Two-dimensional failure modeling with minimal repair

In this paper, we discuss two-dimensional failure modeling for a system where degradation is due to age and usage. We extend the concept of minimal repair for the one-dimensional case to the two-dimensional case and characterize the failures over a two-dimensional region under minimal repair. An application of this important result to a manufacturer's servicing costs for a two-dimensional warranty policy is given and we compare the minimal repair strategy with the strategy of replacement of failure.