A reliability model for a three-state degraded system having random degradation rates

• Three-state system degraded system is studied.
• The degradation rates are random and statistically dependent.
• The dependence is modeled by copulas.

For degraded multi-state systems, it has been assumed in the literature that, for any given system, the instantaneous degradation rates are fixed. This paper attempts to study a three-state degraded system that have random degradation rates among its states. In particular, a reliability model for such a three-state system is presented assuming that the degradation rates are random and statistically dependent. The dependence is modeled by copulas, and dynamic reliability analysis of the system is performed. Graphical illustrations are provided, and comparisons are made with the corresponding results for the classical fixed rates model.