A Repairable System Subjected to Hierarchical Competing Risks: Modeling and Applications

Abstract

In this paper, we propose modeling for a single repairable system with a hierarchical structure under the assumption that the failures follow a nonhomogeneous Poisson process (which corresponds to minimal repair action) with a power-law intensity function. The properties of the new model are discussed in detail. The parameter estimators are obtained using the maximum likelihood method. A corrective approach is used to remove bias with order O(n −1), and the respective exact confidence intervals are proposed. A simulation study is conducted to show that our estimators are bias-free. The proposed modeling is illustrated via a toy example on a butterfly valve system, an example of an early-stage real project related to the traction system of an in-pipe robot, and also a real example on a blowout preventer system.

Frailty model for multiple repairable systems hierarchically represented in serial/parallel structures under assumption of ARAm imperfect repairs

“…It is also assumed that repairs are minimal and each failure mode has a power-law intensity. Our proposed model generalizes the one presented in Somboonsavatdee and Sen (2015) and continues the study begun in Louzada et al (2019). Some properties of the new model are discussed.…”

“…In this chapter, we have continued the study started in (LOUZADA et al, 2019), presenting the model under consideration of an arbitrary number of hierarchical levels and maintaining the assumptions of competing risks with independent failure modes, in a MR regime with a reparametrized PLP intensity function. In this context, we have obtained Bayesian estimators with corrected biases, as well as we have derived exact credibility intervals for the parameters.…”

“…Our model can be regarded as a generalization of the Somboonsavatdee and Sen (SOMBOONSAVATDEE;SEN, 2015)'s model for the cases where there are two or more levels of hierarchy, that is, secondary, tertiary, quaternary and so on failure causes (or subsystems). The model proposed here is also an extension of the work by Louzada et al (LOUZADA et al, 2019). This situation is illustrated in Figure 25, which depicts a fault tree.…”

“…In Louzada et al (2019), the Annelida's traction subsystem was used to illustrate the methodology discussed at the time. With the advance in the development of the robotic unit, the applications exposed here refine the previous one with the inclusion of more details about this important subsystem (Section 4.5.2), and also adding the new results obtained in this chapter to another subsystem as well (pressure vessel subsystem in Section 4.5.1).…”

“…To obtain such prior, the expected Kullback-Leibler divergence between a prior distribution and a posterior distribution was maximized. The posterior distribution obtained using this prior has interesting properties, such as invariance and consistency in marginalization and sample properties (BERNARDO, 2005) This chapter aims to continue the study begun in Louzada et al (2019), which generalized model of Somboonsavatdee and Sen (2015). For this, we describe a statistical model for a repairable system hierarchically represented subject to competing risks under MR regime with PLP intensity function.…”