In reliability studies, the goal is to gain knowledge about a product's failure times or life expectancy. Precedence tests do not require large sample sizes and are used in reliability studies to compare the life-time distributions from two samples. Precedence tests are useful since they provide reliable results early in a life-test and the surviving units can be used in other tests. Ng and Balakrishnan (2010) proposed a precedence-type test based on the Kaplan-Meier estimator of the cumulative distribution function. A precedence-type test based on the Nelson-Aalen estimator of the cumulative hazard function has been proposed. This test was developed for both Type-II right censoring and progressive Type-II right censoring. Numerical results, including illustrative examples, critical values and a power study have been provided. The results from this test were compared with those from the test based on the Kaplan-Meier estimator.

In reliability studies, the goal is to gain knowledge about a product's failure times or life expectancy. Precedence tests do not require large sample sizes and are used in reliability studies to compare the life-time distributions from two samples. Precedence tests are useful since they provide reliable results early in a life-test and the surviving units can be used in other tests. Ng and Balakrishnan (2010) proposed a precedence-type test based on the Kaplan-Meier estimator of the cumulative distribution function. A precedence-type test based on the Nelson-Aalen estimator of the cumulative hazard function has been proposed. This test was developed for both Type-II right censoring and progressive Type-II right censoring. Numerical results, including illustrative examples, critical values and a power study have been provided. The results from this test were compared with those from the test based on the Kaplan-Meier estimator.

En raison de leurs performances en termes de densités énergétiques et de puissance, les batteries Li-ion sont les systèmes de stockage électrique privilégiés pour les nouvelles générations de véhicules électriques. Leur modélisation est indispensable pour fournir une évaluation de leurs performances tout au long de leur durée de vie tout en limitant le nombre d'essais expérimentaux, et ceci dans le but de concevoir des configurations et des gestions optimales des packs batteries pour une application envisagée. Le but de ce travail consiste à proposer un modèle physique capable de prédire le comportement et le vieillissement de la batterie sous différentes conditions. Un modèle simplifié électrochimique et thermique capable de prédire le comportement physicochimique et le vieillissement de batteries Li-ion a été étudié. Une analyse de sensibilité a été menée sur l'ensemble des paramètres du modèle dans différentes conditions afin de mettre en évidence leurs influences sur les sorties du modèle. Sur cette base, une méthode d'identification a été proposée pour préserver une indépendance des résultats de l'identification paramétrique par rapport à la sensibilité des paramètres. Cette méthode a permis d'améliorer les prédictions de vieillissement avec des estimations très proches des résultats expérimentaux. Au-delà des gains en compréhension et prédiction, ce modèle physique ouvre de nouvelles possibilités pour établir des protocoles de vieillissement accélérés. / Due to their high power and energy densities, Li-ion batteries are the leading systems for the new generations of electric vehicles, for which an optimum cell design, management and configuration is essential. Modeling provides tools to perform complex analysis of the performance of Li-ion batteries and reduces the amount of time spent on experimental testing. The aim of our research is to propose a physics-based model that can predict battery behavior and aging under various conditions during the entire lifespan. A simplified electrochemical and thermal model that can predict both physicochemical and aging behaviors of Li-ion batteries has been studied. A sensitivity analysis of all its physical parameters has been performed in order to find out their influence on the model outputs based on simulations under various conditions. The results gave hints on whether a parameter needs particular attention when measured or identified and on the conditions under which it is the most sensitive. A specific simulation profile has been designed for parameters involved in aging equations in order to determine their sensitivity. Finally, a step-wise method has been followed to limit the influence of parameter values when identifying sorne of them. This sensitivity analysis and the subsequent step-wise identification method show very good results, such as a better fitting of the experimental data with simulated cell voltage. Beyond advanced comprehension and prediction, this physical model opens new possibilities to define accelerated aging tests.

