Abstract In safety-critical applications, deformation monitoring systems are required to issue timely alerts when a deformation beyond a critical threshold occurs. Only a very small probability of failing to issue an alert when in fact one should have been given, is acceptable. This probability is referred to as integrity risk. In this contribution, we show how to evaluate this risk, thereby taking the intimate link between testing and estimation into account. Using a simple example, the basic integrity components of deformation monitoring are introduced and illustrated. The integrity risk is then formulated for the generalized case where multiple-hypothesis testing is involved. As monitoring systems, in addition to issuing timely alerts, are also required to provide deformation estimates, it is also crucial to assess their confidence levels. In doing so, the statistical testing, that preceded the estimation of the deformation parameters, needs to be accounted for. As this is not the customary procedure followed in practice, we show how the combined estimation and testing can be probabilistically accounted for, and thereby demonstrate that the customary practice can give a too optimistic outcome of the stated confidence levels. The presented methodology is worked out and numerically illustrated by means of two deformation examples.

中文翻译：

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论变形监测的完整性

摘要 在安全关键应用中，变形监测系统需要在变形超过临界阈值时及时发出警报。只有非常小的概率在实际上应该发出警报时未能发出警报，这是可以接受的。这种可能性被称为完整性风险。在这篇文章中，我们展示了如何评估这种风险，从而将测试和估计之间的密切联系考虑在内。通过一个简单的例子，介绍和说明了变形监测的基本完整性组件。然后针对涉及多假设检验的一般情况制定完整性风险。由于监测系统除了及时发出警报外，还需要提供变形估计，因此评估其置信水平也至关重要。在这样做时，需要考虑在估计变形参数之前进行的统计测试。由于这不是实践中遵循的习惯程序，我们展示了如何在概率上解释组合的估计和测试，从而证明习惯做法可以给出所述置信水平的过于乐观的结果。所提出的方法是通过两个变形例子来制定和数值说明的。从而证明习惯做法可以给出所述置信水平的过于乐观的结果。所提出的方法是通过两个变形例子来制定和数值说明的。从而证明习惯做法可以给出所述置信水平的过于乐观的结果。所提出的方法是通过两个变形例子来制定和数值说明的。