The manufacturing field encompasses a number of problems in which some experts formulate their rankings of a set of objects, which should be aggregated into a collective judgment. For example, consider the aggregation of (1) the opinions of designers on alternative design concepts, (2) the opinions of reliability/safety engineers on the criticality of a set of failures, (3) the perceptions of a panel of customers on alternative aesthetic features of a product, etc. For these problems, Kendall’s concordance coefficient (W) can be used to express the degree of agreement between experts in a simple and practical way. Unfortunately, this indicator is applicable to complete rankings only, while experts often find it more practical to formulate incomplete rankings, e.g., identifying only the most/less relevant objects and/or deliberately excluding some of them, if they are not sufficiently relevant or well known. This research aims at extending the use of the traditional W to incomplete rankings, preserving its practical meaning and simplicity. In a nutshell, the proposed methodological approach associates a so-called “midrank” to all objects, even the ones that are not easily comparable with the other ones; subsequently, W can be applied to these midranks. The description is supported by several pedagogical examples.

中文翻译：

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与制造应用中不完整专家排名的决策一致性

制造领域包含一些问题，其中一些专家制定他们对一组对象的排名，这些排名应该汇总为集体判断。例如，考虑以下汇总：(1) 设计师对替代设计概念的意见，(2) 可靠性/安全工程师对一组故障的严重程度的意见，(3) 一组客户对替代设计的看法产品的审美特征等。对于这些问题，可以用肯德尔的一致性系数（W）以简单实用的方式表达专家之间的一致程度。不幸的是，该指标仅适用于完整排名，而专家通常发现制定不完整排名更实用，例如，仅识别最相关/最不相关的对象和/或故意排除其中一些（如果它们不够相关或不为人所知）。本研究旨在将传统 W 的使用扩展到不完整排名，保留其实际意义和简单性。简而言之，所提出的方法论方法将所谓的“中阶”与所有对象相关联，即使是那些不容易与其他对象进行比较的对象；随后，W 可以应用于这些中级。该描述得到了几个教学示例的支持。即使是那些不容易与其他人相比的人；随后，W 可以应用于这些中级。该描述得到了几个教学示例的支持。即使是那些不容易与其他人相比的人；随后，W 可以应用于这些中级。该描述得到了几个教学示例的支持。