Optimal Allocation of Resources in Reliability Growth

Reliability growth testing seeks to identify and remove failure modes in order to improve system reliability. This dissertation centers around the resource allocation across the components of a multi-component system to maximize system reliability. We summarize this dissertation’s contributions to optimal resource allocation in reliability growth. Chapter 2 seeks to deploy limited testing resources across the components of a series-parallel system in effort to maximize system reliability under the assumption that each component’s reliability exhibits growth according to an AMSAA model with known parameters. An optimization model for this problem is developed and then extended to consider the allocation of testing resources in a series-parallel system with consideration for the possibility of testing at different levels (system, subsystem, and component). We contribute a class of exact algorithms that decomposes the problem based upon the series-parallel structure. We prove the algorithm is finite, compare it with heuristic approaches on a set of test instances, and provide detailed analyses of numerical examples. In Chapter 3, we extend model in Chapter 2 to solve a robust optimization version of this problem in which AMSAA parameters are uncertain but assumed to lie within a budget-restricted uncertainty set. We model the problem of robust allocation of testing resources to maximize system reliability for both series and series-parallel systems, and we develop and analyze exact solution approaches for this problem based on a cutting plane algorithm. Computational results demonstrate the value of the robust optimization approach as compared to deterministic alternatives. In the last chapter, we develop a new model that merges testing components and installing redundancies within an integrated optimization model that maximizes system reliability. Specifically, our model considers a series-parallel system in which the system reliability can be improved by both testing components and installing redundant components. We contribute an exact algorithm that decomposes the problem into smaller integer linear programs. We prove that this algorithm is finite and apply it to a set of instances. Experiments demonstrate that the integrated approach generates greater reliabilities than applying test planning and redundancy allocation models iteratively, and moreover, it yields significant savings in computational time