Northern Plateau (Spain)

Natural regeneration in stone pine (Pinus pinea L.) managed forests in the Spanish Northern Plateau is not achieved successfully under current silviculture practices, constituting a main concern for forest managers. We modelled spatio-temporal features of primary dispersal to test whether (a) present low stand densities constrain natural regeneration success and (b) seed release is a climate-controlled process. The present study is based on data collected from a 6 years seed trap experiment considering different regeneration felling intensities. From a spatial perspective, we attempted alternate established kernels under different data distribution assumptions to fit a spatial model able to predict P. pinea seed rain. Due to P. pinea umbrella-like crown, models were adapted to account for crown effect through correction of distances between potential seed arrival locations and seed sources. In addition, individual tree fecundity was assessed independently from existing models, improving parameter estimation stability. Seed rain simulation enabled to calculate seed dispersal indexes for diverse silvicultural regeneration treatments. The selected spatial model of best fit (Weibull, Poisson assumption) predicted a highly clumped dispersal pattern that resulted in a proportion of gaps where no seed arrival is expected (dispersal limitation) between 0.25 and 0.30 for intermediate intensity regeneration fellings and over 0.50 for intense fellings. To describe the temporal pattern, the proportion of seeds released during monthly intervals was modelled as a function of climate variables – rainfall events – through a linear model that considered temporal autocorrelation, whereas cone opening took place over a temperature threshold. Our findings suggest the application of less intensive regeneration fellings, to be carried out after years of successful seedling establishment and, seasonally, subsequent to the main rainfall period (late fall). This schedule would avoid dispersal limitation and would allow for a complete seed release. These modifications in present silviculture practices would produce a more efficient seed shadow in managed stands.

Damage reduction of the laser drilling process on back contact solar cells by chemical treatment

Production of back contact solar cells requires holes generations on the wafers to keep both positive and negative contacts on the back side of the cell. This drilling process weakens the wafer mechanically due to the presence of the holes and the damage introduced during the process as microcracks. In this study, several chemical processes have been applied to drilled wafers in order to eliminate or reduce the damage generated during this fabrication step. The treatments analyzed are the followings: alkaline etching during 1, 3 and 5 minutes, acid etching for 2 and 4 minutes and texturisation. To determine mechanical strength of the samples a common mechanical study has been carried out testing the samples by the Ring on Ring bending test and obtaining the stress state in the moment of failure by FE simulation. Finally the results obtained for each treatment were fitted to a three parameter Weibull distribution

Preliminary temperature Accelerated Life Test (ALT) on III-V commercial concentrator triple-junction solar cells

A quantitative temperature accelerated life test on sixty GaInP/GaInAs/Ge triple-junction commercial concentrator solar cells is being carried out. The final objective of this experiment is to evaluate the reliability, warranty period, and failure mechanism of high concentration solar cells in a moderate period of time. The acceleration of the degradation is realized by subjecting the solar cells at temperatures markedly higher than the nominal working temperature under a concentrator Three experiments at three different temperatures are necessary in order to obtain the acceleration factor which relates the time at the stress level with the time at nominal working conditions. . However, up to now only the test at the highest temperature has finished. Therefore, we can not provide complete reliability information but we have analyzed the life data and the failure mode of the solar cells inside the climatic chamber at the highest temperature. The failures have been all of them catastrophic. In fact, the solar cells have turned into short circuits. We have fitted the failure distribution to a two parameters Weibull function. The failures are wear-out type. We have observed that the busbar and the surrounding fingers are completely deteriorate

