Mixture Representations Based on Signatures for Coherent Systems with Heterogeneous Components
Jorge Navarro1, Francisco J. Samaniego2, Narayanaswamy Balakrishnan3
1Universidad de Murcia, Spain; 2University of California, Davis, CA, United States; 3McMaster University, Hamilton, ON, Canada

Signature-based representations of the reliability functions of coherent systems with independent and identically distributed (i.i.d.) component lifetimes have proven very useful in studying the aging characteristics of such systems and in comparing the performance of different systems under varied criteria. In this talk, we consider extensions of these results to systems with heterogeneous components. New representation theorems are established for both the case of components with independent lifetimes and for the case of component lifetimes under specific forms of dependence. These representations may be used to compare the performance of a given n-component system with a fixed and arbitrary, but known, signature under two quite different assumptions on component lifetimes - i.i.d. lifetimes (Xi has distribution F for all i) and independent but heterogeneous lifetimes (Xi has distribution Fi for all i). This is accomplished by showing that the lifetime of the system in the latter case is equivalent in distribution to that of the same system under the assumptions of i.i.d. component lifetimes with a specific common distribution G related to the distributions F1,...,Fn. Also conditions are given under which the lifetimes of different systems with non i.i.d. component lifetimes may be compared via order restrictions such as stochastic, hazard rate and reversed hazard rate ordering.

Keywords: Coherent system; Signature; Stochastic orders; Copula

Biography: Jorge Navarro is a Full Professor in the university of Murcia in Spain. His main research areas of iterest are the characterizations and ordering properties of distributions with applications in reliability theory and survival analysis. He has published about 80 papers on these topics.