Multiple studies have documented declines of forest breeding birds in the eastern United States, but the temporal and spatial scales of most studies limit inference regarding large scale bird-habitat trends. A potential solution to this challenge is integrating existing long-term datasets such as the U.S. Forest Service Forest Inventory and Analysis (FIA) program and U.S. Geological Survey Breeding Bird Survey (BBS) that span large geographic regions. The purposes of this study were to determine if FIA metrics can be related to BBS population indices at multiple spatial and temporal scales and to develop predictive models from these relationships that identify forest conditions favorable to forest songbirds. I accumulated annual route-level BBS data for 4 species guilds (canopy nesting, ground and shrub nesting, cavity nesting, early successional), each containing a minimum of five bird species, from 1966-2004. I developed 41 forest variables describing forest structure at the county level using FIA data from for the 2000 inventory cycle within 5 physiographic regions in 14 states (AL, GA, IL, IN, KY, MD, NC, NY, OH, PA, SC, TN, VA, and WV). I examine spatial relationships between the BBS and FIA data at 3 hierarchical scales: 1) individual BBS routes, 2) FIA units, and 3) and physiographic sections. At the BBS route scale, I buffered each BBS route with a 100m, 1km, and 10km buffer, intersected these buffers with the county boundaries, and developed a weighted average for each forest variable within each buffer, with the weight being a function of the percent of area each county had within a given buffer. I calculated 28 variables describing landscape structure from 1992 NLCD imagery using Fragstats within each buffer size. I developed predictive models relating spatial variations in bird occupancy and abundance to changes in forest and landscape structure using logistic regression and classification and regression trees (CART). Models were developed for each of the 3 buffer sizes, and I pooled the variables selected for the individual models and used them to develop multiscale models with the BBS route still serving as the sample unit. At the FIA unit and physiographic section scales I calculated average abundance/route for each bird species within each FIA unit and physiographic section and extrapolated the plot-level FIA variables to the FIA unit and physiographic section levels. Landscape variables were recalculated within each unit and section using NCLD imagery resampled to a 400 m pixel size. I used regression trees (FIA unit scale) and general linear models (GLM, physiographic section scale) to relate spatial variations in bird abundance to the forest and landscape variables. I examined temporal relationships between the BBS and FIA data between 1966 and 2000. I developed 13 forest variables from statistical summary reports for 4 FIA inventory cycles (1965, 1975, 1989, and 2000) within NY, PA, MD, and WV. I used linear interpolation to estimate annual values of each FIA variable between successive inventory cycles and GLMs to relate annual variations in bird abundance to the forest variables. At the BBS route scale, the CART models accounted for > 50% of the variation in bird presence-absence and abundance. The logistic regression models had sensitivity and specificity rates > 0.50. By incorporating the variables selected for the models developed within each buffer (100m, 1km, and 10km) around the BBS routes into a multiscale model, I was able to further improve the performance of many of the models and gain additional insight regarding the contribution of multiscale influences on bird-habitat relationships. The majority of the best CART models tended to be the multiscale models, and many of the multiscale logistic models had greater sensitivity and specificity than their single-scale counter parts. The relatively fine resolution and extensive coverage of the BBS, FIA, and NLCD datasets coupled with the overlapping multiscale approach of these analyses allowed me to incorporate levels of variation in both habitat and bird occurrence and abundance into my models that likely represented a more comprehensive range of ecological variability in the bird-habitat relationships relative to studies conducted at smaller scales and/or using data at coarser resolutions. At the FIA unit and physiographic section scales, the regression trees accounted for an average of 54.1% of the variability in bird abundance among FIA units, and the GLMs accounted for an average of 66.3% of the variability among physiographic sections. However, increasing the observational and analytical scale to the FIA unit and physiographic section decreased the measurement resolution of the bird abundance and landscape variables. This limits the applicability and interpretive strength of the models developed at these scales, but they may serve as indices to those habitat components exerting the greatest influences on bird abundance at these broader scales. The GLMs relating average annual bird abundance to annual estimates of forest variables developed using statistical report data from the 1965, 1975, 1989, and 2000 FIA inventories explained an average of 62.0% of the variability in annual bird abundance estimates. However, these relationships were a function of both the general habitat characteristics and the trends in bird abundance specific to the 4-state region (MD, NY, PA, and WV) used for these analyses and may not be applicable to other states or regions. The small suite of variables available from the FIA statistical reports and multicollinearity among all forest variables further limited the applicability of these models. As with those developed at the FIA unit and physiographic sections scales, these models may serve as general indices to the habitat components exerting the greatest influences on bird abundance trends through time at regional scales. These results demonstrate that forest variables developed from the FIA, in conjunction with landscape variables, can explain variations in occupancy and abundance estimated from BBS data for forest bird species with a variety of habitat requirements across spatial and temporal scales. / Ph. D.

