Qualitative probability modelling with applications to systems maintenance

Probability models are necessary for the analysis of systems reliability and maintenance because of the inevitable uncertainty involved. However, probability terminology is rather obscure for most engineers who therefore may not use effectively mathematical models that have been developed in the literature or may even avoid them altogether. To overcome this difficulty the author suggests an approach that enables the engineer to use mathematical, or indeed probabilistic, maintenance models through concepts and notions that he or she is familiar with. This is achieved by formulating the basic assumptions of the model through qualitative assumptions, or physical quantities, that are clearly understood by the user-engineer, and the exact mathematical model is only formed in the next stage through translation of these qualitative assumptions into probability terms and functions. With this modelling process, which is most effectively done in the framework of a (carefully planned) dialogue between the user-engineer and a probability professional, the underlying distributions or processes of the model are, essentially, being derived rather than assumed (as is usually done in the literature, and quite arbitrarily so). This results in greater accuracy of the model, with regard to the real-life situation it relates to, as well as in making the results of the analysis and the ensuing maintenance policy prescription more dependable to the model user.