Matthew Revie

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.

Estimating the probability of rare events: addressing zero failure data

Traditional statistical procedures for estimating the probability of an event result in an estimate of zero when no events are realized. Alternative inferential procedures have been proposed for the situation where zero events have been realized but often these are ad hoc, relying on selecting methods dependent on the data that have been realized. Such data-dependent inference decisions violate fundamental statistical principles, resulting in estimation procedures whose benefits are difficult to assess. In this article, we propose estimating the probability of an event occurring through minimax inference on the probability that future samples of equal size realize no more events than that in the data on which the inference is based. Although motivated by inference on rare events, the method is not restricted to zero event data and closely approximates the maximum likelihood estimate (MLE) for nonzero data. The use of the minimax procedure provides a risk adverse inferential procedure where there are no events realized. A comparison is made with the MLE and regions of the underlying probability are identified where this approach is superior. Moreover, a comparison is made with three standard approaches to supporting inference where no event data are realized, which we argue are unduly pessimistic. We show that for situations of zero events the estimator can be simply approximated with 1/2.5n, where n is the number of trials.

Supporting Reliability Decisions During Defense Procurement Using a Bayes Linear Methodology

Defense procuring authorities assess the growth in reliability performance of new systems against requirements using evidence provided by contractors during product design and development. Since projects can be lengthy and complex, a structured methodology is required to support consistent assessment and inform decisions. A methodology grounded in the principles of Bayes linear is proposed because it provides a theoretical framework for modeling the epistemic uncertainty in the reliability management process during which the decision maker synthesizes information from supplier analyses to form an assessment that will be updated as new information becomes available. Methods for structuring and populating a Bayes linear model are developed and a strategy for sensitivity analysis to explore the robustness of results to variations in subjective engineering beliefs is proposed. The feasibility of the methodology is examined through an industrial application to support reliability assessment during a defense procurement project. Based on feedback, our findings show that it is feasible to develop a requisite Bayes linear model to support reliability assessment. We find that many strengths and weaknesses of a Bayes linear approach are shared by other Bayesian models, but that a Bayes linear method has potential benefits through reduced elicitation burden and straightforward sensitivity analysis.

Associations between obesity and cognition in the pre-school years

To test the hypothesis that obesity is associated with impaired cognitive outcomes in the pre‐school years.

Screening, sensitivity, and uncertainty for the CREAM method of human reliability analysis

This paper reports a sensitivity analysis of the Cognitive Reliability and Error Analysis Method for Human Reliability Analysis. We consider three different aspects: the difference between the outputs of the Basic and Extended methods, on the same HRA scenario; the variability in outputs through the choices made for common performance conditions (CPCs); and the variability in outputs through the assignment of choices for cognitive function failures (CFFs). We discuss the problem of interpreting categories when applying the method, compare its quantitative structure to that of first generation methods and discuss also how dependence is modelled with the approach. We show that the control mode intervals used in the Basic method are too narrow to be consistent with the Extended method. This motivates a new screening method that gives improved accuracy with respect to the Basic method, in the sense that (on average) halves the uncertainty associated with the Basic method. We make some observations on the design of a screening method that are generally applicable in Risk Analysis. Finally, we propose a new method of combining CPC weights with nominal probabilities so that the calculated probabilities are always in range (i.e. between 0 and 1), while satisfying sensible properties that are consistent with the overall CREAM method.

Evaluation of elicitation methods to quantify Bayes linear models

Abstract The Bayes linear methodology allows decision makers to express their subjective beliefs and adjust these beliefs as observations are made. It is similar in spirit to probabilistic Bayesian approaches, but differs as it uses expectation as its primitive. While substantial work has been carried out in Bayes linear analysis, both in terms of theory development and application, there is little published material on the elicitation of structured expert judgement to quantify models. This paper investigates different methods that could be used by analysts when creating an elicitation process. The theoretical underpinnings of the elicitation methods developed are explored and an evaluation of their use is presented. This work was motivated by, and is a precursor to, an industrial application of Bayes linear modelling of the reliability of defence systems. An illustrative example demonstrates how the methods can be used in practice.