El caos distribucional fue introducido por Schweizer y Smítal en [SS94] a partir de la noción de caos de Li-Yorke con el fín de implicar la entropía topológica positiva para aplicaciones del intervalo compacto en sí mismo. El caos distribucional para operadores fue estudiado por primera vez en [Opr06] y fue analizado en el contexto lineal de dimensión infinita en [MGOP09]. El concepto de caos distribucional para un operador (semigrupo) consiste en la existencia de un conjunto no numerable y un numero real positivo ¿ tal que para dos elementos distintos cualesquiera del conjunto no numerable, tanto la densidad superior del conjunto de iteraciones (tiempos) en las cuales la diferencia entre las órbitas de dichos elementos es mayor que ¿, como la densidad superior del conjunto de iteraciones (tiempos) en las cuales dicha diferencia es tan pequeña como se quiera, es igual a uno. Esta tesis est'a dividida en seis capítulos. En el primero, hacemos un resumen del estado actual de la teoría de la din'amica caótica para C0-semigrupos de operadores lineales. En el segundo capítulo, mostramos la equivalencia entre el caos distribucional de un C0-semigrupo y el caos distribucional de cada uno de sus operadores no triviales. Tambi'en caracterizamos el caos distribucional de un C0-semigrupo en t'erminos de la existencia de un vector distribucionalmente irregular. La noción de hiperciclicidad de un operador (semigrupo) consiste en la existencia de un elemento cuya órbita por el operador (semigrupo) sea densa. Si adem'as el conjunto de puntos periódicos es denso, diremos que el operador (semigrupo) es caótico en el sentido de Devaney. Una de las herramientas mas útiles para comprobar si un operador es hipercíclico es el Criterio de Hiperciclicidad, enunciado inicialmente por Kitai en 1982. En [BBMGP11], Bermúdez, Bonilla, Martínez-Gim'enez y Peris presentan elCriterio para Caos Distribucional (CDC en ingl'es) para operadores. Enunciamos y probamos una versión del CDC para C0-semigrupos. En el contexto de C0-semigrupos, Desch, Schappacher y Webb tambi'en estudiaron en [DSW97] la hiperciclicidad y el caos de Devaney para C0-semigrupos, dando un criterio para caos de Devaney basado en el espectro del generador in¿nitesimal del C0- semigrupo. En el tercer capítulo, establecemos un criterio de existencia de una variedad distribucionalmente irregular densa (DDIM en sus siglas en ingl'es) en t'erminos del espectro del generador in¿nitesimal del C0-semigrupo. En el Capítulo 4, se dan algunas condiciones su¿cientes para que el C0-semigrupo de traslación en espacios L p ponderados sea distribucionalmente caótico en función de la función peso admisible. Ademas, establecemos una analogía completa entre el estudio del caos distribucional para el C0-semigrupo de traslación y para los operadores de desplazamiento hacia atras o ¿backward shifts¿ en espacios ponderados de sucesiones. El capítulo quinto está dedicado al estudio de la existencia de C0-semigrupos para los cuales todo vector no nulo es un vector distribucionalmente irregular. Tambi'en damos un ejemplo de uno de dichos C0-semigrupos que además no es hipercíclico. En el Capítulo 6, el criterio DDIM se aplica a varios ejemplos de C0-semigrupos. Algunos de ellos siendo los semigrupos de solución de ecuaciones en derivadas parciales, como la ecuación hiperbólica de transferencia de calor o la ecuación de von Foerster-Lasota y otros son la solución de un sistema in¿nito de ecuaciones diferenciales ordinarias usado para modelizar la dinámica de una población de c'elulas bajo proliferación y maduración simultáneas. / Barrachina Civera, X. (2013). Distributional chaos of C0-semigroups of operators [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/28241 / Premios Extraordinarios de tesis doctorales

