Modelling imperfect inspection and maintenance in defence aviation through bayesian analysis of the KIJIMA type I general renewal process (GRP)

Abstract

To ensure the effective and efficient operation of Defence aviation equipment there is a clear need for a component life model that is representative of the true life of a component. However, the large and often sophisticated RAM models used to manage defence aviation platforms, through various engineering and logistics activities, use models that cannot accurately represent this life. The main difference is in the underlying repair assumption. Specifically, the Ordinary Renewal Process (ORP) uses an as-good-as-new repair assumption while the Non-Homogenous Poisson Process (NHPP) uses an as-bad-as-old repair assumption. However, it is highly unlikely that any component, typically referred to as a Repairable Item (RI), will readily fit into either repair assumption. Therefore, despite the best endeavours of both engineering and logistics staff given the underlying repair assumption and the limitation these impose on the model, any solution will be suboptimal. Accordingly, there is a need for a RI life model that can contend with imperfect maintenance, imperfect inspection and can adapt to the limitations in data and include a number of additional factors including aging of the component, number of repairs, effectiveness of the repair, skill of the technicians, etc. Eight cases were developed as part of the overall modelling scheme. These eight cases are further divided into 2 main types; the first type representing cases where failure times are known and the second type where failure times are unknown. The cases incrementally modify these types through the addition of factors including multiple failure modes and their inter-dependence, and imperfect inspection and maintenance, in order to achieve a more realistic representation. Each of these cases were then solved using utilising a Markov Chain Monte Carlo (MCMC) sampling procedure, concentrating only on the analysis of the KIJIMA Type I GRP model with an underlying Weibull Time-To- Failure (TTF) distribution. The MCMC was made possible through the use of a Slice Sampling and Auxiliary Variable techniques. The resulting models have the ability to accurately model, and specifically predict, the future failure trends. Furthermore, the model allows the analyst to compare the maintenance effectiveness either in isolation, or in comparison (benchmarking) of various maintenance activities/facilities