In many management science or economic applications, it is common to represent the key uncertain inputs as continuous random variables. However, when analytic techniques fail to provide a closed-form solution to a problem or when one needs to reduce the computational load, it is often necessary to resort to some problem-specific approximation technique or approximate each given continuous probability distribution by a discrete distribution. Many discretization methods have been proposed so far; in this work, we revise the most popular techniques, highlighting their strengths and weaknesses, and empirically investigate their performance through a comparative study applied to a well-known engineering problem, formulated as a stress–strength model, with the aim of weighting up their feasibility and accuracy in recovering the value of the reliability parameter, also with reference to the number of discrete points. The results overall reward a recently introduced method as the best performer, which derives the discrete approximation as the numerical solution of a constrained non-linear optimization, preserving the first two moments of the original distribution. This method provides more accurate results than an ad-hoc first-order approximation technique. However, it is the most computationally demanding as well and the computation time can get even larger than that required by Monte Carlo approximation if the number of discrete points exceeds a certain threshold.

在许多管理科学或经济应用中，通常将关键的不确定性输入表示为连续随机变量。但是，当分析技术无法为问题提供封闭形式的解决方案时，或者当需要减少计算量时，通常必须求助于特定于问题的近似技术，或者通过离散分布来近似每个给定的连续概率分布。 。到目前为止，已经提出了许多离散化方法。在这项工作中，我们修改了最流行的技术，强调了它们的优缺点，并通过将其应用到一个众所周知的工程问题的比较研究中，以应力-强度模型的形式，进行了实证研究，研究了它们的性能，为了增加可靠性，并参考离散点的数量，提高可靠性参数值的准确性。结果总体上奖励了最近引入的最佳性能方法，该方法将离散近似作为约束非线性优化的数值解决方案，并保留了原始分布的前两个时刻。此方法提供的结果比即席一阶逼近技术。但是，这也是对计算的最苛刻要求，并且如果离散点的数量超过某个阈值，则计算时间可能甚至比Monte Carlo近似所需的时间更长。