Die Personalausauswahl an Universitäten ist von hoher Relevanz. Die vorliegende Disseratation beschäftigt sich mit den Auswahlprozessen von Studierenden, Promovierenden und Postdocs und den Berufungsverfahren von Professor:innen. Der Fokus liegt auf drei elementaren Punkten der Prozesse: Verwendungshäufigkeit, Kriteriumsvalidität und Akzeptanz. Die Arbeit beantwortet die Fragen, welche Verfahren bei der Personalauswahl an Universitäten genutzt werden, wie gut sich mit verschiedenen Verfahren und Konstrukten der Erfolg von Studierenden, Promovierenden und Postdocs, und Professor:innen vorhersagen lässt und wie akzeptiert verschiedene Verfahren bei Personalauswahlverfahren an Universitäten sind. In zwei eigenen Studien werden Forschungslücken geschlossen und neue Erkenntnisse der Literatur ergänzt. Für Studie 1 wurde bei N = 164 Promovierenden erhoben, wie diese tatsächlich ausgewählt wurden. Promotionsstellen wurden am häufigsten durch frei geführte Auswahlgespräche und persönliche Kontakte besetzt. Bei N = 170 potenziellen Bewerbenden für eine Promotionsstelle wurden die Akzeptanzurteile für Auswahlverfahren erfragt. Frei geführte Auswahlgespräche, berufliche Erfahrungen, Arbeitsproben und strukturierte Auswahlgespräche erhielten die höchsten Akzeptanzwerte. Studie 2 beleuchtet die Kriteriumsvalidität und identifizierte Prädiktoren, die in einem Längsschnittdesign sowohl den objektiven als auch den subjektiven Laufbahnerfolg zwei Jahre nach Abschluss der Promotion bei N = 2 104 erfolgreich Promovierten vorhersagen konnten. Die Big Five Persönlichkeitseigenschaften Offenheit für neue Erfahrungen und Neurotizismus waren Prädiktoren für objektiven Laufbahnerfolg. Verträglichkeit und Neurotizismus konnten unterschiedliche Aspekte von subjektivem Laufbahnerfolg vorhersagen. Darüber hinaus konnte mittels Response Surface Analysen ein Persönlichkeits-Anforderungs-Fit in Offenheit für neue Erfahrungen und Extraversion objektiven Laufbahnerfolg vorhersagen. / The selection of personnel at universities is of great relevance. This dissertation deals with the selection processes of students, doctoral candidates, and postdocs and professors. The focus is on three elementary points of the processes: frequency of use, criterion validity, and acceptance. The work answers the questions of which procedures are used in the selection of personnel at universities, how well the success of students, doctoral candidates and postdocs, and professors can be predicted with different selection methods and how different selection methods in personnel selection procedures are accepted at universities. In two of our own studies, existing research gaps are closed, and the state of the literature is supplemented with new findings. For Study 1 N = 164 doctoral candidates were asked how they were selected. Doctoral positions were most often filled through unstructured selection interviews and personal contacts. N = 170 potential applicants for a doctoral position were asked about the acceptance ratings for selection procedures. Unstructured interviews, professional experience, work samples, and structured interviews had the highest ratings in acceptance. Study 2 focuses on the criterion validity and identified predictors that, in a longitudinal design, were able to predict both the objective and the subjective career success two years after completing the doctorate in N = 2 104 successful doctoral graduates. Two of the Big Five personality traits, openness to new experiences and neuroticism, were predictors for objective career success. Agreeableness and neuroticism could predict different aspects of subjective career success. In addition, a personality-requirement fit in openness to new experiences and extraversion was able to predict objective career success using response surface analysis.

