Orderings for series systems comprising heterogeneous Modified Chen components

This paper examines the problem of stochastic comparisons of series systems with independent heterogeneous Modified Chen (MC) distributed components. The MC distribution is capable of modeling failure rates with both monotonic and nonmonotonic behaviors, including the bathtub curve commonly used to represent device performance in reliability engineering. We obtain detailed results in the contexts of the usual stochastic order, the hazard rate order and the likelihood ratio order for series systems. The results of this paper can be used to find some bounds for the important aging characteristics of series systems consisting of independent heterogeneous MC distributed components.

Keywords:

Modified Chen distribution , Stochastic ordering , Majorization , Series system