Maximizing the expected remaining useful lifetime of a weakly controlled device

Abstract

A degenerate two-dimensional diffusion process is considered as a model for the amount $X(t)$ of deterioration at time t that a device can suffer before having to be repaired or replaced. The model is such that $X(t)$ is strictly decreasing with time. Moreover, the deterioration rate is assumed to increase after a random amount of time. An approximate solution is sought to the problem of maximizing the expected remaining useful lifetime of the device when it is weakly controlled.

Keywords:

• Brownian motion
• first-passage time
• optimal stochastic control
• random parameters

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada.