Haitao Liao

Maintenance of continuously monitored degrading systems

This paper considers a condition-based maintenance model for continuously degrading systems under continuous monitoring. After maintenance, the states of the system are randomly distributed with residual damage. We investigate a realistic maintenance policy, referred to as condition-based availability limit policy, which achieves the maximum availability level of such a system. The optimum maintenance threshold is determined using a search algorithm. A numerical example for a degrading system modeled by a Gamma process is presented to demonstrate the use of this policy in practical applications.

Condition based maintenance optimization for multi-component systems using proportional hazards model

The objective of condition based maintenance (CBM) is typically to determine an optimal maintenance policy to minimize the overall maintenance cost based on condition monitoring information. The existing work reported in the literature only focuses on determining the optimal CBM policy for a single unit. In this paper, we investigate CBM of multi-component systems, where economic dependency exists among different components subject to condition monitoring. The fixed preventive replacement cost, such as sending a maintenance team to the site, is incurred once a preventive replacement is performed on one component. As a result, it would be more economical to preventively replace multiple components at the same time. In this work, we propose a multi-component system CBM policy based on proportional hazards model (PHM). The cost evaluation of such a CBM policy becomes much more complex when we extend the PHM based CBM policy from a single unit to a multi-component system. A numerical algorithm is developed in this paper for the exact cost evaluation of the PHM based multi-component CBM policy. Examples using real-world condition monitoring data are provided to demonstrate the proposed methods.

Predicting remaining useful life of an individual unit using proportional hazards model and logistic regression model

Reliability of an individual unit during field use is important in many critical applications such as turbine engines, life-maintaining systems and civil engineering structures. The remaining useful life (RUL) of the unit indicates its ability of surviving the operation in the future. When the failure indication (degradation) has been detected, it is essential to estimate the RUL accurately for making a timely maintenance decision for failure avoidance. In recent years, RUL prediction in service has received increasing attention. As many powerful sensors and signal processing techniques appear, multiple degradation features can be extracted for degradation detection and quantification. These features can serve as the basis for RUL prediction. This paper presents the proportional hazards model and logistic regression model, which relates the multiple degradation features of sensor signals to the specific reliability indices of the unit, and enable us to predict its RUL. Comparisons are made for the two models regarding their effectiveness and computation effort. An example of bearing test is provided to demonstrate the proposed approach in practical use. The results show that the models are capable of providing accurate RUL prediction to support timely maintenance decisions

A two-stage approach for multi-objective decision making with applications to system reliability optimization

This paper proposes a two-stage approach for solving multi-objective system reliability optimization problems. In this approach, a Pareto optimal solution set is initially identified at the first stage by applying a multiple objective evolutionary algorithm (MOEA). Quite often there are a large number of Pareto optimal solutions, and it is difficult, if not impossible, to effectively choose the representative solutions for the overall problem. To overcome this challenge, an integrated multiple objective selection optimization (MOSO) method is utilized at the second stage. Specifically, a self-organizing map (SOM), with the capability of preserving the topology of the data, is applied first to classify those Pareto optimal solutions into several clusters with similar properties. Then, within each cluster, the data envelopment analysis (DEA) is performed, by comparing the relative efficiency of those solutions, to determine the final representative solutions for the overall problem. Through this sequential solution identification and pruning process, the final recommended solutions to the multi-objective system reliability optimization problem can be easily determined in a more systematic and meaningful way.

A framework for predicting the remaining useful life of a single unit under time-varying operating conditions

Product reliability in the field is important for a wide variety of critical applications such as manufacturing, transportation, power generation, and health care. In particular, the propensity of achieving zero-downtime emphasizes the need for Remaining Useful Life (RUL) prediction for a single unit. The task is quite challenging when the unit is subject to time-varying operating conditions. This article provides a framework for predicting the RUL of a single unit under time-varying operating conditions by incorporating the results of both accelerated degradation testing and in situ condition monitoring. For illustration purposes, the underlying degradation process is modeled as a Brownian motion evolving in response to the operating conditions. The model is combined with in situ degradation measurements of the unit and the operating conditions to predict the units RUL through a Bayesian technique. When the operating conditions are piecewise constant, statistical approaches using a conjugate prior distribution and Markov chain Monte Carlo approach are developed for cases involving linear and non-linear degradation–stress relationships, respectively. The proposed framework is also extended to handle a more complex case where the projected future operating conditions are stochastic. Simulation experiments and a case study for ball bearings are used to verify the prediction capability and practicality of the framework. In the case study, a quantile regression technique is proposed to handle load-dependent failure threshold values in RUL prediction.

