Thesis (Ph. D.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 184-188).

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 95-98). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: James S. Dyer. Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1965. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, August 1998. / Includes bibliographical references. Also available on the Internet.

Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 48-49). Also available in electronic version.

An attempt is made in this thesis to study some stochastic models of both reliability and inventory systems with reference to the following aspects: (i) the confidence limits with the introduction of common-cause failures. (ii) the Erlangian repair time distributions. (iii) the product interactions and demand interactions. (iv) the products are perishable. This thesis contains six chapters. Chaper 1 is introductory in nature and gives a review of the literature and the techniques used in the analysis of reliability systems. Chapter 2 is a study of component common-cause failure systems. Such failures may greatly reduce the reliability indices. Two models of such systems (series and parallel) have been studied in this chapter. The expressions such as, reliability, availability and expected number of repairs have been obtained. The confidence limits for the steady state availability of these two systems have also been obtained. A numerical example illustrates the results. A 100 (1 - a) % confidence limit for the steady state availability of a two unit hot and warm standby system has been studied, when the failure of an online unit is constant and the repair time of a failed unit is Erlangian. The general introduction of various inventory systems and the techniques used in the analysis of such systems have been explained in chapter 4. Chapter 5 provides two models of two component continuous review inventory systems. Here we assume that demand occurs according to a poisson process and that a demand can be satisfied only if both the components are available in inventory. Back-orders are not permitted. The two components are bought from outside suppliers and are replenished according to (s, S) policy. In model 1 we assume that the lead-time of the components follow an exponential distribution. By identifying the inventory level as a Markov process, a system of difference-differential equations at any time and the steady-state for the state of inventory level are obtained. Tn model 2 we assume that the lead-time distribution of one product is arbitrary and the other is exponential. Identifying the underlying process as a semi-regenerative process we find the stationary distribution of the inventory level. For both these models, we find out the performance measures such as the mean stationary rate of the number of lost demands, the demands satisfied and the reorders made. Numerical examples for the two models are also considered. Chaper 6 is devoted to the study of a two perishable product inventory model in which the products are substitutable. The perishable rates of product 1 and product 2 are two different constants. Demand for product 1 and product 2 follow two independent Poisson processes. For replenishment of product 1 (s, S) ordering policy is followed and the associated lead-time is arbitrary. Replenishment of product 2 is instantaneous. A demand for product 1 which occurs during its stock-out period can be substituted by product 2 with some probability. Expressions are derived for the stationary distribution of the inventor}' level by identifying the underlying stochastic process as a semi-regenerative process. An expression for the expected profit rate is obtained. A numerical illustration is provided and an optimal reordering level maximising the profit rate is also studied. To sum up, this thesis is an effort to improve the state the of art of (i) complex reliability systems and their estimation study (ii) muitiproduct inventory systems. The salient features of the thesis are: (i) Analysis of a two-component reliability system with common-cause failures. (ii) Estimation study of a complex system in which the repair time for both hot standby and warm standby systems are assumed to be Eriangian. (iii) A multi-product continuous review inventory system with product interaction, with a (s, S) policy. (iv) Introduction of the concept of substitutability for products. (v) Derivation of expressions for various statistical measures. (vi) Effective use of the regeneration point technique in deriving various measures for both reliability and inventory systems. (vii) Illustration of the various results by extensive numerical work. (vii) Consideration of relevant optimization problems. / Mathematical Sciences / PhD (Statistics)

Among all stochastic processes with independent increments, essentially only Brownian motion and Poisson process have a chaotic representation property. In the case of a Levy process, several approaches have been proposed in order to construct an orthogonal decomposition of the corresponding L2-space. In this dissertation, we deal with orthogonal (chaotic) decompositions for generalized processes with independent values. We do not suppose stationarity of the process, as a result the Levy measure of the process depends on points of the space. We first construct, in Chapter 3, a unitary isomorphism between a certain symmetric Fock space and the space L2 (D',mu). Here D' is a co-nuclear space of generalized functions (distributions), and mu is a generalized stochastic process with independent values. This isomorphism is constructed by employing the projection spectral theorem for an (uncountable) family of commuting self-adjoint operators. We next derive, in Chapter 4, a counterpart of the Nualart Schoutens decomposition for generalized stochastic process with independent values. Our results here extend those in the papers of Nualart Schoutens and Lytvynov. In Chapter 5, we construct an orthogonal decomposition of the space L2 (D',mu) in terms of orthogonal polynomials on D'. We observe a deep relation between this decomposition and the results of the two previous chapters. Finally, in Chapter 6, we briefly discuss the situation of the generalized stochastic processes of Meixner's type.

No description available.

This thesis examines the statistics and dynamics of turbulent flow structures generated by towing a grid through a tank of water. The structures were made visible by recording the paths of aluminum tracers moving with the water surface. Flow patterns recorded using a time-exposure method were manually analyzed to extract information on the structure statistics. This two-dimensional flow field was found to be composed of closed rotating 'surface eddies', open and largely translational 'river' motion and stagnant regions. Energy distributions of the eddies and rivers were obtained and characterized by Boltzmann type distributions. A newly developed computer-automated structure identification and flow field analysis system was used to study the structure dynamics. The system analyzes digital images obtained from video recordings of the tracer motion. The predominant evolution processes of initial vortex production, eddy pairing, viscous decay and the omega decay were examined. Flow Reynolds numbers, based on bar spacing, of about 10,000 were examined. The structure statistics and dynamics study was performed in order to examine the validity and viability of a new model for turbulence. The model predicts the evolution of a population of structures using rate equations where the rate coefficients are determined by the individual structure dynamics. A summary of the model is presented and contrasted with models based the the Reynolds stresses as well as computational models. / Science, Faculty of / Physics and Astronomy, Department of / Graduate