Can't Trust Your Tech? How to Navigate Dependent Failures and Build More Reliable Systems

The primary failure mechanisms affecting the reliability of micro-electro-mechanical systems (MEMS) include both aging degradation and catastrophic failures. Aging degradation is characterized by the accumulation of damage over time due to internal forces and stresses, leading to processes like corrosion, erosion, fatigue, and wear. Catastrophic failures, on the other hand, involve sudden and complete breakdowns, such as fractures and breaks, often caused by random shocks. Understanding both types is crucial because the interplay between them, such as how degradation affects a system's vulnerability to shocks, is key to predicting reliability.

Traditional reliability tests that primarily focus on time-to-failure are insufficient for today's complex technological systems because they often fail to account for the various degradation processes that occur before a component ultimately fails. These tests do not adequately address the multiple failure risks that products face, creating a competing failure environment where a number of factors influence when a system gives out. Modern systems experience a range of failure modes, including continuous degradation (soft failures) and sudden-impact failures (hard failures). These tests fail to measure these changes. New approaches are necessary to consider more aspects of system dependencies, leading to more realistic and robust assessments.

Copulas are integral to modern reliability modeling because they provide a convenient way to describe the correlations between different failure modes. They are particularly useful in analyzing systems where multiple degradation processes interact. By using copula functions, engineers can model the dependencies between seemingly unrelated failure events and build more accurate reliability predictions. For instance, copulas can help determine specific correlations between the size of damage from degradation and the magnitude of stress from shock loads.

A railway axle provides a compelling example of how a single shock event can affect multiple aspects of a system's health. The axle experiences constant fatigue from rolling loads, representing continuous degradation. Simultaneously, it faces random shocks when wheels hit rail joints. If a shock exceeds the axle's strength, it can cause a fracture. Even smaller shocks can accelerate the progression of degradation, increasing the crack size and contributing to the overall failure. This interaction highlights how a single event can trigger or worsen multiple failure mechanisms.

Statistical methods play a vital role in analyzing and predicting system reliability by enabling engineers to extract, analyze, and model failure data. The process typically involves several key steps. First, statistical methods are used to extract sample data, especially focusing on data related to abrupt degradation damage. Second, the focus shifts to inferring distribution, determining how much aging continuous degradation occurs over time. Third, copulas are used to determine specific correlations between different failure modes. This holistic approach, particularly when using copula theory, provides a more comprehensive understanding of system behavior under stress, leading to more accurate predictions of system reliability. These methods capture the complex relationships between different failure modes and are essential in building more resilient systems.