Termination versus operation extension for degrading systems

Abstract

Optimal cost-wise termination of operation for degrading engineering systems is considered that maximizes the expected profit for the infinite horizon. Termination reduces probability of the future failure that usually results in substantial loss. The cases of non-repairable and minimally repairable systems are discussed. The black-box scenario without additional information on stochastic process of degradation and that with additional information are considered. The novel sequential optimal inspection policy is described. It is proved that the termination time can be postponed in an optimal way if the degradation observed at inspection is smaller than the defined level. The developed approach allows for optimal usage of system’s “resource.” The detailed numerical examples illustrate the findings.

Optimal preventive maintenance strategy for populations of systems that generate outputs

“…Thus, the optimization problem (4) has the unique solution. It can be easily seen, as in Finkelstein et al (2022), the derivative cannot be negative in the vicinity of origin, because in this case,…”

“…Our discussion in the previous sections can be generalized in a rather straightforward but meaningful way to two important in practice settings (see also Finkelstein et al (2022)), where similar generalizations were considered in a different setting not related to populations output optimization. Besides, the main focus in that paper was on degradation modeled by relevant stochastic processes.…”

“…This happens because the sudden failures can lead to, e.g., interruption of the workflow, delays, safety-critical consequences, etc. The following analysis in this section is partially based on our recent paper (Finkelstein, et al (2022)), although the referenced paper is not about optimal PM and the repair action (and the corresponding cost) is not a part of the considered model. Assume first, that ( ) 1 qx  .…”