A note on allocation policy in two-parallel-series and two-series-parallel systems with respect to likelihood ratio order

In a recent article of Laniado and Lillo (2014), the authors obtained some comparison results on component allocation policies in two-parallel-series and two-series-parallel systems with two types of components. They proposed a conjecture that those results can be extended to likelihood ratio order. In this note, we provide an affirmative answer to their conjecture