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

Multi-objective optimisation of safety-critical hierarchical systems

Achieving high reliability, particularly in safety critical systems, is an important and often mandatory requirement. At the same time costs should be kept as low as possible. Finding an optimum balance between maximising a system's reliability and minimising its cost is a hard combinatorial problem. As the size and complexity of a system increases, so does the scale of the problem faced by the designers. To address these difficulties, meta-heuristics such as Genetic Algorithms and Tabu Search algorithms have been applied in the past for automatically determining the optimal allocation of redundancies in a system as a mechanism for optimising the reliability and cost characteristics of that system. In all cases, simple reliability block diagrams with restrictive assumptions, such as failure independence and limited 2-state failure modes, were used for evaluating the reliability of the candidate designs produced by the various algorithms.This thesis argues that a departure from this restrictive evaluation model is possible by using a new model-based reliability evaluation technique called Hierachically Performed Hazard Origin and Propagation Studies (HiP-HOPS). HiP-HOPS can overcome the limitations imposed by reliability block diagrams by providing automatic analysis of complex engineering models with multiple failure modes. The thesis demonstrates that, used as the fitness evaluating component of a multi-objective Genetic Algorithm, HiP-HOPS can be used to solve the problem of redundancy allocation effectively and with relative efficiency. Furthermore, the ability of HiP-HOPS to model and automatically analyse complex engineering models, with multiple failure modes, allows the Genetic Algorithm to potentially optimise systems using more flexible strategies, not just series-parallel. The results of this thesis show the feasibility of the approach and point to a number of directions for future work to consider

An allocation scheme for estimating the reliability of a parallel-series system

We give a hybrid two stage design which can be useful to estimate the reliability of a parallel-series and/or by duality a series-parallel system, when the component reliabilities are unknown as well as the total numbers of units allowed to be tested in each subsystem. When a total sample size is fixed large, asymptotic optimality is proved systematically and validated via Monte Carlo simulation.Comment: 16 pages, 4 figure