Abstract

Angular measurements lie on the circumference of a circle and have different characteristics than standard scalar measurements. For applications involving angular data, treating the measured values as scalars can lead to misinterpretation of results if its wrap-around nature is not taken into account. In this article, we propose a variance components wrapped normal model for angular measurements that is analogous to the standard normal model for continuous measurements. This model allows decomposition of contributions to the overall variance to be separated and compared to understand the drivers of the spread of the data. We analyze gauge R & R study data using Bayesian methods and illustrate the use of this wrapped normal model with simulated and real data. We also performed a small simulation study in considering the design of gauge R & R studies with angular measurements.

摘要

角度测量位于圆的圆周上，与标准标量测量具有不同的特性。对于涉及角度数据的应用程序，如果不考虑其环绕性质，将测量值视为标量可能会导致对结果的误解。在本文中，我们提出了一种用于角度测量的方差分量包裹法线模型，类似于用于连续测量的标准法线模型。该模型允许对整体方差的贡献进行分解和比较，以了解数据传播的驱动因素。我们使用贝叶斯方法分析规范 R&R 研究数据，并用模拟和真实数据说明这种包裹法线模型的使用。我们还进行了一项小型模拟研究，以考虑仪表 R 和