Lesley Walls

Building prior distributions to support Bayesian reliability growth modelling using expert judgement

A sound methodology for the elicitation of subjective expert judgement is a pre-requisite for specifying prior distributions for the parameters of reliability growth models. In this paper, we describe an elicitation process that is developed to ensure valid data are collected by suggesting how possible bias might be identified and managed. As well as discussing the theory underpinning the elicitation process, the paper gives practical guidance concerning its implementation during reliability growth testing. The collection of subjective data using the proposed elicitation process is embedded within a Bayesian reliability growth modelling framework and reflections upon its practical use are described.

Expert Elicitation for Reliable System Design

This paper reviews the role of expert judgement to support reliability assessments within the systems engineering design process. Generic design processes are described to give the context and a discussion is given about the nature of the reliability assessments required in the different systems engineering phases. It is argued that, as far as meeting reliability requirements is concerned, the whole design process is more akin to a statistical control process than to a straightforward statistical problem of assessing an unknown distribution. This leads to features of the expert judgement problem in the design context which are substantially different from those seen, for example, in risk assessment. In particular, the role of experts in problem structuring and in developing failure mitigation options is much more prominent, and there is a need to take into account the reliability potential for future mitigation measures downstream in the system life cycle. An overview is given of the stakeholders typically involved in large scale systems engineering design projects, and this is used to argue the need for methods that expose potential judgemental biases in order to generate analyses that can be said to provide rational consensus about uncertainties. Finally, a number of key points are developed with the aim of moving toward a framework that provides a holistic method for tracking reliability assessment through the design process.

Systemic risk elicitation : using causal maps to engage stakeholders and build a comprehensive view of risks

As evidenced through both a historical and contemporary number of reported over-runs, managing projects can be a risky business. Managers are faced with the need to effectively work with a multitude of parties and deal with a wealth of interlocking uncertainties. This paper describes a modelling process developed to assist managers facing such situations. The process helps managers to develop a comprehensive appreciation of risks and gain an understanding of the impact of the interactions between these risks through explicitly engaging a wide stakeholder base using a group support system and causal mapping process. Using a real case the paper describes the modelling process and outcomes along with its implications, before reflecting on the insights, limitations and future research.

Developing statistical thinking for performance in the food industry

Purpose – The paper aims to describe a recently completed research project on the use of statistical quality control (SQC) methods in the context of food and drinks manufacturing. It discusses issues surrounding the successful uptake of such methods, including organisational motivation, possible application, costs and benefits, critical success factors and the central importance of prerequisite statistical thinking (ST).Design/methodology/approach – A three stage, mixed methods approach was adopted, incorporating surveys augmented by case studies and key informant interviews with industry managers and providers of relevant industry training. All data were combined to produce the final model.Findings – The paper finds that SQC methods are of relevance in the industry, providing the process is appropriate and management have a basic awareness of the fundamentals of ST. Certain organisational and external factors were found to progressively reduce the effectiveness with which such methods are introduced and ...

Trading reliability targets within a supply chain using Shapley's value

The development of complex systems involves a multi-tier supply chain, with each organisation allocated a reliability target for their sub-system or component part apportioned from system requirements. Agreements about targets are made early in the system lifecycle when considerable uncertainty exists about the design detail and potential failure modes. Hence resources required to achieve reliability are unpredictable. Some types of contracts provide incentives for organisations to negotiate targets so that system reliability requirements are met, but at minimum cost to the supply chain. This paper proposes a mechanism for deriving a fair price for trading reliability targets between suppliers using information gained about potential failure modes through development and the costs of activities required to generate such information. The approach is based upon Shapleys value and is illustrated through examples for a particular reliability growth model, and associated empirical cost model, developed for problems motivated by the aerospace industry. The paper aims to demonstrate the feasibility of the method and discuss how it could be extended to other reliability allocation models.

