Stochastic Comparisons of Systems with Heterogeneous Log-Logistic Components

The log-logistic distribution is a resilient family of life distributions that have been applied in an enormous number of fields. In this paper, we study stochastic comparisons for both parallel and series systems having heterogeneous log-logistic distributed components. The comparisons are performed in the sense of stochastic, reversed hazard rate, hazard rate, and likelihood ratio orderings. The consequences of the changes in the scale parameters or the shape parameters on the magnitude of the smallest and largest order statistics are also investigated in the sense of the above-mentioned orderings.