Introduction

Most LCA studies are comparative and to an increasing extent the effects uncertainty are included in LCA results. This raises the question how the best option from a set of product alternatives can be selected when the product scores are uncertain. The starting point of this article is a set of Monte Carlo results for a number of alternative products.

Indicators for single product alternatives

First we discuss different ways of expressing results for product alternatives separately. This includes a discussion of centrality (mean, median, geometric mean, etc.) and dispersion (standard deviation, standard error, confidence interval, etc.).

Indicators of difference for two product alternatives

A critical review of approaches to single out the superior option on case of a comparison of two is given. This includes familiar approaches such as \(t\) tests, but also lesser known ones such the Bhattacharyya coefficient and Cohen’s \(d\). All approaches are defined, discussed, and illustrated with one consistent, downloadable, example.

More than two product alternatives

The findings for two products are generalized for the multi-product situation. In particular, the issue of inflation of type I errors in multiple comparisons is discussed.

Discussion

Two main questions are identified: (1) What is the probability that a randomly selected specimen of product A performs better than a randomly selected specimen of product B? (2) How much will a randomly selected specimen of product A perform better than a randomly selected specimen of product B? These two options can both be relevant, but existing approaches for distinguishing product alternatives address one of these two only, or they even turn out to answer a different, less relevant, question. A proposal for a new indicator that addresses both questions simultaneously is offered and its use is illustrated.

中文翻译：

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在充满不确定性的海洋中选择最佳产品替代品

介绍

大多数LCA研究都是比较性的，并且影响不确定性越来越多地包含在LCA结果中。这就提出了一个问题，即当产品得分不确定时，如何从一组产品替代品中选择最佳选择。本文的出发点是许多替代产品的一组蒙特卡洛结果。

单一产品替代品的指标

首先，我们讨论了分别表示产品替代方案的结果的不同方式。这包括对中心性（均值，中位数，几何均值等）和离散度（标准偏差，标准误差，置信区间等）的讨论。

两种产品替代品的差异指标

给出了对两种方法进行比较时，挑选出高级选择方案的方法的严格审查。这包括熟悉的方法，例如\（t \）测试，还包括鲜为人知的方法，例如Bhattacharyya系数和Cohen的\（d \）。所有方法均通过一个一致的可下载示例进行定义，讨论和说明。

两种以上的产品替代品

针对多种产品情况，概括了两种产品的发现。特别是，讨论了多次比较中I型错误的膨胀问题。

讨论区

确定了两个主要问题：（1）随机选择的产品A样本比随机选择的产品B样本表现更好的概率是多少？（2）随机选择的产品A标本比随机选择的产品B的性能要好多少？这两个选项可能都是相关的，但是区分产品替代方案的现有方法只能解决这两个问题之一，或者它们甚至可以回答一个不那么相关的问题。提供了同时解决两个问题的新指标的建议，并说明了其用法。