Tree height integrated into pantropical forest biomass estimates

Aboveground tropical tree biomass and carbon storage estimates commonly ignore tree height (H). We estimate the effect of incorporating H on tropics-wide forest biomass estimates in 327 plots across four continents using 42 656 H and diameter measurements and harvested trees from 20 sites to answer the following questions: 1. What is the best H-model form and geographic unit to include in biomass models to minimise site-level uncertainty in estimates of destructive biomass? 2. To what extent does including H estimates derived in (1) reduce uncertainty in biomass estimates across all 327 plots? 3. What effect does accounting for H have on plot- and continental-scale forest biomass estimates? The mean relative error in biomass estimates of destructively harvested trees when including H (mean 0.06), was half that when excluding H (mean 0.13). Power- andWeibull-H models provided the greatest reduction in uncertainty, with regional Weibull-H models preferred because they reduce uncertainty in smaller-diameter classes (?40 cm D) that store about one-third of biomass per hectare in most forests. Propagating the relationships from destructively harvested tree biomass to each of the 327 plots from across the tropics shows that including H reduces errors from 41.8Mgha?1 (range 6.6 to 112.4) to 8.0Mgha?1 (?2.5 to 23.0). For all plots, aboveground live biomass was ?52.2 Mgha?1 (?82.0 to ?20.3 bootstrapped 95%CI), or 13%, lower when including H estimates, with the greatest relative reductions in estimated biomass in forests of the Brazilian Shield, east Africa, and Australia, and relatively little change in the Guiana Shield, central Africa and southeast Asia. Appreciably different stand structure was observed among regions across the tropical continents, with some storing significantly more biomass in small diameter stems, which affects selection of the best height models to reduce uncertainty and biomass reductions due to H. After accounting for variation in H, total biomass per hectare is greatest in Australia, the Guiana Shield, Asia, central and east Africa, and lowest in eastcentral Amazonia, W. Africa, W. Amazonia, and the Brazilian Shield (descending order). Thus, if tropical forests span 1668 million km2 and store 285 Pg C (estimate including H), then applying our regional relationships implies that carbon storage is overestimated by 35 PgC (31?39 bootstrapped 95%CI) if H is ignored, assuming that the sampled plots are an unbiased statistical representation of all tropical forest in terms of biomass and height factors. Our results show that tree H is an important allometric factor that needs to be included in future forest biomass estimates to reduce error in estimates of tropical carbon stocks and emissions due to deforestation.

Ensayos acelerados de dispositivos electrónicos LED

El objetivo de este proyecto es el de determinar, a través de una serie de medidas, los tiempos de vida y causas de fallo de diodos LED. Para ello, se someterá a los dispositivos a condiciones extremas de temperatura y humedad dentro de una cámara climática, con el objetivo de acelerar su edad, su tiempo de uso, hecho que provocará la aparición de los fallos mucho antes que en condiciones normales de funcionamiento. Se tomarán medidas tanto de su tensión y corriente para el análisis de las gráficas I-V, dentro y fuera de la cámara, como de las potencias luminosas de cada uno de ellos. Estas medidas se realizarán en dos ocasiones al día, en intervalos de no menos de 6 horas. Para las medidas de tensión y corriente se utilizará un programa desarrollado en el entorno de LabView, tanto para las medidas en el interior de la cámara, lo que nos permite un seguimiento específico del estado de los dispositivos en cada momento, como para las medidas fuera de ella. Para las medidas de la potencia luminosa de cada LED se utilizará un medidor de potencia óptica. Cada ensayo constará de 15 dispositivos LED, que se evaluarán en las mismas condiciones de temperatura y humedad. El resumen de los 8 ensayos realizados es el que sigue: - Ensayo 1: 140ºC 85% HUMEDAD a 10 mA. - Ensayo 2: 140ºC 70% HUMEDAD a 10 mA. - Ensayo 3: 120ºC 85% HUMEDAD a 10 mA. - Ensayo 4: 120ºC 85% HUMEDAD a 30 mA. - Ensayo 5: 140ºC 70% HUMEDAD a 30 mA. - Ensayo 6: 140ºC 85% HUMEDAD a 30 mA. - Ensayo 7: 140ºC 60% HUMEDAD a 30 mA. - Ensayo 8: 140ºC 85% HUMEDAD a 20 mA. Una vez tomadas las medidas, se analizarán los datos, de cara a obtener una ley de degradación del LED a través del análisis de Weibull y se estudiarán las diferentes causas de fallo. ABSTRACT. The aim of this Project is to determine, based on several measures, the lifetime and the causes of LED’s failures. The devices will be tested under extreme both temperature and humidity conditions in a Pressure Cooker, attempting to make faults to appear earlier. Voltage and current measures will be taken, inside and also outside the Pressure cooker, in order to use them in I-V graphs. In addition, luminous power measures for each LED will be taken. All those measures will be obtained twice a day, with 6 hours delay between both of them. A program based on LabView environment will be used to take voltage and current measures, inside and outside the pressure cooker, which allow us to follow the performance of the LED at each moment. The luminous power of each LED will be taken by a measurer. Each test consists of 15 LED devices, which will be evaluated under the same conditions each time. The 8 tests are as follows - Test 1: 140ºC 85% relative humidity at 10 mA. - Test 2: 140ºC 70% relative humidity at 10 mA. - Test 3: 120ºC 85% relative humidity at 10 mA. - Test 4: 120ºC 85% relative humidity at 30 mA. - Test 5: 140ºC 70% relative humidity at 30 mA. - Test 6: 140ºC 85% relative humidity at 30 mA. - Test 7: 140ºC 60% relative humidity at 30 mA. - Test 8: 140ºC 85% relative humidity at 20 mA. When the measures are completely taken, data will be analyzed, in order to obtain a LED’s degradation law using Weibull’s distribution. Also the causes of the failures will be evaluated.