För att verifiera att komponenter håller under en förväntad livslängd kan en Accelererad Livstids Testning (ALT) användas. En av huvudaspekterna som kan förstöra ett ALT-test av plastkomponenter är om kontakttemperaturen överstiger glasövergångstemperaturen. Detta eftersom det förändrar testkomponentens materialegenskaper. För att förhindra att detta inträffar i en ALT byggdes en testrigg medtemperatursensorer för att övervaka kontakttemperaturen. Om kontaktpunkten modifieras med en temperatursensor förändrar det uppbyggnaden av ytan och gör testet ogiltigt. Metoden som används är istället att mäta temperaturen på ytan på testdelen och simulera kontakttemperaturen med en modell baserad på den Finita Elementmetoden. Denna avhandling jämför de två teknikerna Tunn Film RTD och Tunn Termoelement Tråd Typ T i samband med uppbyggnaden av en värmeöverföring FEM-modell. Det undersöktes också vilken teknologi av IR-enpunkts sensor och Tunn Film RTD som har högst prestanda med avseende på fyra kvalitetsparametrar under användning tillsammans med testriggen. Slutsatserna är att Tunn Film RTD och Tunn Termoelement Tråd av Typ T sensorerna båda ger en liknande precision i mätningar för att bygga en användbar FEM-modell. När de används på testriggen presterar Film RTD:n är bättre än IR-sensorn i tre av fyra områden med avseende på de fyra definierade kvalitetsparametrarna. Tunn Film RTD är den rekommenderade teknologin för denna typ av mätning. / To verify that components last for an expected lifetime an Accelerated Life Testing (ALT) can be used. One of the main aspects that can ruin an ALT of plastic components is if the contact temperature rises above the glass transition temperature, since this changes the material properties of the tested component. To prevent this from occurring in a ALT, a test rig was built with temperature sensors to monitor this contact temperature. If the contact point is modified with a temperature sensor, this will change the surface and make the test invalid. The method is instead to couple surface temperature measurements with a Finite Element Model (FEM) to estimate the contact temperature. This thesis compares the two techniques Thin Film RTD and Thin Thermocouple Wire Type T in conjunction with the building of a heat transfer Finite Element Method (FEM)-model. It also investigates which technology of Non Contact IR Single Point sensor or Thin Film RTD have the highest performance in use with the test rig with regard to four quality parameters. The conclusions are that RTD and the Thermocouple Type T sensors both provide equal precision in measurement to build a useful FEM model. In application on the test rig, the Thin Film RTD is better than the Infrared (IR)-sensor in three out of four areas when compared in the four defined quality parameters. Thin Film RTD is the recommended technology in this application.

Researchers conduct life testing on objects of interest in an attempt to determine their life distribution as a means of studying their reliability (or survivability). Determining the life distribution of the objects under study helps manufacturers to identify potential faults, and to improve quality. Researchers sometimes conduct accelerated life tests (ALTs) to ensure that failure among the tested units is earlier than what could result under normal operating (or environmental) conditions. Moreover, such experiments allow the experimenters to examine the effects of high levels of one or more stress factors on the lifetimes of experimental units. Examples of stress factors include, but not limited to, cycling rate, dosage, humidity, load, pressure, temperature, vibration, voltage, etc. A special class of ALT is step-stress accelerated life testing. In this type of experiments, the study sample is tested at initial stresses for a given period of time. Afterwards, the levels of the stress factors are increased in agreement with prefixed points of time called stress-change times. In practice, time and resources are limited; thus, any experiment is expected to be constrained to a deadline which is called a termination time. Hence, the observed information may be subjected to Type-I censoring. This study discusses maximum likelihood inferential methods for the parameters of multiple step-stress models from a generalized Birnbaum-Saunders distribution under time constraint alongside other inference-related problems. A couple of general inference frameworks are studied; namely, the observed likelihood (OL) framework, and the expectation-maximization (EM) framework. The last-mentioned framework is considered since there is a possibility that Type-I censored data are obtained. In the first framework, the scoring algorithm is used to get the maximum likelihood estimators (MLEs) for the model parameters. In the second framework, EM-based algorithms are utilized to determine the required MLEs. Obtaining observed information matrices under both frameworks is also discussed. Accordingly, asymptotic and bootstrap-based interval estimators for the model parameters are derived. Model discrimination within the considered generalized Birnbaum-Saunders distribution is carried out by likelihood ratio test as well as by information-based criteria. The discussed step-stress models are illustrated by analyzing three real-life datasets. Accordingly, establishing optimal multiple step-stress test plans based on cost considerations and three optimality criteria is discussed. Since maximum likelihood estimators are obtained by numerical optimization that involves maximizing some objective functions, optimization methods used, and their software implementations in R are discussed. Because of the computational aspects are in focus in this study, the benefits of parallel computing in R, as a high-performance computational approach, are briefly addressed. Numerical examples and Monte Carlo simulations are used to illustrate and to evaluate the methods presented in this thesis. / Thesis / Doctor of Science (PhD)

