Stats4Grads: Studies on Deteriorating Systems using Repair & Replacement Strategies
23 May 2007 00:00 in CM221
We study deteriorationg systems by means of shock models in which the system is subject to randomly occurring shocks each of which adds a non-negative quantity to the cumulative damage. System failures have been modeled as a first passage problem of the damage process, as well as using the frequency of occurrence of shocks. Maintenance actions are in the form of general repairs, which subsume minimal repair and replacement as special cases. Monotone processes are used to model repair times. Apart from arriving at explicit expressions for the optimal replacement time under varying conditions, stochastic monotonicity properties of the underlying sequences of variables are also studied. Further we study a new age-dependent general repair model and proves a theorem, establishing the correspondence between the real age and the virtual age processes. We further generalize the failure counting process to a class of bivariate processes. A formula for computing the rate of occurrence of failure (ROCOF), an important measure in the analysis of deteriorating systems for such bivariate processes is arrived at.
See the Stats4Grads page for more details about this series.