# Errors Due to Departure from Independence in Exponential Series System

## TL;DR

This paper investigates the errors in reliability measures caused by assuming independence among components in exponential series systems when the components are actually dependent, using bivariate exponential distributions.

## Contribution

It analyzes the impact of departure from independence on reliability measures in exponential systems, providing insights into the errors introduced by such assumptions.

## Key findings

- Quantifies errors in reliability measures due to dependence.
- Highlights importance of considering dependence in reliability analysis.
- Provides formulas for errors under bivariate exponential models.

## Abstract

In reliability and life testing when the exponentially distributed components are put in series, it is generally assumed that the lifetimes of the components are independently distributed, which leads to some errors if they are not actually independent. In this paper, we study the relative errors incurred in different reliability measures due to such assumptions when actually they follow some bivariate exponential distributions.