Ces dernières années, la technologie RFID (identification par radiofréquence) s’est fortement développée dans de nombreuses applications industrielles parmi lesquelles les secteurs de l’aéronautique et l’automobile où il y a une forte demande en systèmes d’auto-identification fonctionnant dans des environnements difficiles. Dans ce contexte, l'objectif de ces travaux de thèse est d'étudier les effets du stockage thermique sur la fiabilité des tags RFID UHF passifs. Pour ce faire nous avons adopté une méthodologie homogène contribuant de façon significative à atteindre nos objectifs. La première étape de cette méthodologie consistait à choisir le tag à tester, deux types de tags Web et Tageos provenant de deux fabricants différents ont été soumis à des tests de vieillissement accélérés sous différentes températures. La deuxième étape était de définir les paramètres des tests de vieillissement et de caractériser les tags vieillis. À l'aide d'un banc de mesure dédié, la puissance réfléchie par l’ensemble des tags vieillis est mesurée après chaque phase de vieillissement en fonction de la distance entre l’antenne du tag et celle du lecteur RFID. La puissance réfléchie diminue considérablement après chaque phase de vieillissement avec différentes dynamiques de dégradation pour tous les tags vieillis. Cette dynamique de dégradation dépend du type de tag testé et de la température de test. La dernière étape de la méthodologie comportait l’analyse statistique et physique de défaillance, des différences claires dans les modes, les mécanismes et les temps de défaillance entre les tags Web et Tageos ont été observées. L’analyse physique de défaillance par microscopie optique et MEB a révélé des fissures dans les conducteurs métalliques de l'antenne pour une partie des tags vieillis, cependant pour l’autre partie des tags, aucune défaillance de l'antenne n'a été observée. Des déformations au niveau de la matrice polymère de l'ACP ont été révélées, ce qui a modifié l'adaptation d'impédance entre le RFIC et l'antenne. Des simulations en utilisant le logiciel de modélisation multi-physique COMSOL a été mise en place dans le but de reproduire les mécanismes de défaillances révélés expérimentalement soit au niveau de l’antenne ou de la RFIC. Ces travaux de thèse ont démontré l'importance d'étudier les effets du stockage en haute température sur la fiabilité des tags RFID passifs. Les défaillances sont apparues plus rapidement et les tests ont coûté considérablement moins onéreux par rapport aux autres types de tests de vieillissement accélérés. / Nowadays, RFID has strongly developed in many industrial applications, including the aeronautics and automotive sectors, where there is a strong demand for auto-identification systems operating in severe environments. In this context, the objective of this thesis is to study the effects of thermal storage on the reliability of passive UHF RFID tags. To achieve this, we adopted a consistent methodology. The first step of this methodology was to choose the tag under test. Two types of tags Web and Tageos from two different manufacturers are aged under high temperatures. The second step was to define the parameters of the aging tests and to characterize the aged tags. Using a dedicated measurement bench, the reflected power is measured after each aging phase for all tested tags to determine the power loss caused by the high temperature storage. Reflected power decrease significantly after each aging phase with different dynamics of degradation for all aged tags. This dynamics of degradation depends on the temperature test and the type of tag. The final step involved statistical and physical failure analysis. Clear differences about modes, mechanisms and failure times between Web and Tageos tags have been observed, it seems that Tageos tags are more reliable than Web tags. Failure analysis of the samples, using an optical microscope and SEM, has revealed, cracks in the antenna metallic conductors on a part of the aged tags. In another part of the tags, no failures in the antenna have been seen, but clear deformations at the polymer matrix of the ACP have been observed, thus changing the impedance matching between the RFIC and the antenna. Simulations using the COMSOL multiphysics software have been implemented in order to reproduce the experimental failure mechanisms. This thesis work has demonstrated the importance of studying the effects of high temperature storage on the reliability of passive RFID tags. Failures appeared faster and tests cost considerably less than other types of accelerated aging tests.

In this thesis, we develop some inferential results for one-shot device testing data analysis. These extend and generalize existing methods in the literature. First, a competing-risk model is introduced for one-shot testing data under accelerated life-tests. One-shot devices are products which will be destroyed immediately after use. Therefore, we can observe only a binary status as data, success or failure, of such products instead of its lifetime. Many one-shot devices contain multiple components and failure of any one of them will lead to the failure of the device. Failed devices are inspected to identify the specific cause of failure. Since the exact lifetime is not observed, EM algorithm becomes a natural tool to obtain the maximum likelihood estimates of the model parameters. Here, we develop the EM algorithm for competing exponential and Weibull cases. Second, a semi-parametric approach is developed for simple one-shot device testing data. Semi-parametric estimation is a model that consists of parametric and non-parametric components. For this purpose, we only assume the hazards at different stress levels are proportional to each other, but no distributional assumption is made on the lifetimes. This provides a greater flexibility in model fitting and enables us to examine the relationship between the reliability of devices and the stress factors. Third, Bayesian inference is developed for one-shot device testing data under exponential distribution and Weibull distribution with non-constant shape parameters for competing risks. Bayesian framework provides statistical inference from another perspective. It assumes the model parameters to be random and then improves the inference by incorporating expert's experience as prior information. This method is shown to be very useful if we have limited failure observation wherein the maximum likelihood estimator may not exist. The thesis proceeds as follows. In Chapter 2, we assume the one-shot devices to have two components with lifetimes having exponential distributions with multiple stress factors. We then develop an EM algorithm for developing likelihood inference for the model parameters as well as some useful reliability characteristics. In Chapter 3, we generalize to the situation when lifetimes follow a Weibull distribution with non-constant shape parameters. In Chapter 4, we propose a semi-parametric model for simple one-shot device test data based on proportional hazards model and develop associated inferential results. In Chapter 5, we consider the competing risk model with exponential lifetimes and develop inference by adopting the Bayesian approach. In Chapter 6, we generalize these results on Bayesian inference to the situation when the lifetimes have a Weibull distribution. Finally, we provide some concluding remarks and indicate some future research directions in Chapter 7. / Thesis / Doctor of Philosophy (PhD)

