What are the key differences between additive, multiplicative, and proportional degradation models in predictive maintenance?

Additive, multiplicative, and proportional degradation models are mathematical frameworks used in predictive maintenance to model how equipment condition deteriorates over time, allowing for prediction of remaining useful life (RUL) and optimized maintenance scheduling. They differ in how they represent the influence of time and other factors on the degradation process. An additive degradation model assumes that degradation accumulates linearly over time, with a constant rate of degradation. The degradation at any given time is simply the sum of the initial degradation level and the degradation that has occurred since then. This model is suitable when the degradation rate is relatively constant and independent of the current condition of the equipment. For example, the wear of a mechanical seal might be modeled as an additive process, where the seal wears down at a constant rate due to friction. A multiplicative degradation model assumes that the degradation rate is proportional to the current condition of the equipment. This means that the degradation accelerates as the equipment deteriorates. The degradation at any given time is the product of the initial degradation level and a factor that increases exponentially with time. This model is suitable when the degradation process exhibits a snowball effect, where the rate of deterioration increases as the equipment gets older or more worn. The corrosion rate of a pipe might be modeled as multiplicative, where the corrosion accelerates as the pipe wall thins. A proportional degradation model assumes that the degradation rate is proportional to one or more external factors, such as operating stress or environmental conditions. The degradation at any given time is a function of these external factors. The baseline degradation is often assumed to be linear, but the rate is modulated by the severity of operation. This model is suitable when the degradation process is primarily driven by external factors rather than the equipment's internal state. The fatigue life of an aircraft component might be modeled as proportional to the number of flight cycles and the severity of the loading during each cycle. The selection of the appropriate degradation model depends on the specific equipment, the degradation mechanism, and the available data. In practice, a combination of these models or more complex models may be used to accurately represent the degradation process.