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

Statistical inferences of Rs;k = Pr(Xk-s+1:k \u3e Y ) for general class of exponentiated inverted exponential distribution with progressively type-II censored samples with uniformly distributed random removal

The problem of statistical inference of the reliability parameter Pr(Xk-s+1:k \u3e Y ) of an s-out-of-k : G system with strength components X1,X2,…,Xk subjected to a common stress Y when X and Y are independent two-parameter general class of exponentiated inverted exponential (GCEIE) progressively type-II right censored data with uniformly random removal random variables, are discussed. We use p-value as a basis for hypothesis testing. There are no exact or approximate inferential procedures for reliability of a multicomponent stress-strength model from the GCEIE based on the progressively type-II right censored data with random or fixed removals available in the literature. Simulation studies and real-world data analyses are given to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected confidence lengths of the confidence interval, and biases of the estimator are also discussed

Accelerated Life Testing Of Subsea Equipment Under Hydrostatic Pressure

Accelerated Life Testing (ALT) is an effective method of demonstrating and improving product reliability in applications where the products are expected to perform for a long period of time. ALT accelerates a given failure mode by testing at amplified stress level(s) in excess of operational limits. Statistical analysis (parameter estimation) is then performed on the data, based on an acceleration model to make life predictions at use level. The acceleration model thus forms the basis of accelerated life testing methodology. Well established accelerated models such as the Arrhenius model and the Inverse Power Law (IPL) model exist for key stresses such as temperature and voltage. But there are other stresses like subsea pressure, where there is no clear model of choice. This research proposes a pressure-life (acceleration) model for the first time for life prediction under subsea pressure for key mechanical/physical failure mechanisms. Three independent accelerated tests were conducted and their results analyzed to identify the best model for the pressure-life relationship. The testing included material tests in standard coupons to investigate the effect of subsea pressure on key physical, mechanical, and electrical properties. Tests were also conducted at the component level on critical components that function as a pressure barrier. By comparing the likelihood values of multiple reasonable candidate models for the individual tests, the exponential model was identified as a good model for the pressure-life relationship. In addition to consistently providing good fit among the three tests, the exponential model was also consistent with field data (validation with over 10 years of field data) and demonstrated several characteristics that enable robust life predictions in a variety iv of scenarios. In addition the research also used the process of Bayesian analysis to incorporate prior information from field and test data to bolster the results and increase the confidence in the predictions from the proposed model

On estimating the reliability in a multicomponent system based on progressively-censored data from Chen distribution

This research deals with classical, Bayesian, and generalized estimation of stress-strength reliability parameter, Rs;k = Pr(at least s of (X1;X2; :::;Xk) exceed Y) = Pr(Xks+1:k \u3eY) of an s-out-of-k : G multicomponent system, based on progressively type-II right-censored samples with random removals when stress and strength are two independent Chen random variables. Under squared-error and LINEX loss functions, Bayes estimates are developed by using Lindley’s approximation and Markov Chain Monte Carlo method. Generalized estimates are developed using generalized variable method while classical estimates - the maximum likelihood estimators, their asymptotic distributions, asymptotic confidence intervals, bootstrap-based confidence intervals - are also developed. A simulation study and a real-world data analysis are provided to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected lengths of the confidence intervals, and biases of the estimators are also computed, compared and contrasted

Ceramics Analysis and Reliability Evaluation of Structures (CARES). Users and programmers manual

This manual describes how to use the Ceramics Analysis and Reliability Evaluation of Structures (CARES) computer program. The primary function of the code is to calculate the fast fracture reliability or failure probability of macroscopically isotropic ceramic components. These components may be subjected to complex thermomechanical loadings, such as those found in heat engine applications. The program uses results from MSC/NASTRAN or ANSYS finite element analysis programs to evaluate component reliability due to inherent surface and/or volume type flaws. CARES utilizes the Batdorf model and the two-parameter Weibull cumulative distribution function to describe the effect of multiaxial stress states on material strength. The principle of independent action (PIA) and the Weibull normal stress averaging models are also included. Weibull material strength parameters, the Batdorf crack density coefficient, and other related statistical quantities are estimated from four-point bend bar or unifrom uniaxial tensile specimen fracture strength data. Parameter estimation can be performed for single or multiple failure modes by using the least-square analysis or the maximum likelihood method. Kolmogorov-Smirnov and Anderson-Darling goodness-of-fit tests, ninety percent confidence intervals on the Weibull parameters, and Kanofsky-Srinivasan ninety percent confidence band values are also provided. The probabilistic fast-fracture theories used in CARES, along with the input and output for CARES, are described. Example problems to demonstrate various feature of the program are also included. This manual describes the MSC/NASTRAN version of the CARES program

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

Modified weibull distributions in reliability engineering

Ph.DDOCTOR OF PHILOSOPH