Sequential Designs with Application in Software Engineering

Title from PDF of title page, viewed on March 31, 2014Dissertation advisor: Kamel RakabVitaIncludes bibliographical references (pages 77-81)Thesis (Ph. D.)--Dept. of Mathematics and Statistics and Dept. of Computer Science and Electrical Engineering. University of Missouri, Kansas City, 2013Presented here is a Bayesian approach to test case allocation in the software reliability estimation. Bayesian analysis allows us to update our beliefs about the reliability of a particular partition as we test, and thus, dynamically re refine our allocation of test cases during the reliability testing process. We started with a fully sequential sampling scheme to estimate the reliability of a software system using partition testing. We have shown both theoretically and through simulation that the proposed scheme always performs at least as well as fixed sampling approaches where test case allocation is predetermined, and in all but the most unlikely circumstances, outperform them. Based on the sequential allocation, a multistage sampling scheme is established, which is less time consuming and more e efficient. Meanwhile, an e efficient sampling scheme is also developed to accommodate more situations. In the last chapter, we extend our study from parallel systems to series systems. We again use a Bayesian approach to allocate test cases to estimate the reliability of a series system with two components. A second-order lower bound for the incurred Bayes risk is established theoretically and Monte Carlo simulations with several proposed sequential designs are implemented to achieve this second-order lower bound for the incurred Bayes risk is established theoretically and Monte Carlo simulations with several proposed sequential designs are implemented to achieve this second-order lower bound.Abstract -- List of tables -- List of notations -- Acknowledgement -- Introduction -- A fully sequential test allocation for software reliability estimation -- A multistage sequential test allocation for software reliability estimation -- An efficient test allocation for software reliability estimation -- Test allocation for estimating reliability of series systems with two components -- Summary and conclusion -- Appendix -- Tables -- Referenc

Design Issues for Generalized Linear Models: A Review

Generalized linear models (GLMs) have been used quite effectively in the modeling of a mean response under nonstandard conditions, where discrete as well as continuous data distributions can be accommodated. The choice of design for a GLM is a very important task in the development and building of an adequate model. However, one major problem that handicaps the construction of a GLM design is its dependence on the unknown parameters of the fitted model. Several approaches have been proposed in the past 25 years to solve this problem. These approaches, however, have provided only partial solutions that apply in only some special cases, and the problem, in general, remains largely unresolved. The purpose of this article is to focus attention on the aforementioned dependence problem. We provide a survey of various existing techniques dealing with the dependence problem. This survey includes discussions concerning locally optimal designs, sequential designs, Bayesian designs and the quantile dispersion graph approach for comparing designs for GLMs.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Operation and planning of distribution networks with integration of renewable distributed generators considering uncertainties: a review

YesDistributed generators (DGs) are a reliable solution to supply economic and reliable electricity to customers. It is the last stage in delivery of electric power which can be defined as an electric power source connected directly to the distribution network or on the customer site. It is necessary to allocate DGs optimally (size, placement and the type) to obtain commercial, technical, environmental and regulatory advantages of power systems. In this context, a comprehensive literature review of uncertainty modeling methods used for modeling uncertain parameters related to renewable DGs as well as methodologies used for the planning and operation of DGs integration into distribution network.This work was supported in part by the SITARA project funded by the British Council and the Department for Business, Innovation and Skills, UK and in part by the University of Bradford, UK under the CCIP grant 66052/000000

Sampling Schemes For Estimating Software Reliability

Title from PDF of title page, viewed January 4, 2023Dissertation advisors: Kamel Rekab and Elizabeth StoddardVitaIncludes bibliographical references (pages 59-63)Dissertation (Ph.D.)--Department of Mathematics and Statistics, Department of Physics and Astronomy. University of Missouri--Kansas City, 2022Any software system of non-trivial size cannot be easily and completely tested because the domain of all possible inputs is complex and very large. In this study, we use a technique called partition testing, in which we divide the input domain of all potential testing cases D into K ≥ 2 non-overlapping sub-domains. Each sub-domain can therefore be tested independently from the others. We employ two methods, a fully sequential method and two-stages method, that are based on a sample of the test cases to allocate the test cases among partitions and minimize the variance of estimated software reliability when usage probabilities are random. These methods allow us to take advantages from the previous testing as we test and, as a result, dynamically improve the distribution of test cases throughout the reliability testing process. By dynamically allocating test cases to partitions, these methods aim to minimize the variance of the reliability estimation. The variance incurred by fully sequential method and the variance incurred by two-stages method are compared with the variance incurred by the optimal and the variance incurred by the balanced sampling method. Using theoretical results and a Monte Carlo simulation, the fully sampling method and the two-stages method perform better than the balanced sampling method and are nearly optimal.Introduction -- Software reliability estimation for K partitions -- Software reliability estimation for two partitions -- Fully sequential estimation in software reliability -- Two-stage estimation in software reliability -- Monte Carlo simulations -- Summary and conclusio

