| Summary: | 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.
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