Reliability analysis of the system lifetime with n working elements and repairing device under condition of the element's fast repair

TL;DR

This paper analyzes the reliability of a system with multiple elements and a repair device, deriving the asymptotic distribution of system lifetime under fast repair conditions.

Contribution

It provides a new asymptotic distribution model for system lifetime with exponential repair times and general working times, considering fast repair scenarios.

Findings

Derived the asymptotic distribution of system lifetime.

Model accounts for exponential repair times and general working times.

Applicable to systems with rapid repair processes.

Abstract

In this paper we consider the system with $n$ identical elements and one repairing device. In each time moment only one element works while the rest elements stay in reserve. The distribution of element repairing period is exponential, the distribution of element working period is general. We obtain the asymptotic distribution of the system lifetime under condition of the element's fast repair.