A thesis submitted in fulfillment of the requirements for the Degree of Doctor of Philosophy, School of Statistics and Actuarial Science, Faculty of Science University of Witwatersrand, Johannesburg. February 2017. / The work done in this thesis on finite planning horizon inspection models has demonstrated that with the advent of powerful computers these days it is possible to easily find an optimal inspection schedule when the lifetime distribution is known. For the case of system time to failure following a uniform distribution, a result for the maximum number of inspections for the finite planning models has been derived. If the time to failure follows an exponential distribution, it has been noted that periodically carrying out inspections may not result in maximization of expected profit. For the Weibull distributions family (of which the exponential distribution is a special case), evenly spreading the inspections over a given finite planning horizon may not lead to any serious prejudice in profit. The case of inspection models where inspections are of non-negligible duration has also been explored. The conditions necessary for inspections that are evenly spread over the entire planning horizon to be near-optimal when system time to failure either follows a uniform distribution or exponential distribution have been explored. Finite and infinite planning horizon models where inspections are imperfect have been researched on. Interesting observations on the impact of Type I and Type II errors in inspection have been made. These observations are listed on page 174. A clear and easy to implement road map on how to get an optimal inspection permutation in problems first discussed by Zuckerman (1989) and later reviewed by Qiu (1991) for both the undiscounted and discounted cases has been given. The only challenge envisaged when a system has a large number of components is that of computer memory requirements - which nowadays is fast being overcome. In particular, it has been clearly demonstrated that the impact of repair times and per unit of time repair costs on the optimal inspection permutation cannot be ignored. The ideas and procedures of determining optimal inspection permutations which have been developed in this thesis will no doubt lead to huge cost savings especially for systems where the cost of inspecting components is huge. / XL2018

The service life and electrocatalytic activity of tantalum oxide/iridium oxide coated titanium plate and mesh anodes used in the electrolytic production of chromic acid were investigated by performing accelerated life tests, voltammetric and chronoamperometric measurements in chrome (VI) solutions. Experimental results showed that the service life for the coated mesh anode was 1059 hours, compared to 828 hours for the plate anode at a current density of 1.2 A cm-2. In addition, the coating failed earlier in higher chromic acid concentration. Physical analysis by SEM and EDS before and after accelerated life test confirmed that the deactivation was a result of corrosion of IrO2 followed by titanium substrate passivation. A simple and rapid method for assessing the electrocatalytic activity of iridium–tantalum oxide coating based on a chronoamperometric technique was developed.

The accelerated lifetime model is considered. To test the influence of the covariate we transform the model in a regression model. Since censoring is allowed this approach leads to a goodness-of-fit problem for regression functions under censoring. So nonparametric estimation of regression functions under censoring is investigated, a limit theorem for a L2-distance is stated and a test procedure is formulated. Finally a Monte Carlo procedure is proposed.

Because of the needs for producing highly reliable products and reducing product development time, Accelerated Life Testing (ALT) has been widely used in new product development as an alternative to traditional testing methods. The basic idea of ALT is to expose a limited number of test units of a product to harsher-than-normal operating conditions to expedite failures. Based on the failure time data collected in a short time period, an ALT model incorporating the underlying failure time distribution and life-stress relationship can be developed to predict the product reliability under the normal operating condition. However, ALT experiments often consume significant amount of energy due to the harsher-than-normal operating conditions created and controlled by the test equipment used in the experiments. This challenge may obstruct successful implementations of ALT in practice. In this dissertation, a new ALT design methodology is developed to improve the reliability estimation precision and the efficiency of energy utilization in ALT. This methodology involves two types of ALT design procedures - the sequential optimization approach and the simultaneous optimization alternative with a fully integrated double-loop design architecture. Using the sequential optimum ALT design procedure, the statistical estimation precision of the ALT experiment will be improved first followed by energy minimization through the optimum design of controller for the test equipment. On the other hand, we can optimize the statistical estimation precision and energy consumption of an ALT plan simultaneously by solving a multi-objective optimization problem using a controlled elitist genetic algorithm. When implementing either of the methods, the resulting statistically and energy efficient ALT plan depends not only on the reliability of the product to be evaluated but also on the physical characteristics of the test equipment and its controller. Particularly, the statistical efficiency of each candidate ALT plan needs to be evaluated and the corresponding controller capable of providing the required stress loadings must be designed and simulated in order to evaluate the total energy consumption of the ALT plan. Moreover, the realistic physical constraints and tracking performance of the test equipment are also addressed in the proposed methods for improving the accuracy of test environment. In this dissertation, mathematical formulations, computational algorithms and simulation tools are provided to handle such complex experimental design problems. To the best of our knowledge, this is the first methodological investigation on experimental design of statistically precise and energy efficient ALT. The new experimental design methodology is different from most of the previous work on planning ALT in that (1) the energy consumption of an ALT experiment, depending on both the designed stress loadings and controllers, cannot be expressed as a simple function of the related decision variables; (2) the associated optimum experimental design procedure involves tuning the parameters of the controller and evaluating the objective function via computer experiment (simulation). Our numerical examples demonstrate the effectiveness of the proposed methodology in improving the reliability estimation precision while minimizing the total energy consumption in ALT. The robustness of the sequential optimization method is also verified through sensitivity analysis.

