We do the error analysis in reliability measures due to the assumption of independence amongst the component lifetimes. In reliability theory, we come across different n-component structures like series, parallel, and k-out-of-n systems. A n component series system works only if all the n components work. While studying the reliability measures of a n-component series system, we mostly assume that all the components have independent lifetimes. Such an assumption eases mathematical complexity while analyzing the data and hence is very common. But in reality, the lifetimes of the components are very much interdependent. Such an assumption of independence hence leads to inaccurate analysis of data. In multiple situations like studying a complex system with many components, we turn to assuming independence keeping some room for error. However, if we have some knowledge of the behaviour of errors or some estimate on the error bound, we could decide if we assume independence and prefer mathematical simplicity (if we know the error is within our allowed limit), or keep the mathematical complexity and get accurate results without assuming independence. We aim to find the relative errors in the reliability measures for a n-component series system.

翻译：我们分析了因假设元件寿命相互独立而导致的可靠性度量误差。在可靠性理论中，常遇到不同类型n元件结构，如串联系统、并联系统及k-out-of-n系统。n元件串联系统仅在所有n个元件均工作时正常运行。在研究n元件串联系统的可靠性度量时，多数情况下我们假设所有元件具有独立寿命。这一假设简化了数据分析中的数学复杂性，因此十分常见。然而实际中元件寿命往往高度相互依赖，独立假设会导致数据分析不准确。在多种情境下（如研究含众多元件的复杂系统），我们转向假设独立性并预留一定误差空间。但若能掌握误差行为特性或误差界估计值，我们便可决定是假设独立性以追求数学简化（当误差在允许范围内时），还是放弃独立假设、保持数学复杂性以获得精确结果。本研究旨在确定n元件串联系统可靠性度量中的相对误差。