Allocation of tasks for reliability growth using multi-attribute utility

In reliability growth models in particular, and project risk management more generally, improving the reliability of a system or product is limited by constraints on cost and time. There are many possible tasks which can be carried out to identify and design out weaknesses in the system under development. This paper considers the allocation problem: which subset of tasks to undertake. While the method is applicable to project risk management generally, the work has been motivated by reliability growth programmes. We utilise a model for reliability growth, based on an efficacy matrix, developed with engineering experts in the aerospace industry. We develop a general multi- attribute utility function based on targets for cost, time on test and system reliability. The optimal subset is identified by maximising the prior expected utility. We derive conditions on the model parameters for risk aversion and loss aversion based on observed properties of preference. We give conditions for multivariate risk aversion under the general form of the utility function. The method is illustrated using an example informed by work with aerospace organisations

Quantifying the benefit of structural health monitoring: can the value of information be negative?

The benefit of Structural Health Monitoring (SHM) can be properly quantified using the concept of Value of Information (VoI), which is, applied to an SHM case, the difference between the utilities of operating the structure with and without the monitoring system. The aim of this contribution is to demonstrate that, in a decision-making process where two different individuals are involved in the decision chain, i.e. the owner and the manager of the structure, the VoI can be negative. Indeed, even if the two decision makers are both rational and exposed to the same background information, their optimal actions can diverge after the installation of the monitoring system due to their different appetite for risk: this scenario could generate a negative VoI, which corresponds exactly to the amount of money the owner is willing to pay to prevent the manager using the monitoring system. In this paper, starting from a literature review about how to quantify the VoI, a mathematical formulation is proposed which allows one to assess when and under which specific conditions, e.g. appropriate combination of prior information and utility functions, the VoI becomes negative. Moreover, to illustrate how this framework works, a hypothetical VoI is evaluated for the Streicker Bridge, a pedestrian bridge on the Princeton University campus equipped with a fiber optic sensing system: the results show how the predominant factor that determines a negative VoI is the different risk appetite of the two decision makers, owner and manager

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