In this paper we consider three topics in reliability and maintenance. Their common feature is the explicit consideration of interdependence, either amongst components within a machine, amongst stages in a logistics chain, or amongst machines sharing maintenance facilities. Chapter 1 examines measures of the contribution of a component towards a system's reliability; these measures include structural importance, marginal reliability importance, joint reliability importance, and link importance. We review these different measures and examine how they relate to each other. We show that some structural results previously derived for independent components continue to hold for associated components. We then propose extensions to each importance measure to cover components which have two failure modes rather than the conventional one, and show that these extensions largely retain the properties of the original definitions. Chapter 2 examines a system containing one machine subject to random failure, for which we wish to determine a maintenance policy and a spare ordering policy. We consider the solvability and desirability of jointly optimizing these two traditionally separate policies. We discuss why the general form of the problem is intractable and show how it might be approached using bounds and heuristic policies; more importantly, we examine several special cases which are more tractable. Particular attention is paid to systems which contain only one spare at a time; we show that these systems have some convexity properties which facilitate cost minimization. We subsequently consider systems which allow more than one spare, but make use of other restrictions or assumptions to simplify analysis. Chapter 3 examines how to coordinate maintenance for machines sharing repair facilities, a task which is commonly called the machine repairman problem. Existing studies of this problem make the restrictive assumption that repairs are performed only after machine failure; our work extends the machine repairman model by allowing preventive repair. We derive analytical results for a single critical age repair policy, and then use numerical studies to investigate other heuristic policies which can improve the system's cost effectiveness.

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This thesis considers the problem of estimating limited dependent variable models when the latent residuals are heteroskedastic normally distributed random variables. Commonly used estimators are generally inconsistent in such situations. Two estimation methods that allow consistent estimation of the parameters of interest are presented and shown to be consistent when the latent residuals are heteroskedastic of unknown form. Both estimators use recent advances in the econometric literature on nonparametric estimation and deal with the unknown form of heteroskedasticity by approximating the variance using a Fourier series type approximation. The first estimator is based on the method of maximum likelihood and involves maximising the likelihood function by choice of the parameters of the variance function approximation and the other parameters of interest. Consistency is shown to hold in the three most popular limited dependent variable models — the Probit, Tobit, and sample selection models — provided that the number of terms in the approximation increases with the sample size. The second estimator, which can be used to estimate the Tobit and sample selection models, is based on a two-step procedure, using Fourier series approximations in both steps. Consistency and asymptotic normality are proven under restrictions on the rate of increase of the number of parameters in the approximating functions. Finally, a small Monte Carlo experiment is conducted to examine the small sample properties of the estimators. The results show that the estimators perform quite well and in many cases reduce the bias, relative to the commonly used estimators, with little or no efficiency loss. / Arts, Faculty of / Vancouver School of Economics / Graduate

In this paper we consider three topics in reliability and maintenance. Their common feature is the explicit consideration of interdependence, either amongst components within a machine, amongst stages in a logistics chain, or amongst machines sharing maintenance facilities. Chapter 1 examines measures of the contribution of a component towards a system's reliability; these measures include structural importance, marginal reliability importance, joint reliability importance, and link importance. We review these different measures and examine how they relate to each other. We show that some structural results previously derived for independent components continue to hold for associated components. We then propose extensions to each importance measure to cover components which have two failure modes rather than the conventional one, and show that these extensions largely retain the properties of the original definitions. Chapter 2 examines a system containing one machine subject to random failure, for which we wish to determine a maintenance policy and a spare ordering policy. We consider the solvability and desirability of jointly optimizing these two traditionally separate policies. We discuss why the general form of the problem is intractable and show how it might be approached using bounds and heuristic policies; more importantly, we examine several special cases which are more tractable. Particular attention is paid to systems which contain only one spare at a time; we show that these systems have some convexity properties which facilitate cost minimization. We subsequently consider systems which allow more than one spare, but make use of other restrictions or assumptions to simplify analysis. Chapter 3 examines how to coordinate maintenance for machines sharing repair facilities, a task which is commonly called the machine repairman problem. Existing studies of this problem make the restrictive assumption that repairs are performed only after machine failure; our work extends the machine repairman model by allowing preventive repair. We derive analytical results for a single critical age repair policy, and then use numerical studies to investigate other heuristic policies which can improve the system's cost effectiveness. / Business, Sauder School of / Graduate