The main objective of the thesis was to investigate the feasibility of accurately and precisely fore- casting the number of both national and provincial bene ciaries of social security grants in South Africa, using simple autoregressive integrated moving average (ARIMA) models. The series of the monthly number of bene ciaries of the old age, child support, foster care and disability grants from April 2004 to March 2010 were used to achieve the objectives of the thesis. The conclusions from analysing the series were that: (1) ARIMA models for forecasting are province and grant-type spe- ci c; (2) for some grants, national forecasts obtained by aggregating provincial ARIMA forecasts are more accurate and precise than those obtained by ARIMA modelling national series; and (3) for some grants, forecasts obtained by modelling the latest half of the series were more accurate and precise than those obtained from modelling the full series. / Mathematical Sciences / M.Sc. (Statistics)

The term aggregation refers to overdispersion and both are used interchangeably in this thesis. In addressing the problem of prevalence of infectious parasite species faced by most rural livestock farmers, we model the distribution of faecal egg counts of 15 parasite species (13 internal parasites and 2 ticks) common in sheep and goats. Aggregation and excess zeroes is addressed through the use of generalised linear models. The abundance of each species was modelled using six different distributions: the Poisson, negative binomial (NB), zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), zero-altered Poisson (ZAP) and zero-altered negative binomial (ZANB) and their fit was later compared. Excess zero models (ZIP, ZINB, ZAP and ZANB) were found to be a better fit compared to standard count models (Poisson and negative binomial) in all 15 cases. We further investigated how distributional assumption a↵ects aggregation and zero inflation. Aggregation and zero inflation (measured by the dispersion parameter k and the zero inflation probability) were found to vary greatly with distributional assumption; this in turn changed the fixed-effects structure. Serial autocorrelation between adjacent observations was later taken into account by fitting observation driven time series models to the data. Simultaneously taking into account autocorrelation, overdispersion and zero inflation proved to be successful as zero inflated autoregressive models performed better than zero inflated models in most cases. Apart from contribution to the knowledge of science, predictability of parasite burden will help farmers with effective disease management interventions. Researchers confronted with the task of analysing count data with excess zeroes can use the findings of this illustrative study as a guideline irrespective of their research discipline. Statistical methods from model selection, quantifying of zero inflation through to accounting for serial autocorrelation are described and illustrated. / Statistics / M.Sc. (Statistics)

The main objective of the thesis was to investigate the feasibility of accurately and precisely fore- casting the number of both national and provincial bene ciaries of social security grants in South Africa, using simple autoregressive integrated moving average (ARIMA) models. The series of the monthly number of bene ciaries of the old age, child support, foster care and disability grants from April 2004 to March 2010 were used to achieve the objectives of the thesis. The conclusions from analysing the series were that: (1) ARIMA models for forecasting are province and grant-type spe- ci c; (2) for some grants, national forecasts obtained by aggregating provincial ARIMA forecasts are more accurate and precise than those obtained by ARIMA modelling national series; and (3) for some grants, forecasts obtained by modelling the latest half of the series were more accurate and precise than those obtained from modelling the full series. / Mathematical Sciences / M.Sc. (Statistics)

The characterization of the Markan disciples has been and continues to be the object of much scholarly reflection and speculation. For many, the Markan author's presentation of Jesus' disciples holds a key, if not the key, to unlocking the purpose and function of the gospel as a whole. Commentators differ as to whether the Markan disciples ultimately serve a pedagogical or polemical function, yet they are generally agreed that the disciples in Mark come off rather badly, especially when compared to their literary counterparts in Matthew, Luke, and John. This narrative-critical study considers the characterization of the Markan disciples within the Sea Crossing movement (Mark 4:1-8:30). While commentators have, on the whole, interpreted the disciples' negative characterization in this movement in terms of lack of faith and/or incomprehension, neither of these, nor a combination of the two, fully accounts for the severity of language leveled against the disciples by the narrator (6:52) and Jesus (8:17-18). Taking as its starting point an argument by Jeffrey B. Gibson (1986) that the harshness of Jesus' rebuke in Mark 8:14-21 is occasioned not by the disciples' lack of faith or incomprehension but by their active resistance to his Gentile mission, this investigation uncovers additional examples of the disciples' resistance to Gentile mission, offering a better account of their negative portrayal within the Sea Crossing movement and helping explain many of their other failures. In short, this study argues that in Mark 4:1-8:26, the disciples are characterized as resistant to Jesus' Gentile mission and to their participation in that mission, the chief consequence being that they are rendered incapable of recognizing Jesus' vocational identity as Israel's Messiah (Thesis A). This leads to a secondary thesis, namely, that in Mark 8:27-30, Peter's recognition of Jesus' messianic identity indicates that the disciples have finally come to accept Jesus' Gentile mission and their participation in it (Thesis B). Chapter One: Introduction: offers a selective review of scholarly treatments of the Markan disciples, which shows that few scholars attribute resistance, let alone purposeful resistance, to the disciples. Chapter Two: The Rhetoric of Repetition: introduces the methodological tools, concepts, and perspectives employed in the study. It includes a section on narrative criticism, which focuses upon the story-as-discoursed and the implied author and reader, and a section on Construction Grammar, a branch of cognitive linguistics founded by Charles Fillmore and further developed by Paul Danove, which focuses upon semantic and narrative frames and case frame analysis. Chapter Three: The Sea Crossing Movement, Mark 4:1-8:30: addresses the question of Markan structure and argues that Mark 4:1-8:30 comprises a single, unified, narrative movement, whose action and plot is oriented to the Sea of Galilee and whose most distinctive feature is the network of sea crossings that transport Jesus and his disciples back and forth between Jewish and Gentile geopolitical spaces. Following William Freedman, Chapter Four: The Literary Motif: introduces two criteria (frequency and avoidability) for determining objectively what constitutes a literary motif and provides the methodological basis and starting point for the analyses performed in chapters five and six. Chapter Five: The Sea Crossing Motif: establishes and then carries out a lengthy narrative analysis of the Sea Crossing motif, which is oriented around Mark's use of ‎θάλασσα (thalassa) and πλοῖον (ploion), and Chapter Six: The Loaves Motif: does the same for The Loaves motif, oriented around Mark's use of ἄρτος (artos). Finally, Chapter Seven: The Narrative Logic of the Disciples (In)comprehension: draws together all narrative, linguistic, and exegetical insights of the previous chapters and offers a single coherent reading of the Sea Crossing movement that establishes Theses A and B.

