Mathematical modelling of maintained systems using point processes

In this paper, the analytical needs of industrial maintained systems are articulated and the mathematical modelling of maintained systems using the theory of point (counting) processes is presented. The adaptation of point processes to the complex nature of maintained systems is brought out. The models with their estimation, inference, validation and prediction based on the data generated by the maintained systems are depicted. Applications of these models to the data from maintained systems are shown and how they have been used to meet the objectives of maintenance is brought out. The issues resolved and the further work to be done is indicated.