Abstract

Approaches and methodologies for failure detection and analysis of their impacts are of utmost relevance and broad applicability in the industry. In sectors with complex equipment, a single failure can stop the entire production line, leading to disruptions and financial losses. These methods improve system performance and operator safety, optimize resource efficiency, and lower costs related to unexpected shutdowns, among other advantages. Many systems or components experience a physical degradation process before failing, often considered unsuitable for continued operation once they reach a critical stage, exceeding a predefined threshold. This degradation process is complex and influenced by various factors, including preventive maintenance effects. In this context, there is a significant interest in exploring different degradation methodologies, as failures are rare or nonexistent in highly reliable systems, highlighting the value of the information provided by the quality characteristics (CQ) of such systems. This information is particularly useful when traditional reliability analysis models show limitations or are inadequate for these specific circumstances. Modeling degradation processes for multiple repairable systems is the main focus of this research, The effects of maintenance are represented by the Arithmetic Reduction of Degradation with memory one (ARD1) and systems are inspected regularly, with degradation levels measured between, immediately before, and after each inspection. Additionally, the study seeks to investigate the approach that considers monotonicity in the degradation process, therefore, we assume the inverse Gaussian process as the baseline process. We examine models for repairable systems under minimal, perfect, and imperfect repair, aiming to gain a deeper understanding of how maintenance effects are integrated into modeling and their impact on key functions of interest. We proposed degradation pathway models assuming an inverse Gaussian process with effects of minimal, perfect, and imperfect maintenance. We conduct a simulation study to evaluate the efficiency and consistency performance of maximum likelihood estimators (MLEs) by maximizing the log-likelihood function of the presented models, aiming to investigate the asymptotic properties of the estimators. We use three metrics based on similar studies in reliability literature: mean relative error (MRE), square root of the mean squared error (RMSE), and confidence interval (CI) coverage probability (CP). Furthermore, we illustrate the applicability of the proposed models on a dataset, providing functions and measures of interest such as reliability functions, lifetime functions, and mean time to failure (MTTF) for different thresholds. In conclusion, we highlight the importance of continuous innovation and adaptation of existing models to meet specific demands of diverse study contexts while outlining the challenges of the study and future research directions.