Reliability Modeling with Load-Shared Data and Product-Ordering Decisions Considering Uncertainty in LogisticsOperations

This dissertation consists of two parts with two different topics.In the first part, we investigate ``Load-Share Model" for modelingdependency among components in a multi-component system. Systems,where the components share the total applied load, are oftenreferred to as load sharing systems. Such systems can arise insoftware reliability models and in multivariate failure-timemodels in biostatistics, for example (see Kvam and Pena(2002)). When it comes to load-share model, the most interestingcomponent is the underlying principle that dictates how failurerates of surviving components change after some components in thesystem fail. This kind of principle depends mostly on thereliability application and how the components within the systeminteract through the reliability structure function. Until now,research involving load-share models have emphasized thecharacterization of system reliability under a knownload-share rule. Methods for reliability analysis based on unknown load-share rules have not been fully developed. So, inthe first part of this dissertation, 1) we model the dependencebetween system components through a load-share framework, with theload-sharing rule containing unknown parameters and 2) we derivemethods for statistical inference on unknown load-share parametersbased on maximum likelihood estimation.In the second half of this thesis, we extend the existinguncertain supply literature to a case where the supply uncertaintydwells in the logistics operations. Of primary interest in thisstudy is to determine the optimal order amount for the retailergiven uncertainty in the supply-chain's logistics network due tounforeseeable disruption or various types of defects (e.g.,shipping damage, missing parts and misplaced products). Mixturedistribution models characterize problems from solitary failuresand contingent events causing network to function ineffectively.The uncertainty in the number of good products successfullyreaching the distribution center and retailer poses a challenge indeciding product-order amounts. Because the commonly used orderingplan developed for maximizing expected profits does not allowretailers to address concerns about contingencies, this researchproposes two improved procedures with risk-averse characteristicstowards low probability and high impact events.