The stochastic ordering of random variables is extended to the cases where the available data are imprecise quantities, rather than crisp. To do this, using some elements of fuzzy set theory, we suggest the fuzzy reversed hazard rate and fuzzy mean inactivity time functions and apply them to construct some new fuzzy stochastic orders for ranking fuzzy random variables. In addition, we study the...

Consistent stochastic orders of processing times and objective functions yield optimal policies in many stochastic scheduling problems. When these orders fail to hold, however, finding optimal values may be difficult. In this paper, we show how to bound these values in general situations including problems with unreliable machines and tardiness-based objectives.

This paper introduces higher-order solutions of the quadratic nonlinear stochastic oscillatory equation. Solutions with different orders and different number of corrections are obtained with the WHEP technique which uses the WienerHermite expansion and perturbation technique. The equivalent deterministic equations are derived for each order and correction. The solution ensemble average and vari...