This thesis is concerned with characterizing the quality of Hidden Markov modeling when learning from limited data. It introduces a new perspective on different sources of errors to describe the impact of undermodeling. Our view is that modeling errors can be decomposed into two primary sources of errors: the approximation error and the estimation error. This thesis takes a first step towards exploring the approximation error of low order HMMs that best approximate the true system of a HMM. We introduce the notion minimality and show that best approximations of the true system with complexity greater or equal to the order of a minimal system are actually equivalent realizations. Understanding this further allows us to explore integer lumping and to present a new way named weighted lumping to find realizations. We also show that best approximations of order strictly less than that of a minimal realization are truly approximations; they are incapable of mimicking the true system exactly. Our work then proves that the resulting approximation error is non-decreasing as the model order decreases, verifying the intuitive idea that increasingly simplified models are less and less descriptive of the true system.

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京都大学 / 新制・課程博士 / 博士(工学) / 甲第24569号 / 工博第5075号 / 新制||工||1972(附属図書館) / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 須崎 純一, 教授 宇野 伸宏, 准教授 松島 格也 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

There are two themes in this dissertation, that is, the effect of universal demand law change on corporate risk-taking in the U.S. property & casualty insurance industry, and the application of hidden Markov model to auto telematics data. The first chapter presents my study in the first theme and the rest two chapters present the other theme. In Chapter 1, "Does Shareholder Litigation Affect Corporate Risk-Taking? Evidence from the Property-Casualty Insurance Industry", I explore whether shareholder litigation affects corporate risk-taking differently depending on distinct organizational structures. I use a law change, called Universal Demand (UD) Law, as an exogenous shock and develop three risk-taking measures that are unique in the U.S. property-casualty insurance industry: leverage risk, asset risk, and underwriting risk. The insurance industry provides an interesting opportunity for the study as shareholders in mutual insurers are an ambiguous concept in the legal world, as opposed to the common argument in the insurance literature. The results show that along with UD law adoption, insurers increase their risk-taking. After taking organizational structures into account, the impact of the law change differentiates. Stock insurers increase all three risk-taking measures while mutual insurers decrease their Leverage Risk and increase Asset Risk measures. For different time windows, stock insurers respond faster with respect to their Asset Risk compared to mutual insurers. In addition, I proceed to examine the main economic channel for the impact and find that the free cash flow argument is not the main channel. Chapters 2 and 3 present the study in auto telematics data using a proprietary data source. Both studies are based on the application of hidden Markov model (HMM). Specifically, Chapter 2, "Auto Insurance Pricing Using Telematics Data: Application of a Hidden Markov Model", develops an HMM-based clustering framework to predict auto insurance losses using driving characteristics extracted from telematics data. Through a simulation experiment based on a proprietary telematics data set, I show that HMM can effectively classify driving trips using model-implied hidden states, and HMM-based pricing methods provide better predictive power measured by both deviance statistics and mean squared error. Importantly, the proposed framework not only enables us to price usage-based insurances at a granular level, but it is also viable for estimating long-term insurance losses utilizing the limiting properties of HMM. Chapter 3, "Theoretical Framework of a 3-Layer Hidden Markov Model for Auto Insurance Pricing", is a theoretical extension of the second chapter to improve the framework at a more granular level. I develop a 3-layer HMM for risk classification, which links driving behavior characteristics with risk classes and loss estimation. The proposed model presents a direct structure among all variables and utilizes time series data without aggregation. Furthermore, this study provides a theoretical framework to estimate the 3-layer HMM using the Expectation-Maximization (EM) algorithm. The parameters of Bernoulli distributed loss count (per unit of time) and Gamma distributed loss severity can be solved at least numerically, and the negative definite Hessian matrix indicates that the solution of the first-order condition of the log-likelihood function achieves its local maximum. / Business Administration/Risk Management and Insurance

