Reliability Modeling with Load-Shared Data and Product-Ordering Decisions Considering Uncertainty in Logistics Operations
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This dissertation consists of two parts with two different topics. In the first part, we investigate ``Load-Share Model" for modeling dependency among components in a multi-component system. Systems, where the components share the total applied load, are often referred to as load sharing systems. Such systems can arise in software reliability models and in multivariate failure-time models in biostatistics, for example (see Kvam and Pena (2002)). When it comes to load-share model, the most interesting component is the underlying principle that dictates how failure rates of surviving components change after some components in the system fail. This kind of principle depends mostly on the reliability application and how the components within the system interact through the reliability structure function. Until now, research involving load-share models have emphasized the characterization of system reliability under a known load-share rule. Methods for reliability analysis based on unknown load-share rules have not been fully developed. So, in the first part of this dissertation, 1) we model the dependence between system components through a load-share framework, with the load-sharing rule containing unknown parameters and 2) we derive methods for statistical inference on unknown load-share parameters based on maximum likelihood estimation. In the second half of this thesis, we extend the existing uncertain supply literature to a case where the supply uncertainty dwells in the logistics operations. Of primary interest in this study is to determine the optimal order amount for the retailer given uncertainty in the supply-chain's logistics network due to unforeseeable disruption or various types of defects (e.g., shipping damage, missing parts and misplaced products). Mixture distribution models characterize problems from solitary failures and contingent events causing network to function ineffectively. The uncertainty in the number of good products successfully reaching the distribution center and retailer poses a challenge in deciding product-order amounts. Because the commonly used ordering plan developed for maximizing expected profits does not allow retailers to address concerns about contingencies, this research proposes two improved procedures with risk-averse characteristics towards low probability and high impact events.