Modelagem de tempo de falha acelerado para sistemas reparáveis considerando fragilidade e diferentes funções de aceleração

Abstract

Reliability analysis in accelerated life testing aims to understand and anticipate the behavior of systems subjected to intensified stress conditions, enabling the estimation of their durability under normal usage conditions. In this context, acceleration functions play a central role, as they describe how stress affects the time to failure. The main objective of this thesis is to investigate, study, and propose acceleration functions that enhance the models’ ability to capture complex relationships between stress and response. To this end, we adopt the context of multiple repairable systems under the assumption of minimal repair, where failures follow a Non-Homogeneous Poisson Process (NHPP) with a baseline intensity function governed by a Power Law Process. The modeling also incorporates unobserved heterogeneity through a frailty term, capturing random effects that influence system performance over time. Model development was carried out in several stages. Initially, an exponential accelerated failure time model with weighted Lindley frailty was proposed and compared to a model with gamma frailty. Next, the scope of acceleration functions was expanded to include the classical forms: Arrhenius, Eyring, and Inverse Power, in comparison with the Exponential form. This methodological extension resulted in eight models: four without frailty and four incorporating gamma frailty. Subsequently, two new acceleration functions were proposed, Exponentiated Exponential and Exponentiated Eyring, aiming to provide greater flexibility in modeling and broaden the potential for application in different accelerated stress scenarios, overcoming limitations of classical forms. Finally, two additional models were developed by combining these new functions with the inclusion of gamma frailty. Parameter estimation for all proposed models was conducted under a frequentist approach, through the construction of the likelihood function and the derivation of maximum likelihood estimators, along with their asymptotic confidence intervals obtained via numerical methods. In all cases, the performance of the estimators was evaluated through a simulation study that covered various scenarios and acceleration levels, and all models yielded satisfactory results. The applicability of these models was illustrated with practical examples involving multiple systems and varying stress levels, highlighting the relevance of these acceleration functions for reliability analysis in accelerated life testing.