Errors due to departure from independence in multivariate Weibull distributions

Abstract

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.