مدل سازی دسترسی به سیستم های تعمیر با استفاده از شبکه های بیزی

We present a hybrid Bayesian network (HBN) framework to model the availability of renewable systems. We use an approximate inference algorithm for HBNs that involves dynamically discretizing the domain of all continuous variables and use this to obtain accurate approximations for the renewal or repair time distributions for a system. We show how we can use HBNs to model corrective repair time, logistics delay times and scheduled maintenance time distributions and combine these with time-to-failure distributions to derive system availability. Example models are presented and are accompanied by detailed descriptions of how repair (renewal) distributions might be modelled using HBNs.

Complex systems are required to be dependable in use and one important aspect of a system’s dependability is availability. Availability is intrinsically uncertain and is typically defined and measured as the probability of the system being available for use at a given point in time. A system might be unavailable if it has failed and is awaiting repair or the system has failed and is undergoing repair before re-entering service. Over a given time period, a system might therefore be available or unavailable depending not only on the system’s reliability but also on how well the support organisation might affect the rate of repair and the duration of such repairs (renewals). Additionally systems may also undergo preventative maintenance usually on a scheduled basis, and we might extend our analysis to consider the modes of failure, the subsystem failure rates, maintenance regimes and different methods of logistical support. Maintenance (renewal time) and reliability (failure time) are stochastic variables and it therefore makes sense to model these using appropriate statistical inference techniques. We could then predict future behaviour and make decisions about the acceptability of the availability one might expect to experience in a given system. For an overview of availability theory, concepts and models see Stapelberg (2009). We have used Bayesian networks (BNs) in a range of real-world applications of system dependability assessment; see for example Neil et al., 2001, Neil et al., 2003 and Neil et al., 2008. In such applications, it is inevitable that there will be a mixture of discrete and continuous nodes (the resulting BNs are called hybrid (HBNs)). The traditional approach to handling (non-Gaussian) continuous nodes is static: you have to discretize the continuous domains using some pre-defined range and intervals. However, this approach is unacceptable for critical systems, where there is a demand for reasonable accuracy. To overcome this problem, we have developed a new and powerful approximate algorithm for performing inference in HBNs. We use a process of dynamic discretization of the domain of all continuous variables in the HBN. The approach to discretizing the domain is influenced by the work of Kozlov and Koller (1997) using an entropy error as the basis for approximation. We differ from their approach by integrating an iterative approximation scheme within existing BN software architectures, such as in junction tree (JT) propagation (Jensen et al., 1990). Thus, rather than support separate data structures and a new propagation algorithm, we use the data structures commonly used in JT algorithms. The power and flexibility of the approach are demonstrated here by applying it to estimate the availability of repairable systems represented by a series of models each designed to model distinct stages in the renewal process: logistics delays, repairs and scheduled maintenance. Traditionally, modelling these events has relied on Monte Carlo simulation, involving many repeated simulation runs. In contrast to the simulation approach, we show how our HBN algorithms can be used to represent repair and support processes and the durations involved, under any assumptions for renewal time distributions (lognormal, exponential, etc.). The modelling has been made possible using the commercial general-purpose Bayesian network software tool AgenaRisk, Agena Ltd. (2010).

We have shown how we can use hybrid Bayesian networks (HBNs) to model renewable systems involving repairs and logistical delays. Particular focus has been given to modelling mixtures of lognormally distributed repair distributions, and this has been extended into the logistical delays case, involving the summation of delay times from many discrete events with normally distributed delay times. We show how to assess the reliability of subsystems using a Bayesian model coupled with component aging assumption and integrating data with an expert opinion. These subsystem TTF distributions could then be aggregated to provide a system level estimate using appropriate logical gates that reflect system structure. The combined scheme of dynamic discretization and robust propagation algorithms on HBNs can be used to obtain accurate results, offering a viable alternative to Monte Carlo simulation approaches, implemented within an easy-to-use and user friendly environment. Finally, we show the simple step of calculating the operational and inherent availability of the system from the various delay and failure distributions, and also demonstrated how point values for availabilities, with and without scheduled maintenance, can be obtained.