Accelerated life testing (ALT) has been widely used in collecting failure time data of highly reliable products. Most parametric ALT models assume that the ALT data follows a specific probability distribution. However, the assumed distribution may not be adequate in describing the underlying failure time distribution. In this dissertation, a more generic method based on a phase-type distribution is presented to model ALT data. To estimate the parameters of such Erlang Coxian-based ALT models, both a mathematical programming approach and a maximum likelihood method are developed. To the best of our knowledge, this dissertation demonstrates, for the first time, the potential of using PH distributions for ALT data analysis. To shorten the test time of ALT, degradation tests have been studied as a useful alternative. Among many degradation tests, destructive degradation tests (DDT) have attracted much attention in reliability engineering. Moreover, some materials/products start degrading only after a random degradation initiation time that is often not even observable. In this dissertation, two-stage delayed-degradation models are developed to evaluate the reliability of a product with random initiation time. For homogeneous and heterogeneous populations, fixed-effects and random-effects Gamma processes are considered, respectively. An expectation-maximization algorithm and a bootstrap method are developed to facilitate the maximum likelihood estimation of model parameters and to construct the confidence intervals of the interested reliability index, respectively. With an Accelerated DDT model, an optimal test plan is presented to improve the statistical efficiency. In designing the ADDT experiment, decision variables related to the experiment must be determined under the constraints on limited resources, such as the number of test units and the total testing time. In this dissertation, the number of test units and stress level are pre-determined in planning an ADDT experiment. The goal is to improve the statistical efficiency by selecting appropriately allocate the test units to different stress levels to minimize the asymptotic variance of the estimator of the p-quantile of failure time. In particular, considering the random degradation initiation time, a three-level constant-stress destructive degradation test is studied. A mathematical programming problem is formulated to minimize the asymptotic variance of reliability estimate.

Fatigue failure of metallic structures operating under dynamic loading is a common occurrence in engineering applications. It is difficult to estimate the response of complicated systems analytically, due to structure&amp / #8217 / s dynamic characteristics and varying loadings. Therefore, experimental, numerical or a combination of both methods are used for fatigue evaluations. Fatigue failure can occur on systems and platforms as well as components to be mounted on the platform. In this thesis, a helicopter&amp / #8217 / s Missile Warning Sensor - Cowling assembly is analyzed. Analytical, numerical and experimental approaches are used wherever necessary to perform stress and fatigue analyses. Operational flight tests are used for obtaining the loading history at the analyzed location by using sensors. Operational vibration profiles are created by synthesizing the data (LMS Mission Synthesis). Numerical fatigue analysis of the assembly is done for determining the natural modes and the critical locations on the assembly by using a finite element model (MSC Fatigue). In addition, numerical multiaxial PSD analysis is performed for relating the experimental results (Ansys). Residual stresses due to riveting are determined (MSC Marc) and included in experimental analysis as mean stresses. Bolt analysis is performed analytically (Hexagon) for keeping the v assembly stresses in safe levels while mounting the experimental prototype to the test fixture. Fatigue tests for determining the accelerated life parameters are done by an electromagnetic shaker and stress data is collected. Afterwards, fatigue test is performed for determining whether the assembly satisfies the required operational life. Resonance test is performed at the frequency in which the critical location is at resonance, since there was no failure observed after fatigue testing. A failure is obtained during resonance test. At the end of the study, an analytical equation is brought up which relates accelerated life test durations with equivalent alternating stresses. Therefore, optimization of the accelerated life test duration can be done, especially in military applications, by avoiding the maximum stress level to reach or exceed the yield limit.

Thesis (M.S.)--University of Texas at El Paso, 2007. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Thesis (Ph.D.)--McMaster University (Canada), 1996. / Source: Dissertation Abstracts International, Volume: 58-06, Section: B, page: 3128. Adviser: N. Balakrishnan.

abstract: Nowadays product reliability becomes the top concern of the manufacturers and customers always prefer the products with good performances under long period. In order to estimate the lifetime of the product, accelerated life testing (ALT) is introduced because most of the products can last years even decades. Much research has been done in the ALT area and optimal design for ALT is a major topic. This dissertation consists of three main studies. First, a methodology of finding optimal design for ALT with right censoring and interval censoring have been developed and it employs the proportional hazard (PH) model and generalized linear model (GLM) to simplify the computational process. A sensitivity study is also given to show the effects brought by parameters to the designs. Second, an extended version of I-optimal design for ALT is discussed and then a dual-objective design criterion is defined and showed with several examples. Also in order to evaluate different candidate designs, several graphical tools are developed. Finally, when there are more than one models available, different model checking designs are discussed. / Dissertation/Thesis / Ph.D. Industrial Engineering 2013

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