A mixed-method optimisation and simulation framework for supporting logistical decisions during offshore wind farm installations

With a typical investment in excess of £100 million for each project, the installation phase of offshore wind farms (OWFs) is an area where substantial cost-reductions can be achieved; however, to-date there have been relatively few studies exploring this. In this paper, we develop a mixed-method framework which exploits the complementary strengths of two decision-support methods: discrete-event simulation and robust optimisation. The simulation component allows developers to estimate the impact of user-defined asset selections on the likely cost and duration of the full or partial completion of the installation process. The optimisation component provides developers with an installation schedule that is robust to changes in operation durations due to weather uncertainties. The combined framework provides a decision-support tool which enhances the individual capability of both models by feedback channels between the two, and provides a mechanism to address current OWF installation projects. The combined framework, verified and validated by external experts, was applied to an installation case study to illustrate the application of the combined approach. An installation schedule was identified which accounted for seasonal uncertainties and optimised the ordering of activities.

Estimating risk when zero events have been observed

Assessing the risk of complications or adverse events following an intervention presents challenges when they have not yet occurred. Suppose, for instance, a chronic shortage of cardiac telemetry beds has prompted a hospital to implement a new policy that places low-risk patients admitted to ‘rule out myocardial infarction’ in regular ward beds (ie, with no telemetry). After 6 months and the admission of 100 such patients, no cardiac arrests or other untoward events have occurred. This absence of harm (ie, zero adverse events) indicates a low risk, but clearly we cannot infer a risk of zero on the basis of only 100 patients. But, what can we say about the true underlying risk? The Rule of Three (Ro3), first proposed by Hanley and Hand,1 provides an estimate for the upper bound of the underlying risk when zero events of interest have occurred through considering the lack of occurrences as moderately rare. The Ro3 estimates the risk as no greater than 3/n, where n is the number of opportunities or exposures to the risk. Technically, 3/n is obtained through assigning the probability 0.95 to measure the likelihood of realising more events than those observed. Note that the Ro3 estimate applies only when one has at least 30 observations. In the above example, the Ro3 would estimate the upper limit for the risk of adverse events associated with the new policy as 3/100 or 3%. This estimate does not sound as reassuring …

Modelling GB rail timetable risk : analysis of SPADs due to human error on the Scotland network between 2004-10

As the timetable dictates the arrival times of trains at junctions and stations, it seems reasonable to assume that different timetables may result in different levels of opportunity for conflict and collision. Although a well designed timetable should have few (if any) conflicts, trains do not always run on time, and consequently the robustness of the timetable to service perturbations is an area of interest to RSSB, the not for profit organisation that collect and analyse safety data on the GB rail network. Our aim is to investigate selected operational data for the GB rail network to examine how variables characterising timetable risk affect the probability of occurrence of Signals Passed at Danger (SPAD) where SPADs represent a precursor for railway accidents. Interviews with RSSB analysts and engineers have surfaced factors such as complexity of the timetable, frequency and density trains, amongst others, that can be used to characterise timetable risk. Data have been extracted from multiple databases and prepared to capture the relationships between, for example, the network junctions and the times at which trains pass the junction. A combination of exploratory statistical analysis and regression modelling has been used to investigate the data and build preliminary models for explaining and predicting the probability of a SPAD as a function of accessible variables representing timetable risk.

On modeling player fitness in training for team sports with application to professional rugby

It is increasingly important for professional sports teams to monitor player fitness in order to optimize performance. Models have been put forward linking fitness in training to performance in competition but rely on regular measurements of player fitness. As formal tests for measuring player fitness are typically time-consuming and inconvenient, measurements are taken infrequently. As such, it may be challenging to accurately predict performance in competition as player fitness is unknown. Alternatively, other data, such as how the players are feeling, may be measured more regularly. This data, however, may be biased as players may answer the questions differently and these differences may dominate the data. Linear mixed methods and support vector machines were used to estimate player fitness from available covariates at times when explicit measures of fitness were unavailable. Using data provided by a professional rugby club, a case study was used to illustrate the application and value of these models. Both models performed well with R2 values ranging from 60% to 85%, demonstrating that the models largely captured the biases introduced by individual players.