Sequential Sampling Designs for Estimating Software Reliability

Title from PDF of title page viewed August 25, 2020Dissertation advisors: Kamel Rekab and Paul RulisVitaIncludes bibliographical references (pages 58-62)Thesis (Ph.D.)--Department of Mathematics and Statistics and Department of Physics and Astronomy. University of Missouri--Kansas City, 2020For any non-trivial system, it is impossible to reach the exact reliability of software due to the complexity, cost, and time required to complete the testing. Instead, a sample of test cases can be used to estimate the overall software reliability. Our objective is to obtain the most accurate estimate of software reliability by allocating test cases among partitions. In the traditional approach, the method of allocating test cases among partitions is determined before reliability testing begins. By allocating test cases in advance, there is no opportunity to take advantage of the errors in choosing the distributions of test cases that may occur during the testing of the software. The inability to use these errors to adjust the estimate during testing is a shortcoming of a fixed sampling scheme. We applied sequential sampling schemes to make allocation decisions dynamically throughout the testing process. Under these sampling schemes, we can refine the allocation of test cases sequentially based on the information gained as the testing proceeds. Using theoretical results and Monte Carlo simulation, we have shown that the proposed sequential sampling scheme performs at least as well as the balanced sampling scheme.Introduction -- A fully sequential sampling scheme for software reliability estimation -- A Two-Stage Sampling Scheme for Software Reliability Estimation -- Summary and conclusion -- Appendi

Essays on Multistage Stochastic Programming applied to Asset Liability Management

Uncertainty is a key element of reality. Thus, it becomes natural that the search for methods allows us to represent the unknown in mathematical terms. These problems originate a large class of probabilistic programs recognized as stochastic programming models. They are more realistic than deterministic ones, and their aim is to incorporate uncertainty into their definitions. This dissertation approaches the probabilistic problem class of multistage stochastic problems with chance constraints and joint-chance constraints. Initially, we propose a multistage stochastic asset liability management (ALM) model for a Brazilian pension fund industry. Our model is formalized in compliance with the Brazilian laws and policies. Next, given the relevance of the input parameters for these optimization models, we turn our attention to different sampling models, which compose the discretization process of these stochastic models. We check how these different sampling methodologies impact on the final solution and the portfolio allocation, outlining good options for ALM models. Finally, we propose a framework for the scenario-tree generation and optimization of multistage stochastic programming problems. Relying on the Knuth transform, we generate the scenario trees, taking advantage of the left-child, right-sibling representation, which makes the simulation more efficient in terms of time and the number of scenarios. We also formalize an ALM model reformulation based on implicit extensive form for the optimization model. This technique is designed by the definition of a filtration process with bundles, and coded with the support of an algebraic modeling language. The efficiency of this methodology is tested in a multistage stochastic ALM model with joint-chance constraints. Our framework makes it possible to reach the optimal solution for trees with a reasonable number of scenarios.A incerteza é um elemento fundamental da realidade. Então, torna-se natural a busca por métodos que nos permitam representar o desconhecido em termos matemáticos. Esses problemas originam uma grande classe de programas probabilísticos reconhecidos como modelos de programação estocástica. Eles são mais realísticos que os modelos determinísticos, e tem por objetivo incorporar a incerteza em suas definições. Essa tese aborda os problemas probabilísticos da classe de problemas de multi-estágio com incerteza e com restrições probabilísticas e com restrições probabilísticas conjuntas. Inicialmente, nós propomos um modelo de administração de ativos e passivos multi-estágio estocástico para a indústria de fundos de pensão brasileira. Nosso modelo é formalizado em conformidade com a leis e políticas brasileiras. A seguir, dada a relevância dos dados de entrada para esses modelos de otimização, tornamos nossa atenção às diferentes técnicas de amostragem. Elas compõem o processo de discretização desses modelos estocásticos Nós verificamos como as diferentes metodologias de amostragem impactam a solução final e a alocação do portfólio, destacando boas opções para modelos de administração de ativos e passivos. Finalmente, nós propomos um “framework” para a geração de árvores de cenário e otimização de modelos com incerteza multi-estágio. Baseados na tranformação de Knuth, nós geramos a árvore de cenários considerando a representação filho-esqueda, irmão-direita o que torna a simulação mais eficiente em termos de tempo e de número de cenários. Nós também formalizamos uma reformulação do modelo de administração de ativos e passivos baseada na abordagem extensiva implícita para o modelo de otimização. Essa técnica é projetada pela definição de um processo de filtragem com “bundles”; e codifciada com o auxílio de uma linguagem de modelagem algébrica. A eficiência dessa metodologia é testada em um modelo de administração de ativos e passivos com incerteza com restrições probabilísticas conjuntas. Nosso framework torna possível encontrar a solução ótima para árvores com um número razoável de cenários

