a note on ther comparison among coherent systems

Using the concept of system signature introduced by Samaniego(1985), Kochar et al. (1999) compared the lifetimes of the systems in whichthe lifetimes of the components are independent and identically distributed(i.i.d.) random variables. Their results are extended to the systems withexchangeable components by Navarro et al. (2005). This paper gives somealternative proofs to obtain their results. Particularly in view of the hazardrate ordering, we compare two systems with different structures andcomponents, which extends Theorem 8 in Navarro et al. (2005). We alsocompare two systems with different structures and components in view ofthe likelihood ratio ordering. Some illustrative examples are mentioned.