Author's personal copy Optimal interval for major maintenance actions in electricity distribution networks Darko Louit a , Rodrigo Pascual a, * , Dragan Banjevic b a Centro de Minería, Pontificia Universidad Católica de Chile, Av. Vicuña MacKenna, 4860 Santiago, Chile b Centre for Maintenance Optimization and Reliability Engineering, University of Toronto, 5 King’s College Rd., Toronto, Ontario, Canada M5S 3G8 article info Article history: Received 21 July 2008 Received in revised form 18 March 2009 Accepted 20 March 2009 Keywords: Asset management Major maintenance actions Electricity network abstract Many systems require the periodic undertaking of major (preventive) maintenance actions (MMAs) such as overhauls in mechanical equipment, reconditioning of train lines, resurfacing of roads, etc. In the long term, these actions contribute to achieving a lower rate of occurrence of failures, though in many cases they increase the intensity of the failure process shortly after performed, resulting in a non-monotonic trend for failure intensity. Also, in the special case of distributed assets such as communications and energy networks, pipelines, etc., it is likely that the maintenance action takes place sequentially over an extended period of time, implying that different sections of the network underwent the MMAs at dif- ferent periods. This forces the development of a model based on a relative time scale (i.e. time since last major maintenance event) and the combination of data from different sections of a grid, under a normal- ization scheme. Additionally, extended maintenance times and sequential execution of the MMAs make it difficult to identify failures occurring before and after the preventive maintenance action. This results in the loss of important information for the characterization of the failure process. A simple model is intro- duced to determine the optimal MMA interval considering such restrictions. Furthermore, a case study illustrates the optimal tree trimming interval around an electricity distribution network. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction For complex systems, composed of many parts, each subject to different failure modes, when a failure occurs, repairs are typically specific to the failed part, leaving the rest of the system untouched (Sherwin [14]). In such cases, the use of non-homogeneous Poisson processes (NHPPs) to represent the failure pattern of the system is common, as these models assume that, when the equipment fails, the maintenance/repair action returns the equipment to its previ- ous state (just before the failure occurred). This is referred to as minimal repair, as opposed to major maintenance actions (MMAs) such as overhauls, which can be regarded as general repairs (im- prove the state of the system further than just returning it to the state just before failure). It can be assumed that, in between MMAs, complex systems are subject to failures that can be remedied without altering the over- all system reliability (i.e. with minimal repairs). Particularly in the case of distributed assets, normally each failure affects only one small section (part) of the entire system, thus repair does not have a significant effect on the complete system’s risk of failure. An example is given of a leak in a section of a pipeline: once the leak has been fixed, the pipeline is likely to suffer from leaks in different sections if the probability of occurrence of leaks is age related (a reasonable assumption). This risk of a leak occurring would only be modified after a significant maintenance operation, such as recoating of the entire pipeline. The system, then, behaves as a repairable system (with minimal repairs only), or NHPP, between MMAs. Mathematically, and independently of the type of model chosen to represent the failure pattern (NHPPs or other), failure intensity can be used to describe the failures of such a repairable system, or instantaneous rate of failure of a system at a specified age. Given a process in which two or more failures never occur in the same in- stant (or infinitesimal interval dt, with dt ? 0), the failure inten- sity, k(t), tends to the probability of a failure occurring in the next interval dt (Baker [2]): kðtÞ¼ lim dt!0 Pða failure in ðt; t þ dtÞÞ dt ð1Þ Sometimes, failure intensity increases with age. Otherwise, it may decrease with the age of the system, and in some other cases, it follows a non-monotonic trend, such as the generally called bath-tub shape (initially decreases and later on increases with time). It is a common experience that, just after an MMA, the sys- tem has an increased intensity of failure. This can be due to new problems created by the maintenance action, low quality control when performing the maintenance action, or other reasons (the case study provided in Section 3 of this paper advances an interest- ing example). Once these initial failures have been overcome, the 0142-0615/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2009.03.021 * Corresponding author. E-mail address: rpascual@ing.puc.cl (R. Pascual). Electrical Power and Energy Systems 31 (2009) 396–401 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes