Modified Imperfect Repair Model (ARAM₁) and new PLP parameterization

Author(s)

Lopes, Tito ; Tomazella, Vera ; Leao, Jeremias ; Louzada, Francisco

• Document type: Journal article
• Source: QUALITY ENGINEERING; v. 36, n. 4, p. 16-pg., 2023-12-29.

Abstract

The class of models known as Arithmetic Reduction of Age (ARA) has found widespread use in modeling equipment maintenance data, assuming that the system continuously degrades between failures, as indicated by beta>1 in the Power Law Process (PLP), commonly employed for fitting such data. However, there are situations where system improvement between failures may occur, as signaled by beta<1 in the PLP. Systems or equipment that enhance over time to a certain degree are less common, as degradation often proves to be a more typical feature. Nevertheless, some systems may exhibit this initial improvement due to various factors such as adaptation, maturation, or updates. In this context, the study introduces the modified ARA(1) model (ARAM(1)), enabling the modeling of systems in a state of reduction or degradation, thereby overcoming this limitation. Additionally, it proposes a new reparameterization of the PLP as a time truncation while preserving the original interpretation of the PLP parameters. An example with a real-world dataset illustrates the potential applications of the proposed model. From the results, it is evident that the ARAM(1) model serves as a valuable tool for enhancing the understanding of the reliability of systems subject to imperfect repairs. (AU)