Probabilistic structural mechanics research for parallel processing computers

Aerospace structures and spacecraft are a complex assemblage of structural components that are subjected to a variety of complex, cyclic, and transient loading conditions. Significant modeling uncertainties are present in these structures, in addition to the inherent randomness of material properties and loads. To properly account for these uncertainties in evaluating and assessing the reliability of these components and structures, probabilistic structural mechanics (PSM) procedures must be used. Much research has focused on basic theory development and the development of approximate analytic solution methods in random vibrations and structural reliability. Practical application of PSM methods was hampered by their computationally intense nature. Solution of PSM problems requires repeated analyses of structures that are often large, and exhibit nonlinear and/or dynamic response behavior. These methods are all inherently parallel and ideally suited to implementation on parallel processing computers. New hardware architectures and innovative control software and solution methodologies are needed to make solution of large scale PSM problems practical

Reliability assessment of manufacturing systems: A comprehensive overview, challenges and opportunities

Reliability assessment refers to the process of evaluating reliability of components or systems during their lifespan or prior to their implementation. In the manufacturing industry, the reliability of systems is directly linked to production efficiency, product quality, energy consumption, and other crucial performance indicators. Therefore, reliability plays a critical role in every aspect of manufacturing. In this review, we provide a comprehensive overview of the most significant advancements and trends in the assessment of manufacturing system reliability. For this, we also consider the three main facets of reliability analysis of cyber–physical systems, i.e., hardware, software, and human-related reliability. Beyond the overview of literature, we derive challenges and opportunities for reliability assessment of manufacturing systems based on the reviewed literature. Identified challenges encompass aspects like failure data availability and quality, fast-paced technological advancements, and the increasing complexity of manufacturing systems. In turn, the opportunities include the potential for integrating various assessment methods, and leveraging data to automate the assessment process and to increase accuracy of derived reliability models

A TOP-DOWN APPROACH FOR OPTIMALLY DESIGNING MULTISTAGE-ADAPTIVE TESTS

In multistage-adaptive testing (MST), there are many interrelated design variables that impact the nature and quality of ability estimation. Previous research has identified general principles for the effective design of MSTs in terms of measurement performance. However, those principles are unlikely to apply uniformly to every testing context. The purpose of this dissertation is to propose a process of finding an MST design that has optimal measurement properties, given a specific set of test circumstances. To achieve this goal, an efficient strategy was introduced at each of three phases to discover the optimal design of the MST; constructing MSTs, systematically searching a design space of the MST, and evaluating the MST performance. For the first phase, a top-down approach was applied in this study. For the second phase, a way to systematically search the parameterized design space of an MST was used. For the third phase, a new analytical evaluation method for MST was proposed. In the dissertation, Study 1 proposed a new analytical evaluation method for MST. Using this new approach, measurement precision of ability estimation and classification accuracy could be derived analytically. The simulation results indicated that the new analytical method produced more exact measurement properties of an MST than the Monte Carlo simulation method. Therefore, the new analytical method would be the most efficient and competitive tool to asses measurement performance of an MST among other evaluation methods. Study 2 proposed a process to find a design of an MST that shows optimal measurement properties applying the three efficient strategies, given a specific set of testing context. The process consists of four important features: (1) setting a testing circumstance and MST design space, (2) systematically searching the MST design space using the top-down approach, (3) analytically evaluating measurement performance of an MST, and (4) computing objective functions. The suggested process was applied to a real item pool from a large-scale assessment. The results of the application study provided evidence that the process could be generalized to more complex and realistic test circumstances to create optimal designs of MST