On exponential convergence rate of distribution for some non-regenerative reliability system

TL;DR

This paper establishes exponential upper bounds for the convergence rate of the distribution of a restorable element with standby redundancy, even when working and repair times are dependent and bounded by exponential distributions.

Contribution

It provides new bounds for convergence rates in reliability systems with dependent, bounded, and partially energized components, extending previous results to more general cases.

Findings

Derived exponential upper bounds for convergence rates.

Estimated bounds for the availability factor.

Applicable to systems with dependent working and repair times.

Abstract

The exponential upper bounds for the convergence rate of the distribution of restorable element with partially energized standby redundancy are founded, in the case when all working and repair times are bounded by exponential random variable (upper and lower), and working and repair times can by dependent. The bounds for the convergence rate of the availability factor are estimated. -------------------------------------- Polucheny ocenki sverhu dlya skorosti skhodimosti raspredeleniya sostoyaniya vosstanavlivaemogo ehlementa s tyoplym rezervom v sluchae, kogda vremena raboty i vosstanovleniya oboih ehlementov mogut byt' zavisimy, i oni ogranicheny sverhu i snizu ehksponencial'nym raspredeleniem. Poluchennyj rezul'tat pozvolyaet ocenivat' skorost' skhodimosti koehfficienta gotovnosti k stacionarnomu znacheniyu