An approach to modeling residual life of a renewal process for reliability analysis and maintenance planning

This paper extends and relaxes the structure of a mean remaining time to renewal model for a failure prone system subject to minimal repairs. Compared to existing related works, the contributions of our model are threefold. It not only accounts for changes in operating states and age factor, but also can adapt itself to minimal repair process history. It is implemented through the use of a damage process X(t) coupled with a supplementary variable N(t) counting the number of failures. The bivariate approach allows a wide class of models to be considered including age-based models and those ignoring the repair effect. Another feature enhancing the domain of its applicability is to predict failures and quantify some reliability indexes. These impose a challenge when coping with models either characterized by inter-correlated failure times or developed under varying operating conditions. Further, the structure of the devised model called state-dependent mean remaining time to renewal (in short SD-MRTR) enables the implementation of maintenance policy on the basis of renewal-reward arguments. In present setting, a renewal is defined with respect to the supplementary variable. That means, a renewal (perfect repair) is carried out as soon as the number of failures reaches a give value j. Using the renewal-reward theorem argument and the explored SD-MRTR, the practical contribution of the model is enhanced by proposing a j-based preventive replacement policy achieving minimum repair costs. The proposed model and the behavior of the optimal solution as the model parameters change are illustrated through numerical examples.