Mixed-Effects Nonhomogeneous Poisson Process Model for Multiple Repairable Systems

Byeong Min Mun,Suk Joo Bae,Paul H Kvam

doi:10.1109/access.2021.3077605

Byeong Min Mun, Suk Joo Bae + Show 1 more

Open Access

https://doi.org/10.1109/access.2021.3077605

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Journal: IEEE Access	Publication Date: Jan 1, 2021
Citations: 2	License type: CC BY 4.0

Affiliation: Hanyang University, University of Richmond

Abstract

The nonhomogeneous Poisson process (NHPP) has become a useful approach for modeling failure patterns of recurrent failure data revealed by minimal repairs from an individual repairable system. Sometimes, multiple repairable systems may present system-to-system variability owing to operation environments or working intensities of individual systems. In this paper, we go over the application of generalized mixed-effects models to recurrent failure data from multiple repairable systems based on the NHPP. The generalized mixed-effects models explicitly involve between-system variation through randomeffects, along with a common baseline for all the systems through fixed-effects for non-normal data. Details on estimation of the parameters of the mixed-effects NHPP models and construction of their confidence intervals are examined. An applicative example shows prominent proof of the mixed-effects NHPP models for the purpose of reliability analysis.

Highlights

M ODERN systems consist of numerous parts working together, making the maintenance action for the systems more difficult
We aim to provide flexible applications of the generalized mixed-effects model for the reliability analysis of multiple repairable systems, based mainly on the nonhomogeneous Poisson process (NHPP)
NHPPs represent a broad class of models for failure data generated by repairable systems

Summary

INTRODUCTION

M ODERN systems consist of numerous parts working together, making the maintenance action for the systems more difficult. We will go over the application of mixedeffects models for recurrent failure data from multiple repairable systems for the purpose of reliability analysis. Giorgio et al [9] proposed a regression model for the PLP intensity function of the power train system of a fleet of 33 buses employed in urban or suburban service They modeled the unobservable heterogeneity among the buses by assuming prior distributions for the model parameters in a Bayesian framework. Applications of nonlinear mixed-effects Poisson process models to multiple repairable systems, have been seldom observed in the reliability literature.

NONHOMOGENEOUS POISSON PROCESS MODEL

GENERALIZED MIXED-EFFECTS MODEL

MIXED-EFFECTS NHPP MODEL

HYDRAULIC SYSTEMS DATA

4: Parameter estimates of both individually fitted

CONCLUSION