In this paper, we discuss the hazard rate order of (n-1)-out-of-n systems arising from two sets of independent multiple-outlier modified proportional hazard rates components. Under certain conditions on the parameters and the sub-majorization order between the sample size vectors, the hazard rate order between the (n-1)-out-of-n systems from multiple-outlier modified proportional hazard rates is established.

This paper considers series and parallel systems with independent and identically distributed component lifetimes. The reliability of these systems can be improved by using the reduction method. In the reduction method, system reliability is increased by reducing the failure rates of some of its components by a factor 0<ρ<1, called the equivalent reliability factor. Closed formulas are obtained for some reliability equivalence factors. In comparisons among the performance of the systems, these factors are helpful. We discuss that the reduction method can be considered as a particular case of the proportional hazard rates (PHR) model. Sufficient conditions for the relative aging comparison of the improved series and parallel systems under the PHR model and reduction method are also developed.