Phil Scarf

On the application of a model of condition-based maintenance

In this paper the modelling of condition monitoring information for three critical water pumps at a large soft-drinks manufacturing plant is described. The purpose of the model is to predict the distribution of the residual lifetimes of the individual pumps. This information is used to aid maintenance management decision-making, principally relating to overhaul. We describe a simple decision rule to determine whether maintenance action is necessary given monitoring information to date.

Modelling the dependence of goals scored by opposing teams in international soccer matches

This paper presents models for the number of goals scored by opposing teams in international soccer matches. The bivariate discrete distributions employed are defined in terms of the marginal distributions and a dependence copula. This copula representation allows dependence in the bivariate distribution to be modelled in a flexible manner by specifying a suitable family of copula functions and fitting this to the bivariate data using maximum likelihood. Marginal means are modelled with match covariates. The nature of the dependence in the number of goals scored is complex, and we develop the idea that the strength of dependence depends on the competitive balance of a match. Our analysis suggests that for games between closely matched teams, the overall dependence is low, and that the dependence becomes increasingly negative as the competitiveness of a match decreases. In this way, we relate dependence to competitive balance and suggest a method to measure the latter quantity. The models developed here may also offer better forecasts than those offered by match outcome models with independent marginal distributions.

A stochastic model of crack growth under periodic inspections

Abstract A stochastic model is described and fitted to a set of data on maximum crack depths in welds on a large system. The initial model is a two-stage empirical one, in that it models crack initiation and crack growth with time, and concentrates on explaining the data rather than on the physical processes which give rise to cracks. The model is fitted to the data by the method of maximum likelihood, and the goodness-of-fit is considered. Possible extensions of the basic model are also discussed, including a three stage model, in which the delay before which a defect becomes ‘visible’ is also considered. The main purpose of the modelling is to consider the prediction of crack growth in time and the consequences of carrying out periodical inspections, with the aim of minimizing the long term total cost per unit time of maintaining structural integrity.

Asset replacement for an urban railway using a modified two-cycle replacement model

This paper considers the application of capital replacement models at Mass Transit Railway Corporation Limited (MTRCL), Hong Kong. A particular characteristic of the replacement problems considered is that costs relating to existing equipment are generally constant or increasing only slowly. Consequently, replacement is often driven by technical obsolescence, but other criteria are used for informing decisions. The applicability of traditional OR models of replacement is then problematic. We recommend the use of a modified two-cycle replacement model and compare this model to existing capital replacement models. Issues relating to the estimation of delay costs and failure consequences and their influence on the replacement decision are also considered—this is done using a fixed horizon model, which is a special case of the modified two-cycle model. Track points and escalators are used as particular examples. In addition to modelling recommendations, we discuss the management of asset replacement with emphasis on the procedures necessary to ensure that asset replacement requirements are considered appropriately and effectively. The paper treats, in particular, the procedural issues of asset replacement, and the discussion of asset replacement system methodology reflects the current practise at MTRCL, Hong Kong, and developments within that organization through collaboration with academia. The modified two-cycle replacement model is recommended by us for general replacement applications. The asset replacement procedure is presented as an exemplar for business and industry.

To lead or not to lead: analysis of the sprint in track cycling

Abstract This paper uses a statistical analysis of match sprint outcomes to guide tactical decisions in this highly tactical contest and to provide competitors and coaches with a potential, marginal gain. Logistic regression models are developed to predict the probability of the leading rider winning at different points of the race, based on how the race proceeds up to each point. Key tactics are successfully identified from the models, including how the leading rider might hold the lead and how the following rider might optimize overtaking.

Condition-based maintenance for a two-component system with stochastic and economic dependencies

This paper develops a model of a condition-based maintenance policy for a two-component system with both stochastic and economic dependencies. The stochastic dependency is such that the degradation rate of each component depends not only on its own state (degradation level) but also on the state of the other component. The economic dependency is such that combining multiple maintenance activities has lower cost than performing maintenance on components separately. To select a component or components to be preventively maintained, adaptive preventive maintenance and opportunistic maintenance rules are proposed. A cost model is developed to find the optimal values of decision variables. A case study of a gearbox system demonstrates the utility of the proposed model.

On outcome uncertainty and scoring rates in sport: The case of international rugby union

In this paper we investigate the relationship between outcome uncertainty and scoring rates in the framework of a “Poisson match”. We argue that increasing scoring rates in the hope of increasing entertainment may have a detrimental impact on the popularity of sport. The basis of our argument is that higher scoring-rates decrease outcome uncertainty. We use international rugby to demonstrate our findings and show that scoring rates have indeed increased significantly over the previous half-century in this sport. Therefore, administrators should recognise our general point and we suggest that rugby union administrators in particular ought to consider the introduction of new laws to reduce scoring-rates. Scenarios in which the scoring-rate is radically reduced are illustrated through a simulation of the Rugby World Cup tournament.

Sequential regression measurement error models with application

Sequential regression approaches can be used to analyze processes in which covariates are revealed in stages. Such processes occur widely, with examples including medical intervention, sports contests and political campaigns. The naïve sequential approach involves fitting regression models using the covariates revealed by the end of the current stage, but this is only practical if the number of covariates is not too large. An alternative approach is to incorporate the score (linear predictor) from the model developed at the previous stage as a covariate at the current stage. This score takes into account the history of the process prior to the stage under consideration. However, the score is a function of fitted parameter estimates and, therefore, contains measurement error. In this article, we propose a novel technique to account for error in the score. The approach is demonstrated with application to the sprint event in track cycling and is shown to reduce bias in the estimated effect of the score and avoid unrealistically extreme predictions.