Accelerated degradation tests planning with competing failure modes

Accelerated degradation tests (ADT) have been widely used to assess the reliability of products with long lifetime. For many products, environmental stress not only accelerates their degradation rate but also elevates the probability of traumatic shocks. When random traumatic shocks occur during an ADT, it is possible that the degradation measurements cannot be taken afterward, which brings challenges to reliability assessment. In this paper, we propose an ADT optimization approach for products suffering from both degradation failures and random shock failures. The degradation path is modeled by a Wiener process. Under various stress levels, the arrival process of random shocks is assumed to follow a nonhomogeneous Poisson process. Parameters of acceleration models for both failure modes need to be estimated from the ADT. Three common optimality criteria based on the Fisher information are considered and compared to optimize the ADT plan under a given number of test units and a predetermined test duration. Optimal two- and three-level optimal ADT plans are obtained by numerical methods. We use the general equivalence theorems to verify the global optimality of ADT plans. A numerical example is presented to illustrate the proposed methods. The result shows that the optimal ADT plans in the presence of random shocks differ significantly from the traditional ADT plans. Sensitivity analysis is carried out to study the robustness of optimal ADT plans with respect to the changes in planning input

Modified weibull distributions in reliability engineering

Ph.DDOCTOR OF PHILOSOPH

Order-statistics-based inferences for censored lifetime data and financial risk analysis

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis focuses on applying order-statistics-based inferences on lifetime analysis and financial risk measurement. The first problem is raised from fitting the Weibull distribution to progressively censored and accelerated life-test data. A new orderstatistics- based inference is proposed for both parameter and con dence interval estimation. The second problem can be summarised as adopting the inference used in the first problem for fitting the generalised Pareto distribution, especially when sample size is small. With some modifications, the proposed inference is compared with classical methods and several relatively new methods emerged from recent literature. The third problem studies a distribution free approach for forecasting financial volatility, which is essentially the standard deviation of financial returns. Classical models of this approach use the interval between two symmetric extreme quantiles of the return distribution as a proxy of volatility. Two new models are proposed, which use intervals of expected shortfalls and expectiles, instead of interval of quantiles. Different models are compared with empirical stock indices data. Finally, attentions are drawn towards the heteroskedasticity quantile regression. The proposed joint modelling approach, which makes use of the parametric link between the quantile regression and the asymmetric Laplace distribution, can provide estimations of the regression quantile and of the log linear heteroskedastic scale simultaneously. Furthermore, the use of the expectation of the check function as a measure of quantile deviation is discussed

Planning and inference of sequential accelerated life tests

Ph.DDOCTOR OF PHILOSOPH

Inferencia estadística robusta basada en divergencias para dispositivos de un sólo uso

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 30-06-2021A one-shot device is a unit that performs its function only once and, after use, the device either gets destroyed or must be rebuilt. For this kind of device, one can only know whether the failure time is either before or after a speci c inspection time, and consequently the lifetimes are either left- or right-censored, with the lifetime being less than the inspection time if the test outcome is a failure (resulting in left censoring) and the lifetime being more than the inspection time if the test outcome is a success (resulting in right censoring). An accelerated life test (ALT) plan is usually employed to evaluate the reliability of such products by increasing the levels of stress factors and then extrapolating the life characteristics from high stress conditions to normal operating conditions. This acceleration process will shorten the life span of devices and reduce the costs associated with the experiment. The study of one-shot device from ALT data has been developed considerably recently, mainly motivated by the work of Fan et al. [2009]...Los dispositivos de un solo uso (one shot devices en ingles), son aquellos que, una vez usados, dejan de funcionar. La mayor dificultad a la hora de modelizar su tiempo de vida es que solo se puede saber si el momento de fallo se produce antes o despues de un momento específico de inspeccion. As pues, se trata de un caso extremo de censura intervalica: si el tiempo de vida es inferior al de inspeccion observaremos un fallo (censura por la izquierda), mientras que si el tiempo de vida es mayor que el tiempo de inspeccion, observaremos un exito (censura por la derecha). Para la observacion y modelizacion de este tipo de dispositivos es comun el uso de tests de vida acelerados. Los tests de vida acelerados permiten evaluar la fiabilidad de los productos en menos tiempo, incrementando las condiciones a las que se ven sometidos los dispositivos para extrapolar despues estos resultados a condiciones mas normales. El estudio de los dispositivos de un solo uso por medio de tests de vida acelerados se ha incrementado considerablemente en los ultimos a~nos motivado, principalmente, por el trabajo de Fan et al. [2009]...Fac. de Ciencias MatemáticasTRUEunpu