Comparisons of Multi-State Systems with Binary Components of Different Sizes

The system signatures of multi-state coherent or mixed systems with i.i.d. (independent and identically distributed) binary-state components are considered in this paper. For any multi-state coherent or mixed system with m i.i.d. components, the signature of its equivalent system of size m + l can be written as a mixture of signatures of several multi-state vector k -out-of- m + l: F systems. This facilitates the comparison of two multi-state systems of different sizes upon transforming the signature of the system of smaller size to the signature of its equivalent system of larger size along the lines of Navarro et al. (2008) for the usual Samaniego signature. Some numerical examples are finally presented to illustrate all the results established here.