Abstract
Any system when put on operation deteriorates over a period of time and fails on crossing a threshold. Maintenance is performed either on failure or for mitigating the effects of this deterioration. In general the system is either partially maintained or renewed to bring it back to its operating state. The general behaviour of the failure process of a maintained system is modelled by means of stochastic processes called general repair processes. In these processes the effect of the maintenance carried out on the system is captured by means of a variable called the maintenance indicator which indicates the degree to which the system has been maintained. Such a maintenance indicator acting on the system’s failure age or intensity post maintenance generalizes the modelling of the failure processes. The general repair process models based on the type of the maintenance indicator can be broadly classified into two categories based on age or intensity loss or recovery and two sub-categories based on whether these take place additively or multiplicatively. This paper focuses on such models, their inference, their uses, the physical reality they depict and their shortcomings when modelling the failure processes of maintained systems. DOI: http://dx.doi.org/10.4038/sljastats.v12i0.4971 Sri Lankan Journal of Applied Statistics Vol.12 2011 pp.117-143
Highlights
Any system when put on operation deteriorates over a period of time and fails on crossing a threshold
G-Renewal Process (GRP), proportional age reduction (PAR), ARA1 or ARI1 models providing a better fit indicate that the maintenance actions in general are not effective in reducing the cumulative deterioration of the system while the exact opposite is the case with Kijima model II, ARA and ARI models wherein the cumulative deterioration of the system is addressed
The general repair models do not provide any information on the nature of the maintenance action to be carried out or the parts, components or sub-systems required to be changed other than indicating that the actions should depend on the state of the systems
Summary
Any system when put on operation deteriorates over a period of time and fails on crossing a threshold. When the performance of the system deteriorates or it breaks down and the whole system is replaced every time this happens, the maintenance is termed as maximal Such a system’s failure process is modelled by a renewal process. The present paper depicts and classifies all general repair models based on the effectiveness of the maintenance actions taken as represented by a maintenance indicator. It studies the methods of their inference, and the physical reality that they depict when modelling the failure processes of maintained systems.
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