This article proposes two-stage Bayesian and frequentist procedures for determining whether a number of systems—each characterized by the same number of performance measures—belongs to a set Γ defined by a finite collection of linear inequalities. A system is “in (not in) Γ” if the vector of the means is in (not in) Γ, where the means must be estimated using Monte Carlo simulation. We develop algorithms for classifying the systems with a user-specified level of confidence using the minimum number of simulation replications so the probability of correct classification over all r systems satisfies a user-specified minimum value. Once the analyst provides prior values for the means and standard deviations of the random variables in each system, an initial number of simulation replications is performed to obtain current estimates of the means and standard deviations to assess whether the systems can be classified with the desired level of confidence. For any system that cannot be classified, heuristics are proposed to determine the number of additional simulation replications that would enable correct classification. Our contributions include the introduction of intuitive algorithms that are not only easy to implement, but also effective with their performance. Compared to other feasibility determination approaches, they also appear to be competitive. While the algorithms were initially developed in settings where system variance is assumed to be known and the random variables are independent, their performance remains satisfactory when those assumptions are relaxed.

中文翻译：

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可行性确定的新方法

本文提出了两阶段贝叶斯和频率论程序，用于确定多个系统（每个系统都以相同数量的性能度量为特征）是否属于由线性不等式的有限集合定义的集合 Γ。如果均值的向量在（不在）Γ 中，则系统是“在（不在）Γ 中”，其中必须使用蒙特卡罗模拟来估计均值。我们开发算法，使用最少的模拟复制次数以用户指定的置信度对系统进行分类，从而提高所有分类的正确概率r系统满足用户指定的最小值。一旦分析师提供了每个系统中随机变量的均值和标准差的先验值，就会执行初始模拟复制次数以获得均值和标准差的当前估计值，以评估系统是否可以按所需级别分类的信心。对于任何无法分类的系统，建议使用启发式方法来确定能够实现正确分类的额外模拟复制的数量。我们的贡献包括引入了直观的算法，这些算法不仅易于实现，而且性能也很有效。与其他可行性确定方法相比，它们似乎也具有竞争力。