A Study of Mathematical Modeling of Remaining Useful Life, Assessment, and Prognostics & Health Management (PHM)

This research centers on mathematical modeling of remaining useful life (RUL) and its assessment of a device or system. Remaining useful life has always been an essential part of reliability theory. It has also been equally important in various other fields such as actuarial science, engineering management, survival analysis, etc. This thesis explores two different methods of RUL modeling and assessment: lifetime data analysis and degradation based analysis. Traditionally, reliability estimation has been based on analysis of time-to-failure data of a device/system. However, the increase in production of highly reliable devices has led to decrease in failure time data availability. Degradation (device or device performance) analysis is the method of predicting RUL with the help of degradation data collected through real-time performance condition monitoring (CM). The research studies degradation signal and its application in RUL assessment and PHM. Monotonicity of the degradation signal with respect to model error is explored in a simulation using Matlab. The decomposition of observation data for online degradation analysis is also studied. Furthermore, a concept of online RUL assessment computer system using degradation signal is also proposed