Stochastic analysis, Proportional hazards models, Random variables -- Mathematical models
In the article "Stochastic comparisons of parallel systems when component have proportional hazard rates" we found a gap in the middle of the proof of Theorem 3.2. Therefore, we do not know whether Theorem 3.2 is true for the reverse hazard rate order. However, we could prove the following weaker result for the stochastic order.
Kochar, S., & Xu, M. (2008). Correction to "Stochastic comparisons of parallel systems when components have proportional hazard rates". Probability in the Engineering & Informational Sciences, 22(3), 473-474.