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Abstract or Table of Contents
The goal of this thesis is to specify a probability model for time-to-failure items in a manufacturing process. Specifically, I am interested in the time-to-failure of containers, called pots, in which aluminum is produced. Aluminum smelting is a very complex and sensitive process. The process uses specialized large carbon lined steel pots that contain a carbon rod and a molten cryolite bath, in which the final product aluminum is produced. A problem arises when the pots fail, for example, when a pot is unable to operate at a certain temperature the molten aluminum hardens resulting not only in wasted product, but also wasted time and resources to clean and remove the pot. In this thesis, I investigate different parametric models for the time-to-failure distribution for aluminum pots: the Weibull model, the Weibull change-point model, the Gompertz model, and the Gompertz-Makeham model. My work involves understanding the structure of the data, specifying which distributions to investigate and why, estimating parameters using maximum likelihood estimation, visualization methods for time-to-failure data, and how to test the fit of the models. These topics will all be discussed using a data set provided by Alcoa, Inc.