• DOI:10.1017/S0001867800019923
• Corpus ID: 124772199

Optimal strategies for some repair replacement models

@article{Stadje1990OptimalSF,
  title={Optimal strategies for some repair replacement models},
  author={Wolfgang Stadje and Dror Zuckerman},
  journal={Advances in Applied Probability},
  year={1990},
  volume={22},
  pages={641-656}
}

• W. Stadje, D. Zuckerman
• Published 1 September 1990
• Engineering
• Advances in Applied Probability

The problem of finding optimal replacement strategies for certain classes of failure systems is considered. These systems can be repaired upon failure, but are stochastically deteriorating, i.e., the lengths of the operating intervals decrease in some sense, whereas the durations of the repairs increase. For several models of this type optimal replacement strategies are derived under natural assumptions on the reward and the cost structure. This study deals with the problem of optimal replacement for various failure systems. In the models under consideration, a system (one may for instance think of a technical unit) is supposed to have a random lifetime until its first failure, after which it can be repaired. This repair takes a random amount of time and causes costs proportional to its duration. Thereafter the system operates again until its next breakdown, and so on. During the time of the functioning of the system a reward is produced at a constant rate. The systems in the proposed models are 'stochastically deteriorating' in the sense that the operating periods will become shorter and shorter, whereas the mean lengths of the repair periods are increasing. Further each operating period is assumed to have a non-decreasing failure rate (IFR) so that the probability of an imminent damage increases with the lifetime since the last failure; on the other hand, regarding the repair periods, we suppose the NBUE property (new better than used in expectation) so that the expected remaining repair time, given that current repair has already taken say t time units, is not greater than the corresponding unconditional mean repair time. At any time t, the system can be replaced by a new identical one, and the replacement cycles are repeated indefinitely. The replacement cost depends on the state (operating or being in repair) of the system.