In this thesis we define and study the existence of an equilibrium situation in which producers maximize their profits relative to the production vectors in their production sets, consumers satisfy their preferences in their consumption sets under certain budget constraint, and for every commodity total demand equals total supply. This competitive equilibrium situation is referred to as the Walrasian equilibrium. The existence of this equilibrium is investigated from a various mathematical points of view. These include microeconomic theory, simplicial spaces, global analysis and lattice theory.

Wang Xin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 61-63). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction and Literature Review --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- The Objective --- p.2 / Chapter 1.3 --- Literature Review --- p.3 / Chapter Chapter 2 --- The Model --- p.7 / Chapter Chapter 3 --- The Consistent Estimation of Chang-Point --- p.11 / Chapter 3.1 --- The Consistency of ιT --- p.11 / Chapter 3.2 --- The Case of Single Regressor --- p.15 / Chapter Chapter 4 --- The SupWald Test and Sample-Splitting Method --- p.20 / Chapter 4.1 --- The SupWald Test --- p.20 / Chapter 4.2 --- " The Distribution of WT (ι,0,1)" --- p.23 / Chapter 4.3 --- The Sample-Splitting Method --- p.25 / Chapter Chapter 5 --- Experimental Results --- p.27 / Chapter Chapter 6 --- Empirical Example --- p.41 / Chapter Chapter 7 --- Conclusion --- p.44 / Appendix --- p.46 / References --- p.61

Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Economics. / Microfiche copy available in Archives and Dewey. / Vita. / Bibliography: leaves 26-28, 79-80. / Learning behavior and the noncooperative equilibrium.--A game of fair division. / Ph.D.

Cheung, Man Wah. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 50-53). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Stochastic Stability --- p.2 / Chapter 1.2 --- Some Examples --- p.3 / Chapter 1.3 --- Our Main Focus --- p.5 / Chapter 1.4 --- Thesis Outline --- p.6 / Chapter 2 --- KMR's Approach and its Variations --- p.7 / Chapter 2.1 --- KMR's Approach --- p.7 / Chapter 2.2 --- Variations --- p.12 / Chapter 2.2.1 --- Bergin and Lipman (1996) --- p.12 / Chapter 2.2.2 --- Anderlini and Ianni (1996) --- p.12 / Chapter 2.2.3 --- Robson and Vega-Redondo (1996) --- p.13 / Chapter 2.2.4 --- Robles (1998) and Pak (2008) --- p.13 / Chapter 3 --- Mathematical Reviews on Nonstationary Markov Chain --- p.15 / Chapter 3.1 --- Ergodic Coefficient --- p.15 / Chapter 3.2 --- Weak Ergodicity --- p.16 / Chapter 3.3 --- Strong Ergodicity --- p.18 / Chapter 4 --- Existing Works on Time-Dependent Mutation Rates --- p.20 / Chapter 4.1 --- Model and Definitions --- p.20 / Chapter 4.2 --- Sufficient Condition for Weak Ergodicity --- p.23 / Chapter 4.3 --- Sufficient Condition for Strong Ergodicity --- p.24 / Chapter 5 --- Time-Dependent Mutations and Empirical Distribution --- p.26 / Chapter 5.1 --- Model --- p.28 / Chapter 5.2 --- Convergence of Empirical Distribution --- p.30 / Chapter 5.3 --- Proofs of Claims --- p.35 / Chapter 5.3.1 --- Proofs of Claims l(a)-(d) --- p.36 / Chapter 5.3.2 --- Proof of Claim 2 --- p.39 / Chapter 6 --- Open Problems --- p.42 / Chapter 6.1 --- Numerical Example and Simulations --- p.43 / Chapter 6.2 --- Numerical Results --- p.44 / Chapter 6.3 --- Other Discussions --- p.47 / Chapter 7 --- Conclusion --- p.48 / Bibliography --- p.50

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