Jorge Navarro, Francisco Samaniego, Narayanaswamy Balakrishnan

System signatures are useful tools in the study and comparison of coherent systems. In this talk, in collaboration with Jorge Navarro (University of Murcia, Spain) and Francisco Samaniego (University of California, Davis, USA), I will define and discuss a similar concept, called joint signature, for two coherent systems which share some components. Under an i.i.d. assumption on component lifetimes, I will obtain a pseudo-mixture representation based on this joint signature for the joint distribution of the lifetimes of both systems. Finally, I will present sufficient conditions based on the respective joint signatures of two pairs of systems, each with shared components, to ensure various forms of bivariate stochastic orderings between the joint lifetimes of the two pairs of systems.

**Keywords:** Coherent system; Signature; Order statistics; Matrix orderings

**Biography:** He is a Professor of Mathematics and Statistics at McMaster University, Hamilton, Ontario, Canada. He is a Fellow of the American Statistical Association and the Institute of Statistical Mathematics, and an Elected Member of the International Statistical Institute. He is the Editor-in-Chief of Communications in Statistics and the Executive Editor of Journal of Statistical Planning and Inference, and the Don Owen Award Winner of the American Statistical Association.