Optimizing Markov Probabilities for Generation of a Weibull Model to Characterize Building Component Failure Processes

Numerous studies have highlighted the importance of condition forecasting and service life estimation for building components, but many previous approaches do not account for the uncertainty inherent in failure processes where similar components may have differing degradation paths. This study focuses on incorporating a probabilistic approach to more accurately model independent component failures and mitigate this deficiency found in other methods by expanding upon existing research to develop a Weibull model through Monte Carlo simulation to characterize a failure process. The study institutes a different gradient descent approach than previous methods by modifying an algorithm designed for unconstrained optimization in order to be suitable for the constraints of the problem. Comparisons were drawn between the proposed method and a traditional Markov process model where the proposal improved accuracy across all studies to a $p<0.01$ level of significance. Results show that an optimized characteristic Markov transition matrix utilizing variable inspection frequencies improves condition forecasting accuracy across multiple time-series intervals and generalizes well across different classification schemes. The analysis on data partitioning demonstrates that the method is applicable to smaller data sets than may be necessary for other approaches, such as machine learning algorithms, and results in a two-parameter Weibull model that can be used to predict equipment degradation.