Evaluation of the reliability of commercial concentrator triple-junction solar cells by means of accelerated life tests (ALT)

A temperature accelerated life test on commercial concentrator lattice-matched GaInP/GaInAs/Ge triple-junction solar cells has been carried out. The solar cells have been tested at three different temperatures: 119, 126 and 164 °C and the nominal photo-current condition (820 X) has been emulated by injecting current in darkness. All the solar cells have presented catastrophic failures. The failure distributions at the three tested temperatures have been fitted to an Arrhenius-Weibull model. An Arrhenius activation energy of 1.58 eV was determined from the fit. The main reliability functions and parameters (reliability function, instantaneous failure rate, mean time to failure, warranty time) of these solar cells at the nominal working temperature (80 °C) have been obtained. The warranty time obtained for a failure population of 5 % has been 69 years. Thus, a long-term warranty could be offered for these particular solar cells working at 820 X, 8 hours per day at 80 °C.

Estudio de las propiedades mecánicas de obleas de silicio

En esta tesis se propone un procedimiento para evaluar la resistencia mecánica de obleas de silicio cristalino y se aplica en diferentes casos válidos para la industria. En el sector de la industria fotovoltaica predomina la tecnología basada en paneles de silicio cristalino. Estos paneles están compuestos por células solares conectadas en serie y estas células se forman a partir de obleas de silicio. Con el objetivo de disminuir el coste del panel, en los últimos años se ha observado una clara tendencia a la reducción del espesor de las obleas. Esta reducción del espesor modifica la rigidez de las obleas por lo que ha sido necesario modificar la manera tradicional de manipularlas con el objetivo de mantener un bajo ratio de rotura. Para ello, es necesario conocer la resistencia mecánica de las obleas. En la primera parte del trabajo se describen las obleas de silicio, desde su proceso de formación hasta sus propiedades mecánicas. Se muestra la influencia de la estructura cristalográfica en la resistencia y en el comportamiento ya que el cristal de silicio es anisótropo. Se propone también el método de caracterización de la resistencia. Se utiliza un criterio probabilista basado en los métodos de dimensionamiento de materiales frágiles en el que la resistencia queda determinada por los parámetros de la ley de Weibull triparamétrica. Se propone el procedimiento para obtener estos parámetros a partir de campañas de ensayos, modelización numérica por elementos finitos y un algoritmo iterativo de ajuste de los resultados. En la segunda parte de la tesis se describen los diferentes tipos de ensayos que se suelen llevar a cabo con este material. Se muestra además, para cada uno de los ensayos descritos, un estudio comparativo de diferentes modelos de elementos finitos simulando los ensayos. Se comparan tanto los resultados aportados por cada modelo como los tiempos de cálculo. Por último, se presentan tres aplicaciones diferentes donde se ha aplicado este procedimiento de estudio. La primera aplicación consiste en la comparación de la resistencia mecánica de obleas de silicio en función del método de crecimiento del lingote. La resistencia de las tradicionales obleas monocristalinas obtenidas por el método Czochralski y obleas multicristalinas es comparada con las novedosas obleas quasi-monocristalinas obtenidas por métodos de fundición. En la segunda aplicación se evalúa la profundidad de las grietas generadas en el proceso de corte del lingote en obleas. Este estudio se realiza de manera indirecta: caracterizando la