David F. Percy

Determining economical maintenance intervals

Abstract Several models have been proposed for scheduling the preventive maintenance (PM) of complex repairable systems in industry. These are often application-specific and some make unrealistic assumptions about stationarity of the process and quality of repairs. We investigate two principal types of general model, which have wider applicability. The first considers fixed PM intervals and is based on the delayed alternating renewal process. The second is adaptable, allowing variable PM intervals, and is based on proportional hazards or intensities. We describe how Bayesian methods of analysis can improve the decision making process for these models and discuss simulation algorithms for fitting the models to observed data. Finally, we identify some issues that need more research.

A full history proportional hazards model for preventive maintenance scheduling

This paper is concerned with the development of a realistic preventive maintenance (PM) scheduling model. A heuristic approach for implementing the semi-parametric proportional-hazards model (PHM) to schedule the next preventive maintenance interval on the basis of the equipments full condition history is introduced. This heuristic can be used with repairable systems and does not require the unrealistic assumption of renewal during repair, or even during PM. Two PHMs are fitted, for the life of equipment following corrective work and the life of equipment following PM, using appropriate explanatory variables. These models are then used within a simulation framework to schedule the next preventive maintenance interval. Optimal PM schedules are estimated using two different criteria, namely maximizing availability over a single PM interval and over a fixed horizon. History data from a set of four pumps operating in a continuous process industry is also used to demonstrate the proposed approach. The results indicate a higher availability for the recommended schedule than the availability resulting from applying the optimal PM intervals as suggested by using the conventional stationary models.

Bayesian enhanced strategic decision making for reliability

Successful strategies for maintenance and replacement require good decisions. We might wish to determine how often to perform preventive maintenance, or the optimal time to replace a system. Alternatively, our interest might be in selecting a threshold to adopt for action under condition monitoring, or in choosing suitable warranty schemes for our products. Stochastic reliability models involving unknown parameters are often used to answer such questions. In common with other problems in operational research, some applications of maintenance and replacement are notorious for their lack of data. We present a general review and some new ideas for improving decisions by adopting Bayesian methodology to allow for the uncertainty of model parameters. These include recommendations for specifying suitable prior distributions using predictive elicitation and simple methods for Bayesian simulation. Practical demonstrations are given to illustrate the potential benefits of this approach.

Setting preventive maintenance schedules when data are sparse

Abstract When new production lines are established, little information is available about their reliability. The evaluation of such systems is a learning process and knowledge is continually updated as more information becomes available. This paper considers stochastic models when data are sparse, with emphasis on preventive maintenance intervention to avoid system failure. Bayesian methods are adopted, leading to optimal strategies under the model assumptions. This approach also includes prior knowledge about the manufacturing process and similar systems. Our approach is a first reconnaissance into a new field, exemplary of ways to solve these problems, rather than an algorithm that can be readily applied.

Scheduling preventive maintenance for oil pumps using generalized proportional intensities models

Percy and Alkali presented generalizations of the proportional intensities model introduced by Cox. They identified several features of these models that are particularly relevant for modelling complex repairable systems subject to preventive maintenance (PM). These include the baseline intensity, scaling factors and explanatory variables. We investigate these aspects in detail and apply the models to five sets of reliability data collected from the main pumps at oil refineries. We use likelihood methods to estimate the model parameters and compare how well the models fit the data. Our analyses suggest that a log-linear baseline intensity function performs well and that an exponential deterministic scaling function is useful for corrective maintenance. The inclusion of explanatory variables to represent the quality of last maintenance and time since last maintenance also proves to be beneficial. We develop algorithms for simulating the reliability behaviour of a complex repairable system into the future, in order to schedule appropriate maintenance activities, identifying special cases that simplify the algebra. Applying these methods to the oil pump data, we derive recommendations for PM plans and demonstrate that adopting this strategy can lead to substantial savings.

Preventive maintenance modelling

Develops practical models for preventive maintenance policies using Bayesian methods of statistical inference. Considers the analysis of a delayed renewal process and a delayed alternating renewal process with exponential times to failure. This approach has the advantage of generating predictive distributions for numbers of failures and downtimes rather than relying on estimated renewal functions. Demonstrates the superiority of this approach in analysing situations with non‐linear cost functions, which arise in reality, by means of an example.

A mathematical analysis of badminton scoring systems

The International Badminton Federation recently introduced rule changes to make the game faster and more entertaining, by influencing how players score points and win games. We assess the fairness of both systems by applying combinatorics, probability theory and simulation to extrapolate known probabilities of winning individual rallies into probabilities of winning games and matches. We also measure how effective the rule changes are by comparing the numbers of rallies per game and the scoring patterns within each game, using data from the 2006 Commonwealth Games to demonstrate our results. We then develop subjective Bayesian methods for specifying the probabilities of winning. Finally, we describe how to propagate this information with observed data to determine posterior predictive distributions that enable us to predict match outcomes before and during play.

Subjective priors for maintenance models

Successful strategies for maintenance require good decisions and we commonly use stochastic reliability models to help this process. These models involve unknown parameters, so we gather data to learn about these parameters. However, such data are often difficult to collect for maintenance applications, leading to poor parameter estimates and incorrect decisions. A subjective modelling approach can resolve this problem, but requires us to specify suitable prior distributions for the unknown parameters. This paper considers which priors to adopt for common maintenance models and describes the method of predictive elicitation for determining unknown hyperparameters associated with these prior distributions. We discuss the computational difficulties of this approach and consider numerical methods for resolving this problem. Finally, we present practical demonstrations to illustrate the potential benefits of predictive elicitation and subjective analysis. This work provides a major step forward in making the methods of subjective Bayesian inference available to maintenance decision makers in practice. Practical implications. This paper recommends powerful strategies for expressing subjective knowledge about unknown model parameters, in the context of maintenance applications that involve making decisions.

Vector-borne infectious disease mapping with stochastic difference equations: an analysis of dengue disease in Malaysia

Few publications consider the estimation of relative risk for vector-borne infectious diseases. Most of these articles involve exploratory analysis that includes the study of covariates and their effects on disease distribution and the study of geographic information systems to integrate patient-related information. The aim of this paper is to introduce an alternative method of relative risk estimation based on discrete time–space stochastic SIR-SI models (susceptible–infective–recovered for human populations; susceptible–infective for vector populations) for the transmission of vector-borne infectious diseases, particularly dengue disease. First, we describe deterministic compartmental SIR-SI models that are suitable for dengue disease transmission. We then adapt these to develop corresponding discrete time–space stochastic SIR-SI models. Finally, we develop an alternative method of estimating the relative risk for dengue disease mapping based on these models and apply them to analyse dengue data from Malaysia. This new approach offers a better model for estimating the relative risk for dengue disease mapping compared with the other common approaches, because it takes into account the transmission process of the disease while allowing for covariates and spatial correlation between risks in adjacent regions.

Small data sets and preventive maintenance modelling

Preventive maintenance (PM) is an effective maintenance policy which is widely applied in industry. Reviews the main approaches of modelling PM and discusses the characteristics of real life PM data which influence the methods for modelling PM. The most salient features of these data are the limited size and intensive censoring effect. Then introduces a parametric bootstrap method for fitting PM data to distributions. A simulation study to compare this method with the established Akaike and Schwarz criteria shows that while the bootstrap method is marginally better in identifying the true distribution, this is counterbalanced by the intensive computational effort needed.