本文所探討的中心為貝氏模型運用於加速壽命試驗，並且假設受測項目之壽命服從Weibull分配。加速實驗環境有三種，其中第二種環境代表正常狀態，採用加速壽命試驗的方式涵蓋了三種：固定應力、漸進之逐步應力和變量曲線之逐步應力。對於先驗參數，並不是直接給予特定的值，而是透過專家評估，給定各種環境之下的產品可靠度之中位數或百分位數，再利用這些資訊經過數值運算解出先驗參數。資料的型態分成兩種，一為區間資料，另一為型一設限資料，透過蒙地卡羅法模擬出後驗分配，並且估計正常環境狀態的可靠度。 / This article develops a Bayes inference model for accelerated life testing assuming failure times at each stress level are Weibull distributed. Using the approach, there are three stressed to be used, and the three testing scenarios to be adapted are as follows：fixed-stress, progressive step-stress and profile step-stress. Prior information is used to indirectly define a multivariate prior distribution for the scale parameters at the various stress levels. The inference procedure accommodates both the interval data sampling strategy and type I censored sampling strategy for the collection of ALT test data. The inference procedure uses the well-known Markov Chain Monte Carlo methods to derive posterior approximations.

In this thesis, we investigate several inferential issues regarding the lifetime data from exponential distribution under different censoring schemes. For reasons of time constraint and cost reduction, censored sampling is commonly employed in practice, especially in reliability engineering. Among various censoring schemes, progressive Type-I censoring provides not only the practical advantage of known termination time but also greater flexibility to the experimenter in the design stage by allowing for the removal of test units at non-terminal time points. Hence, we first consider the inference for a progressively Type-I censored life-testing experiment with k uniformly spaced intervals. For small to moderate sample sizes, a practical modification is proposed to the censoring scheme in order to guarantee a feasible life-test under progressive Type-I censoring. Under this setup, we obtain the maximum likelihood estimator (MLE) of the unknown mean parameter and derive the exact sampling distribution of the MLE through the use of conditional moment generating function under the condition that the existence of the MLE is ensured. Using the exact distribution of the MLE as well as its asymptotic distribution and the parametric bootstrap method, we discuss the construction of confidence intervals for the mean parameter and their performance is then assessed through Monte Carlo simulations. Next, we consider a special class of accelerated life tests, known as step-stress tests in reliability testing. In a step-stress test, the stress levels increase discretely at pre-fixed time points and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. Here, we consider a k-step-stress accelerated life testing experiment with an equal step duration τ. In particular, the case of progressively Type-I censored data with a single stress variable is investigated. For small to moderate sample sizes, we introduce another practical modification to the model for a feasible k-step-stress test under progressive censoring, and the optimal τ is searched using the modified model. Next, we seek the optimal τ under the condition that the step-stress test proceeds to the k-th stress level, and the efficiency of this conditional inference is compared to the preceding models. In all cases, censoring is allowed at each change stress point iτ, i = 1, 2, ... , k, and the problem of selecting the optimal Tis discussed using C-optimality, D-optimality, and A-optimality criteria. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. Thus, we also consider the simple stepstress models under Type-I and Type-II censoring situations when the lifetime distributions corresponding to the different risk factors are independently exponentially distributed. Under this setup, we derive the MLEs of the unknown mean parameters of the different causes under the assumption of a cumulative exposure model. The exact distributions of the MLEs of the parameters are then derived through the use of conditional moment generating functions. Using these exact distributions as well as the asymptotic distributions and the parametric bootstrap method, we discuss the construction of confidence intervals for the parameters and then assess their performance through Monte Carlo simulations. / 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