<p>The decision making processes in today's manufacturing systems represent very complex and challenging tasks. The desired flexibility in terms of the functionality of a machine adds more components to the machine. The real time monitoring and reporting generates large streams of data. However the intelligent and real time processing of this large collection of system data is at the core of the manufacturing decision support tools. </p> <p>This thesis outlines the use of Frequent Episodes in Event Sequences and Hidden Markov Modeling of throughput, quality and maintenance data to model the deterioration of performance in the components that make up the manufacturing system. The thesis also introduces the concept of decision points and outlines how to integrate the total cost function in a business model. </p> This thesis deals with the following three topics: <p>First, the component-based data structure of the manufacturing system is outlined especially throughput, quality and maintenance data. In this approach, the manufacturing system is considered as a group of components that interact with each other and with raw materials to produce the manufactured product. This interaction creates a considerable amount of data which can be associated with the relevant components of the system. The relations between the manufacturing components are established on a physical and logical basis. The components properties are clearly defined in database tables specifically created for this application. The thesis also discusses the web services in manufacturing systems and the portable technologies used in plant decision support tools. </p> <p>Second, the thesis presents a novel application of Frequent Episodes in Event Sequences to identify patterns in the deterioration of performance in a component using frequent episodes of operational failures, quality failures and maintenance activities. A Hidden Markov Model (HMM) is used to model each deterioration episode to estimate the states of performance and the transition rates between the states. The thesis compares the results generated by this model to other existing models of component performance deterioration while emphasizing the benefits ofthe proposed model through the use of the plant data.</p> <p>Finally the thesis presents a methodology usmg HMM probability distributions and Bayesian Decision theory framework to provide a set of decisions and recommendations under the condition of data uncertainty. The results of this analysis are then integrated in the plant maintenance business model.</p> <p>It is worthwhile mentioning that to develop the techniques and validate the results in this research; a Manufacturing Execution System (MES) was developed to operate in an automotive engine plant. All the data and results in this research are based on the plant data. The MES which was developed in this research provided significant benefits in the plant and was adapted by many other GM plants around the world.</p> / Thesis / Doctor of Philosophy (PhD)

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The majority of aircraft structures are designed to be damage-tolerant such that safe operation can continue in the presence of minor damage. It is necessary to schedule inspections so that minor damage can be found and repaired. It is generally not possible to perform structural inspections prior to every flight. The scheduling is traditionally accomplished through a deterministic set of methods referred to as Damage Tolerance Analysis (DTA). DTA has proven to produce safe aircraft but does not provide estimates of the probability of failure of future flights or the probability of repair of future inspections. Without these estimates maintenance costs cannot be accurately predicted. Also, estimation of failure probabilities is now a regulatory requirement for some aircraft. The set of methods concerned with the probabilistic formulation of this problem are collectively referred to as Probabilistic Damage Tolerance Analysis (PDTA). The goal of PDTA is to control the failure probability while holding maintenance costs to a reasonable level. This work focuses specifically on PDTA for fatigue cracking of metallic aircraft structures. The growth of a crack (or cracks) must be modeled using all available data and engineering knowledge. The length of a crack can be assessed only indirectly through evidence such as non-destructive inspection results, failures or lack of failures, and the observed severity of usage of the structure. The current set of industry PDTA tools are lacking in several ways: they may in some cases yield poor estimates of failure probabilities, they cannot realistically represent the variety of possible failure and maintenance scenarios, and they do not allow for model updates which incorporate observed evidence. A PDTA modeling methodology must be flexible enough to estimate accurately the failure and repair probabilities under a variety of maintenance scenarios, and be capable of incorporating observed evidence as it becomes available. This dissertation describes and develops new PDTA methodologies that directly address the deficiencies of the currently used tools. The new methods are implemented as a free, publicly licensed and open source R software package that can be downloaded from the Comprehensive R Archive Network. The tools consist of two main components. First, an explicit (and expensive) Monte Carlo approach is presented which simulates the life of an aircraft structural component flight-by-flight. This straightforward MC routine can be used to provide defensible estimates of the failure probabilities for future flights and repair probabilities for future inspections under a variety of failure and maintenance scenarios. This routine is intended to provide baseline estimates against which to compare the results of other, more efficient approaches. Second, an original approach is described which models the fatigue process and future scheduled inspections as a hidden Markov model. This model is solved using a particle-based approximation and the sequential importance sampling algorithm, which provides an efficient solution to the PDTA problem. Sequential importance sampling is an extension of importance sampling to a Markov process, allowing for efficient Bayesian updating of model parameters. This model updating capability, the benefit of which is demonstrated, is lacking in other PDTA approaches. The results of this approach are shown to agree with the results of the explicit Monte Carlo routine for a number of PDTA problems. Extensions to the typical PDTA problem, which cannot be solved using currently available tools, are presented and solved in this work. These extensions include incorporating observed evidence (such as non-destructive inspection results), more realistic treatment of possible future repairs, and the modeling of failure involving more than one crack (the so-called continuing damage problem). The described hidden Markov model / sequential importance sampling approach to PDTA has the potential to improve aerospace structural safety and reduce maintenance costs by providing a more accurate assessment of the risk of failure and the likelihood of repairs throughout the life of an aircraft. / Statistics