Estimating rate of occurrence of rare events with empirical bayes : A railway application

Classical approaches to estimating the rate of occurrence of events perform poorly when data are few. Maximum likelihood estimators result in overly optimistic point estimates of zero for situations where there have been no events. Alternative empirical-based approaches have been proposed based on median estimators or non-informative prior distributions. While these alternatives offer an improvement over point estimates of zero, they can be overly conservative. Empirical Bayes procedures offer an unbiased approach through pooling data across different hazards to support stronger statistical inference. This paper considers the application of Empirical Bayes to high consequence low-frequency events, where estimates are required for risk mitigation decision support such as as low as reasonably possible. A summary of empirical Bayes methods is given and the choices of estimation procedures to obtain interval estimates are discussed. The approaches illustrated within the case study are based on the estimation of the rate of occurrence of train derailments within the UK. The usefulness of empirical Bayes within this context is discussed

A load sharing system reliability model with managed component degradation

Motivated by an industrial problem affecting a water utility, we develop a model for a load sharing system where an operator dispatches work load to components in a manner that manages their degradation. We assume degradation is the dominant failure type, and that the system will not be subject to sudden failure due to a shock. By deriving the time to degradation failure of the system, estimates of system probability of failure are generated, and optimal designs can be obtained to minimize the long run average cost of a future system. The model can be used to support asset maintenance and design decisions. Our model is developed under a common set of core assumptions. That is, the operator allocates work to balance the level of the degradation condition of all components to achieve system performance. A system is assumed to be replaced when the cumulative work load reaches some random threshold. We adopt cumulative work load as the measure of total usage because it represents the primary cause of component degradation. We model the cumulative work load of the system as a monotone increasing and stationary stochastic process. The cumulative work load to degradation failure of a component is assumed to be inverse Gaussian distributed. An example, informed by an industry problem, is presented to illustrate the application of the model under different operating scenarios.

Modeling to support reliability enhancement during product development with applications in the U.K. Aerospace industry

Reliability improvement is the conceptual norm but has not been achieved by all sectors of industry. The U.K. aerospace industry is one that has aspired to make the transition from a culture of reliability demonstration to enhancement. This paper presents action research that examines the challenges facing this industry. A statistical model is developed to help measure the likely impact of failure modes on operational performance, hence providing a basis for managing the enhancement process. The model, which has general applicability to other product development processes, is stated and justified. The industrial interventions are described and an analysis of findings is presented. The proposed model is better than traditional approaches because it provides a systematic process to capture and integrate data from different sources to estimate reliability by directly measuring the engineering improvement achieved through product design and development. The estimates can be used to inform a traceable coherent argument about the level and growth in reliability to management and the customer as well as to provide insight into the impact of alternative engineering modifications to the design team. The modeling process has contributed to the partial transition to reliability enhancement of a consortium of companies who have changed their standard operating procedures to reflect the lessons learned from the research intervention. The insights gained contribute to an understanding of how the U.K. aerospace industry is changing its management of reliability enhancement in design.

Measuring the effectiveness of reliability growth testing

Assessing the effectiveness of reliability growth testing allows decisions to be made about the management of the programme; for example, decisions to allocate resources in an attempt to realize improvements in system reliability, or decisions to terminate testing when there is evidence that reliability has matured. However, such assessments are commonly based on measures of change in the average time between failures, which do not always provide informative measures of effectiveness. We argue that a more appropriate approach is to focus on the identification and realization of faults, which if removed are likely to lead to the improvement in system reliability. Therefore we introduce a model that incorporates the concerns of engineering experts about the likely faults in the initial system design with the information about faults that are realized on test. This model distinguishes between the processes of detecting and removing faults and so captures the effectiveness of test as well as the development of the system design. Using this model, the likely number of faults remaining in the system and the additional test time required to realize them can be estimated. This model was motivated by and assessed by engineers conducting growth tests for complex electronic systems. They consider our measures useful for supporting assessment of test effectiveness.

The use of statistical process control in food packing

Presents a synthesis of the early findings from an ongoing project researching the issues surrounding the use of SPC in a food packing environment. A cognitive mapping approach has been utilised to make sense of the complex and varied data resulting from the survey, case studies and interviews carried out to date. This methodological approach is described, and its application illustrated in relation to the research topic. Argues that SPC is one weapon in an arsenal of quality management techniques that food companies can use to consolidate or improve their position in an increasingly competitive marketplace. Once successfully adopted SPC can offer proven operational and financial benefits, but the ability of the organisation to successfully achieve implementation will depend upon a number of organisational factors. Finally, presents the agenda for further research which outlines how this ongoing project is intended to be taken forward from this point.