| This dissertation develops stochastic models for two different areas, warranty cost analysis and online purchase prediction, both motivated by the problems encountered in my collaboration work with General Motors over the past three years.; The first three chapters are related to the warranty research. We propose an infinite-server queueing framework for warranty cost analysis and warranty reserve determination. Motivated by this idea, we extend the existing heavy-traffic limit theory for stationary infinite-server queues to the general non-stationary Gt/Gt/infinity setting. Specifically, we develop functional central limit theorems, Gaussian approximations, large deviations, and exact asymptotics for the aggregate cumulative claim costs. These results are then used to approximate the default probability of the warranty reserve fund and to determine the appropriate reserve level. We argue that this new approach to warranty cost analysis has a number of advantages over existing models in the literature. In addition, the framework and theoretical results can be applied to other application settings, including electricity demand, communication network traffic, make-to-order production systems with supplier delay, and life insurance.; Knowledge about individual-level visit-to-purchase conversion behaviors is of great value to E-Commerce web site managers. In the last chapter, we present a stochastic model that uses web server log data to predict the online purchase conversion probability for a given customer at a given visit, based not only on an observed history of visits and purchases, but on the ongoing active session as well. The model regards the purchase probability as a result of an accumulated visit effect and a purchasing threshold, both components allowing for heterogeneity across customers and evolution over time. In contrast with most existing models, we incorporate both inter-session evolution dynamics and intra-session pageview influences within each visit into a unified model structure. The methodology is applied to the server log data from Retail.com's Chevy Showroom pilot web site. The experimental results demonstrate superior performance by our integrated model over pure inter-session models and intra-session models, as measured by in-sample fit, out-of-sample fit, and prediction lift. |