Joint Production and Spare Part Inventory Control Strategy Driven by Condition Based Maintenance

Throughput of a manufacturing process depends on the effectiveness of equipment maintenance, and the availability of spare(service) parts. This paper addresses a joint production and spare part inventory control strategy driven by condition based maintenance(CBM) for a piece of manufacturing equipment. Specifically, a critical unit is continuously monitored for performance degradation during operation. The amount of degradation is utilized to initiate replacement actions in conjunction with spare part inventory control under both production lot size, and due date constraints. A degradation limit maintenance policy is combined with a base stock spare part inventory control policy to manage the manufacturing process. The objectives are to minimize the spare part inventory, and the expected total operating cost. Constrained least squares approximation, and simulation-based optimization are utilized, in a heuristic two-step approach, to determine the optimal base-stock level of spare parts, along with the preventive maintenance threshold. The resulting joint decision ascertains the allowed stockout probability for spare parts, while incurring the minimal operating cost for the required production within a fixed production duration. A case study of an automotive engine manufacturing process is provided to demonstrate the proposed decision-making methodology in practical use.

Maximizing system availability through joint decision on component redundancy and spares inventory

For a repairable k-out-of-n:G system consisting of line-replaceable units, its operational availability depends on component reliability, its redundancy level, and spare parts availability. As a result, it is important to consider redundancy allocation and spare parts provisioning simultaneously in maximizing the system’s operational availability. In prior studies, however, these important aspects are often handled separately in the areas of reliability engineering and spare parts logistics. In this paper, we study a collection of operational availability maximization problems, in which the component redundancy and the spares stocking quantities are to be determined simultaneously under economic and physical constraints. To solve this type of problem, continuous-time Markov chain models are developed first for a single repairable k-out-of-n:G system under different shut-off rules, and some important properties of the corresponding operational availability and spare parts availability are derived. Then, we extend the models to series systems consisting of multiple repairable k-out-of-n:G subsystems. The related optimization problems are reformulated as binary integer linear programs and solved using a branch-and-bound method. Numerical examples, including a real-world application of automatic test equipment, are presented to illustrate this integrated product-service solution and to offer valuable managerial insights.

Availability Optimization of Systems Subject to Competing Risk

This paper considers a competing risk (degradation and sudden failure) maintenance situation. A maintenance model and a repair cost model are presented. The degradation state of the units is continuously monitored. When either the degradation level reaches a predetermined threshold or a sudden failure occurs before the unit reaches the degradation threshold level, the unit is immediately repaired (renewed) and restored to operation. The subsequent repair times increase with the number of renewals. This process is repeated until a predetermined time is reached for preventive maintenance to be performed. The optimal maintenance schedule that maximizes the unit availability subject to repair cost constraint is determined in terms of the degradation threshold level and the time to perform preventive maintenance.

A New Stochastic Model for Systems Under General Repairs

Numerous stochastic models for repairable systems have been developed by assuming different time trends, and repair effects. In this paper, a new general repair model based on the repair history is presented. Unlike the existing models, the closed-form solutions of the reliability metrics can be derived analytically by solving a set of differential equations. Consequently, the confidence bounds of these metrics can be easily estimated. The proposed model, as well as the estimation approach, overcomes the drawbacks of the existing models. The practical use of the proposed model is demonstrated by a much-discussed set of data. Compared to the existing models, the new model is convenient, and provides accurate estimation results

Spare parts inventory control considering stochastic growth of an installed base

Installed base is a measure describing the number of units of a particular system actually in use. To maintain the performance of the installed units, spare parts inventory control is extremely important and becomes very challenging when the installed base changes over time. This problem is often encountered when a manufacturer starts to deliver a new product to customers and agrees to provide spare parts to replace failed units in the future. To cope with the resulting non-stationary stochastic maintenance demand, a spare parts control strategy needs to be carefully developed. The goal is to ensure that timely replacements can be provided to customers while minimizing the overall cost for spare parts inventory control. This paper provides a model for the aggregate maintenance demand generated by a product whose installed base grows according to a homogeneous Poisson process. Under a special case where the products failure time follows the exponential distribution, the closed form solutions for the mean and variance of the aggregate maintenance demand are obtained. Based on the model, a dynamic (Q, r) restocking policy is formulated and solved using a multi-resolution approach. Two numerical examples are provided to demonstrate the application of the proposed method in controlling spare parts inventory under a service level constraint. Simulation is utilized to explore the effectiveness of the multi-resolution approach.