Survival analytic methods help to analyze lifetime data arising from medical and reliability experiments. The popular proportional hazards model, proposed by Cox (1972), is widely used in survival analysis to study the effect of risk factors on lifetimes. An important assumption in regression type analysis is that all relative risk factors should be included in the model. However, not all relative risk factors are observed due to measurement difficulty, inaccessibility, cost considerations, and so on. These unobservable risk factors can be modelled by the so-called frailty model, originally introduced by Vaupel et al. (1979). Furthermore, the frailty model is also applicable to clustered data. Cluster data possesses the feature that observations within the same cluster share similar conditions and environment, which are sometimes difficult to observe. For example, patients from the same family share similar genetics, and patients treated in the same hospital share the same group of profes- sionals and same environmental conditions. These factors are indeed hard to quantify or measure. In addition, this type of similarity introduces correlation among subjects within clusters. In this thesis, a semi-parametric frailty model is proposed to address aforementioned issues. The baseline hazards function is approximated by a piecewise constant function and the frailty distribution is assumed to be a Birnbaum-Saunders distribution. Due to the advancement in modern medical sciences, many diseases are curable, which in turn leads to the need of incorporating cure proportion in the survival model. The frailty model discussed here is further extended to a mixture cure rate frailty model by integrating the frailty model into the mixture cure rate model proposed originally by Boag (1949) and Berkson and Gage (1952). By linking the covariates to the cure proportion through logistic/logit link function and linking observable covariates and unobservable covariates to the lifetime of the uncured population through the frailty model, we obtain a flexible model to study the effect of risk factors on lifetimes. The mixture cure frailty model can be reduced to a mixture cure model if the effect of frailty term is negligible (i.e., the variance of the frailty distribution is close to 0). On the other hand, it also reduces to the usual frailty model if the cure proportion is 0. Therefore, we can use a likelihood ratio test to test whether the reduced model is adequate to model the given data. We assume the baseline hazard to be that of Weibull distribution since Weibull distribution possesses increasing, constant or decreasing hazard rate, and the frailty distribution to be Birnbaum-Saunders distribution. D ́ıaz-Garc ́ıa and Leiva-Sa ́nchez (2005) proposed a new family of life distributions, called generalized Birnbaum-Saunders distribution, including Birnbaum-Saunders distribution as a special case. It allows for various degrees of kurtosis and skewness, and also permits unimodality as well as bimodality. Therefore, integration of a generalized Birnbaum-Saunders distribution as the frailty distribution in the mixture cure frailty model results in a very flexible model. For this general model, parameter estimation is carried out using a marginal likelihood approach. One of the difficulties in the parameter estimation is that the likelihood function is intractable. The current technology in computation enables us to develop a numerical method through Monte Carlo simulation, and in this approach, the likelihood function is approximated by the Monte Carlo method and the maximum likelihood estimates and standard errors of the model parameters are then obtained numerically by maximizing this approximate likelihood function. An EM algorithm is also developed for the Birnbaum-Saunders mixture cure frailty model. The performance of this estimation method is then assessed by simulation studies for each proposed model. Model discriminations is also performed between the Birnbaum-Saunders frailty model and the generalized Birnbaum-Saunders mixture cure frailty model. Some illustrative real life examples are presented to illustrate the models and inferential methods developed here. / Thesis / Doctor of Science (PhD)

Cure rate models, introduced by Boag (1949), are very commonly used while modelling lifetime data involving long time survivors. Applications of cure rate models can be seen in biomedical science, industrial reliability, finance, manufacturing, demography and criminology. In this thesis, cure rate models are discussed under a competing cause scenario, with the assumption of proportional odds (PO) lifetime distributions for the susceptibles, and statistical inferential methods are then developed based on right-censored data. In Chapter 2, a flexible cure rate model is discussed by assuming the number of competing causes for the event of interest following the Conway-Maxwell (COM) Poisson distribution, and their corresponding lifetimes of non-cured or susceptible individuals can be described by PO model. This provides a natural extension of the work of Gu et al. (2011) who had considered a geometric number of competing causes. Under right censoring, maximum likelihood estimators (MLEs) are obtained by the use of expectation-maximization (EM) algorithm. An extensive Monte Carlo simulation study is carried out for various scenarios, and model discrimination between some well-known cure models like geometric, Poisson and Bernoulli is also examined. The goodness-of-fit and model diagnostics of the model are also discussed. