Optimal Experimental Planning of Reliability Experiments Based on Coherent Systems

In industrial engineering and manufacturing, assessing the reliability of a product or system is an important topic. Life-testing and reliability experiments are commonly used reliability assessment methods to gain sound knowledge about product or system lifetime distributions. Usually, a sample of items of interest is subjected to stresses and environmental conditions that characterize the normal operating conditions. During the life-test, successive times to failure are recorded and lifetime data are collected. Life-testing is useful in many industrial environments, including the automobile, materials, telecommunications, and electronics industries. There are different kinds of life-testing experiments that can be applied for different purposes. For instance, accelerated life tests (ALTs) and censored life tests are commonly used to acquire information in reliability and life-testing experiments with the presence of time and resource limitations. Statistical inference based on the data obtained from a life test and effectively planning a life-testing experiment subject to some constraints are two important problems statisticians are interested in. The experimental design problem for a life test has long been studied; however, the experimental planning considering putting the experimental units into systems for a life-test has not been studied. In this thesis, we study the optimal experimental planning problem in multiple stress levels life-testing experiments and progressively Type-II censored life-testing experiments when the test units can be put into coherent systems for the experiment. Based on the notion of system signature, a tool in structure reliability to represent the structure of a coherent system, under different experimental settings, models and assumptions, we derive the maximum likelihood estimators of the model parameters and the expected Fisher information matrix. Then, we use the expected Fisher information matrix to obtain the asymptotic variance-covariance matrix of the maximum likelihood estimators when $n$-component coherent systems are used in the life-testing experiment. Based on different optimality criteria, such as $D$-optimality, $A$-optimality and $V$-optimality, we obtain the optimal experimental plans under different settings. Numerical and Monte Carlo simulation studies are used to demonstrate the advantages and disadvantages of using systems in life-testing experiments

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

Optimal Test Plan of Step Stress Partially Accelerated Life Testing for Alpha Power Inverse Weibull Distribution under Adaptive Progressive Hybrid Censored Data and Different Loss Functions

Accelerated life tests are used to explore the lifetime of extremely reliable items by subjecting them to elevated stress levels from stressors to cause early failures, such as temperature, voltage, pressure, and so on. The alpha power inverse Weibull (APIW) distribution is of great significance and practical applications due to its appealing characteristics, such as its flexibilities in the probability density function and the hazard rate function. We analyze the step stress partially accelerated life testing model with samples from the APIW distribution under adaptive type II progressively hybrid censoring. We first obtain the maximum likelihood estimates and two types of approximate confidence intervals of the distributional parameters and then derive Bayes estimates of the unknownparameters under different loss functions. Furthermore, we analyze three probable optimum test techniques for identifying the best censoring under different optimality criteria methods. We conduct simulation studies to assess the finite sample performance of the proposed methodology. Finally, we provide a real data example to further demonstrate the proposed technique

Planning Step-Stress Life Tests for the Generalized Rayleigh Distribution under Progressive Type-II Censoring with Binomial Removals

In this article, both the parameter estimation and optimal design problems of step-stress partially accelerated life test units whose lifetimes follow the generalized Rayleigh distribution are considered under progressive type-II censoring scheme with binomial removals. The maximum likelihood estimators of the scale and shape parameters as well as the acceleration factor are obtained. The concert of the estimators is assessed. In addition, approximate confidence intervals of the model parameters are constructed and their coverage probabilities are computed. Moreover, optimum test plans are also developed to improve/guarantee the quality of the statistical inference. Finally, simulation studies and a numerical example are provided for illustrative purposes.Рассмотрены параметр оценки и оптимальное проектирование частично ускоренных испытаний на долговечность при ступенчатой нагрузке на основе обобщенного рэлеевского распределения при прогрессивном цензурировании типа II с биномиальными выборками. В качестве фактора ускорения используются максимальные оценки вероятности параметров масштаба и формы, которые согласуются между собой. Построены приближенные доверительные интервалы параметров модели и рассчитаны границы вероятности. Разработаны оптимальные планы испытаний для улучшения статистического анализа. Предложены результаты моделирования и числовой пример.Розглянуто параметр оцінки і оптимальне проектування частково прискорених випробувань на довговічність при ступеневому навантаженні на основі узагальненого релеївського розподілу при прогресивному цензуруванні типу ІІ з біноміальними виборками. Як фактор прискорення використовуються максимальні оцінки імовірності параметрів масштабу і форми, які узгоджуються між собою. Побудовано наближені довірчі інтервали параметрів моделі і розраховано границі імовірності. Розроблено оптимальні плани випробувань із метою покращання статистичного аналізу. Запропоновано результати моделювання і числовий приклад

Planning progressive type-I interval censoring life tests with competing risks

[[abstract]]In this article, we investigate some reliability and quality problems when the competing risks data are progressive type-I interval censored with binomial removals. The failure times of the individual causes are assumed to be statistically independent and exponentially distributed with different parameters. We obtain the estimates of the unknown parameters through a maximum likelihood method, and also derive the Fisher's information matrix. The optimal lengths of the inspection intervals are determined under two different criteria. The reliability sampling plans are established under given producer's and customer's risks. A Monte Carlo simulation is conducted to evaluate the performance of the estimators, and also some numerical results are presented.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]電子

Bayesian Life Test Planning for the Log-Location-Scale Family of Distributions

This paper describes Bayesian methods for life test planning with censored data from a log-location-scale distribution, when prior information of the distribution parameters is available. We use a Bayesian criterion based on the estimation precision of a distribution quantile. A large sample normal approximation gives a simplified, easy-tointerpret, yet valid approach to this planning problem, where in general no closed form solutions are available. To illustrate this approach, we present numerical investigations using the Weibull distribution with Type II censoring. We also assess the effects of prior distribution choice. A simulation approach of the same Bayesian problem is also presented as a tool for visualization and validation. The validation results generally are consistent with those from the large sample approximation approach

Inference and optimal design for the k-level step-stress accelerated life test based on progressive Type-I interval censored power Rayleigh data

In this paper, a new generalization of the one parameter Rayleigh distribution called the Power Rayleigh (PRD) was employed to model the life of the tested units in the step-stress accelerated life test. Under progressive Type-I interval censored data, the cumulative exposure distribution was considered to formulate the life model, assuming the scale parameter of PRD has the inverse power function at each stress level. Point estimates of the model parameters were obtained via the maximum likelihood estimation method, while interval estimates were obtained using the asymptotic normality of the derived estimators and the bootstrap resampling method. An extensive simulation study of $k = 4$ levels of stress in different combinations of the life test under different progressive censoring schemes was conducted to investigate the performance of the obtained point and interval estimates. Simulation results indicated that point estimates of the model parameters are closest to their initial true values and have relatively small mean squared errors. Accordingly, the interval estimates have small lengths and their coverage probabilities are almost convergent to the 95% significance level. Based on the Fisher information matrix, the D-optimality and the A-optimality criteria are implemented to determine the optimal design of the life test by obtaining the optimum inspection times and optimum stress levels that improve the estimation procedures and give more efficient estimates of the model parameters. Finally, the developed inferential procedures were also applied to a real dataset