Concepts and Measures of Dependence in Reliability

9.13 Conclusion

In this chapter, we present several concepts of multivariate dependence, in particular bivariate positive dependence. While there does not appear to have relationship between the traditional concepts of dependence and ageing concepts, there is a strong relationship between positive dependence and rank correlations such as Kendall’s τ and Spearman’s ρ_S. Also the relationship between these two non-parametric measures of association can be interpreted by positive dependence concepts such as PQD and LTD, RTI. (PQD implies 3τ ≥ ρ_S ≥ 0; whereas simultaneous LTD and RTI implies 3τ ≥ ρ_S ≥ τ ≥ 0).

Although the concept of local dependence and measure of local dependence are not fully developed yet, they would likely provide us more information about the dependence between two time intervals as in the medical studies example mentioned in the last section.