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. Next, in Chapter 3, the destructive cure rate models, introduced by Rodrigues et al. (2011), are discussed under the PO assumption. Here, the initial number of competing causes is modelled by a weighted Poisson distribution with special focus on exponentially weighted Poisson, length-biased Poisson and negative binomial distributions. Then, a damage distribution is introduced for the number of initial causes which do not get destroyed. An EM-type algorithm for computing the MLEs is developed. An extensive simulation study is carried out for various scenarios, and model discrimination between the three weighted Poisson distributions is also examined. All the models and methods of estimation are evaluated through a simulation study. A cutaneous melanoma dataset example is used to illustrate the models as well as the inferential methods. In Chapter 4, frailty cure rate models are discussed under a gamma frailty wherein the initial number of competing causes is described by a Conway-Maxwell (COM) Poisson distribution in which the lifetimes of non-cured individuals can be described by PO model. The detailed steps of the EM algorithm are then developed for this model and an extensive simulation study is carried out to evaluate the performance of the proposed model and the estimation method. A cutaneous melanoma dataset as well as a simulated data are used for illustrative purposes. Finally, Chapter 5 outlines the work carried out in the thesis and also suggests some problems of further research interest. / Thesis / Doctor of Philosophy (PhD)

A device that is accompanied by an irreversible chemical reaction or physical destruction and could no longer function properly after performing its intended function is referred to as a one-shot device. One-shot device test data differ from typical data obtained by measuring lifetimes in standard life-tests. Due to the very nature of one-shot devices, actual lifetimes of one-shot devices under test cannot be observed, and they are either left- or right-censored. In addition, a one-shot device often has multiple components that could cause the failure of the device. The components are coupled together in the manufacturing process or assembly, resulting in the failure modes possessing latent heterogeneity and dependence. Frailty models enable us to describe the influence of common, but unobservable covariates, on the hazard function as a random effect in a model and also provide an easily understandable interpretation. In this thesis, we develop some inferential results for one-shot device testing data with gamma frailty model. We first develop an efficient expectation-maximization (EM) algorithm for determining the maximum likelihood estimates of model parameters of a gamma frailty model with exponential lifetime distributions for components based on one-shot device test data with multiple failure modes, wherein the data are obtained from a constant-stress accelerated life-test. The maximum likelihood estimate of the mean lifetime of $k$-out-of-$M$ structured one-shot devices under normal operating conditions is also presented. In addition, the asymptotic variance–covariance matrix of the maximum likelihood estimates is derived, which is then used to construct asymptotic confidence intervals for the model parameters. The performance of the proposed inferential methods is finally evaluated through Monte Carlo simulations and then illustrated with a numerical example. A gamma frailty model with Weibull baseline hazards is considered next for fitting one-shot device testing data. The Weibull baseline hazards enable us to analyze time-varying failure rates more accurately, allowing for a deeper understanding of the dynamic nature of system's reliability. We develop an EM algorithm for estimating the model parameters utilizing the complete likelihood function. A detailed simulation study evaluates the performance of the Weibull baseline hazard model with that of the exponential baseline hazard model. The introduction of shape parameters in the component's lifetime distribution within the Weibull baseline hazard model offers enhanced flexibility in model fitting. Finally, Bayesian inference is then developed for the gamma frailty model with exponential baseline hazard for one-shot device testing data. We introduce the Bayesian estimation procedure using Markov chain Monte Carlo (MCMC) technique for estimating the model parameters as well as for developing credible intervals for those parameters. The performance of the proposed method is evaluated in a simulation study. Model comparison between independence model and the frailty model is made using Bayesian model selection criterion. / Thesis / Candidate in Philosophy