resistencia de grupos de obleas sometidas a baños químicos de diferente duración. El baño químico reduce el espesor de las obleas eliminando las capas más dañadas. La resistencia de cada grupo es analizada y la comparación permite obtener la profundidad de las grietas generadas en el proceso de corte. Por último, se aplica este procedimiento a un grupo de obleas con características muy especiales: obleas preparadas para formar células de contacto posterior EWT. Estas obleas presentan miles de agujeros que las debilitan considerablemente. Se aplica el procedimiento de estudio propuesto con un grupo de estas obleas y se compara la resistencia obtenida con un grupo de referencia. Además, se propone un método simplificado de estudio basado en la aplicación de una superficie de intensificación de tensiones. ABSTRACT In this thesis, a procedure to evaluate the mechanical strength of crystalline silicon wafers is proposed and applied in different studies. The photovoltaic industry is mainly based on crystalline silicon modules. These modules are composed of solar cells which are based on silicon wafers. Regarding the cost reduction of solar modules, a clear tendency to use thinner wafers has been observed during last years. Since the stiffness varies with thickness, the manipulation techniques need to be modified in order to guarantee a low breakage rate. To this end, the mechanical strength has to be characterized correctly. In the first part of the thesis, silicon wafers are described including the different ways to produce them and the mechanical properties of interest. The influence of the crystallographic structure in the strength and the behaviour (the anisotropy of the silicon crystal) is shown. In addition, a method to characterize the mechanical strength is proposed. This probabilistic procedure is based on methods to characterize brittle materials. The strength is characterized by the values of the three parameters of the Weibull cumulative distribution function (cdf). The proposed method requires carrying out several tests, to simulate them through Finite Element models and an iterative algorithm in order to estimate the parameters of the Weibull cdf. In the second part of the thesis, the different types of test that are usually employed with these samples are described. Moreover, different Finite Element models for the simulation of each test are compared regarding the information supplied by each model and the calculation times. Finally, the method of characterization is applied to three examples of practical applications. The first application consists in the comparison of the mechanical strength of silicon wafers depending on the ingot growth method. The conventional monocrystalline wafers based on the Czochralski method and the multicrystalline ones are compared with the new quasi-monocrystalline substrates. The second application is related to the estimation of the crack length caused by the drilling process. An indirect way is used to this end: several sets of silicon wafers are subjected to chemical etchings of different duration. The etching procedure reduces the thickness of the wafers removing the most damaged layers. The strength of each set is obtained by means of the proposed method and the comparison permits to estimate the crack length. At last, the procedure is applied to determine the strength of wafers used for the design of back-contact cells of type ETW. These samples are drilled in a first step resulting in silicon wafers with thousands of tiny holes. The strength of the drilled wafers is obtained and compared with the one of a standard set without holes. Moreover, a simplified approach based on a stress intensification surface is proposed.