Title: Advances in Optimizing Condition-based Maintenance and Spare Parts Provisioning

Student: Heraldo Rozas

Date: May 16th , 2024

Time: 11:30-13:30 ET

Location: Groseclose 303 or https://gatech.zoom.us/j/93382040134?pwd=WHRiUGxsY3J3RkVBZlhkSnI3bUU5UT09

Committee

Dr. Nagi Gebraeel, School of Industrial and Systems Engineering, Georgia Institute of Technology (Advisor)

Dr. Weijun Xie, School of Industrial and Systems Engineering, Georgia Institute of Technology

Dr. Jianjun Shi, School of Industrial and Systems Engineering, Georgia Institute of Technology

Dr. Kamran Paynabar, School of Industrial and Systems Engineering, Georgia Institute of Technology

Dr. Stephen  Robinson, Department of Mechanical and  Aerospace Engineering, University of California, Davis

Abstract:

This dissertation extends the scope of traditional models for optimizing maintenance and spare provisioning by exploring new challenging problem settings and developing innovative optimization methodologies. These methodologies aim to transform condition monitoring data into actionable and robust decisions regarding maintenance and spares provisioning.

Chapter 2 revisits the integration of failure prognostics into the joint optimization of condition-based maintenance (CBM) and spare parts provisioning. It develops a chance-constrained stochastic mixed-integer linear programming (MILP) model to jointly optimize CBM and spare parts provisioning. The formulation utilizes remaining lifetime distributions (RLDs) of partially degraded components estimated by prognostic algorithms. It also incorporates chance constraints restricting the unavailability of critical components and the number of corrective repairs with high probability. The nonlinearities induced by the chance constraints are circumvented by deriving two linearization methods based on scenario representation and safe approximations. The optimization model is applied to coordinating maintenance and spare parts provisioning in the novel application domain of deep space habitats.

Chapter 3 re-examines the problem of maintenance optimization incorporating estimated RLDs by investigating more realistic problem settings, where the estimated RLDs can be inaccurate due to sparse historical failure data. To tackle this problem, Chapter 3 proposes a CBM strategy based on a Distributionally Robust Chance-Constrained (DRCC) optimization model. Unlike existing works, this formulation acknowledges the inherent uncertainty around RLD estimation and seeks solutions that are robust against distributional perturbations within a Wasserstein ambiguity set.  Chapter 3 shows that the proposed DRCC optimization problem can be exactly reformulated as an integer linear program. The optimization model is implemented to optimize the maintenance schedules in fleet applications, such as of wind turbines.

Chapter 4 extends the DRCC optimization model presented in Chapter 3 to address the joint optimization of CBM and spares provisioning. The new DRO formulation is constructed using general discrepancy-based ambiguity sets that capture potential distribution perturbations of the estimated RLDs. Chapter 4 also shows that this formulation admits a Mixed Integer Linear Programming (MILP) reformulation, providing explicit formulas to simplify the general discrepancy-based ambiguity sets. The numerical studies adopt a type-$\infty$ Wasserstein ambiguity set and derive closed-form expressions for the parameters of the resulting MILP reformulation. The efficacy of this methodology is showcased in a wind turbine case study.

Finally, Chapter 5 explores, for the first time, the use of contextual DRO frameworks for computing preventive maintenance (PM) intervals of industrial components in applications where condition monitoring technologies are not necessarily cost-effective. The problem setting assumes that the component’s time-to-failure (TTF) distribution is influenced by external covariates, such as temperature and speed. The objective is to exploit the knowledge about the covariates to compute efficient PM decisions conditional on the observed covariates. The contextual PM problem is formulated as a DRO model, which directly integrates failure time data while accounting for potential misspecifications of the empirical TTF distribution. The formulation aims to minimize the long-term maintenance cost rate over the infinite space of PM decision policies, which map covariate information to optimal PM intervals. Chapter 5 shows that the proposed DRO model admits tractable MILP reformulations in various practical cases. The efficacy of the proposed model is demonstrated through computational studies involving simulated and real-world failure time data.