# On polynomial recurrence for reliability system with a warm reserve

## TL;DR

This paper establishes conditions for positive and polynomial recurrence in a reliability model with two elements, proving the uniqueness of its stationary distribution and enabling theoretical evaluation of convergence rates.

## Contribution

It introduces new recurrence conditions for a two-element reliability model, ensuring stationary distribution uniqueness and providing a basis for convergence rate analysis.

## Key findings

- Conditions for positive recurrence are established.
- Uniqueness of the stationary distribution is proved.
- Theoretical evaluation of convergence rate is possible.

## Abstract

Conditions for positive and polynomial recurrence have been proposed for a class of reliability models of two elements with transitions from working state to failure and back. As a consequence, uniqueness of stationary distribution of the model is proved; the rate of convergence towards this distribution may be theoretically evaluated on the basis of the established recurrence.