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Industry decision makers often rely on a risk-based approach to perform inspection and maintenance planning. According to the Risk-Based Inspection and Maintenance Procedure project for the European industry, risk has two main components: probability of failure (PoF) and consequence of failure (CoF). As one of these risk drivers, a more accurate estimation of the PoF will contribute to a more accurate risk assessment. Current methods to estimate the PoF are either time-based or founded on expert judgement. This paper suggests an approach that incorporates the proportional hazards model (PHM), which is a statistical procedure to estimate the risk of failure for a component subject to condition monitoring, into the risk-based inspection (RBI) methodology, so that the PoF estimation is enhanced to optimize inspection policies.

To achieve the overall goal of this paper, a case study applying the PHM to determine the PoF for the real-time condition data component is discussed. Due to a lack of published data for risk assessment at this stage of the research, the case study considered here uses failure data obtained from the simple but readily available Intelligent Maintenance Systems bearing data, to illustrate the methodology.

The benefit of incorporating PHM into the RBI approach is that PHM uses real-time condition data, allowing dynamic decision-making on inspection and maintenance planning. An additional advantage of the PHM is that where traditional techniques might not give an accurate estimation of the remaining useful life to plan inspection, the PHM method has the ability to consider the condition as well as the age of the component.

This paper is proposing the development of an approach to incorporate the PHM into an RBI methodology using bearing data to illustrate the methodology. The CoF estimation is not addressed in this paper.

This paper presents the benefits related to the use of PHM as an approach to optimize the PoF estimation, which drives to the optimal risk assessment, in comparison to the time-based approach.

Most current condition‐based maintenance (CBM) systems using proportional hazards model (PHM) assume that enough historical data are available. However, in many practical cases, it is usually costly to collect much historical data prior to real practice (model implementation). This paper aims to focus on the necessity and benefits of updating a PHM with new samples generated in the process of model implementation.

First, an updating scheme is presented and embedded into the entire cycle of PHM establishment, its application/implementation, and its updating. Next, a simulation evaluation is conducted based on a typical degradation model.

By updating a PHM using newly generated samples, the precision and reliability of residual life (RL) prediction can be improved, especially close to system failure.

The current version of PHM is typically for non‐repairable systems or those systems only receiving renewal maintenance. Further research should focus on the inclusion of the effect of imperfect maintenance.

The updating scheme enables maintenance practitioners to more precisely and reliably predict the RL of an in‐operation system, and enhances further CBM decision making.

This paper highlights the necessity and benefits of updating a PHM using emerging new training resources, which has not received enough attention in existing research/practice of a PHM.

This paper aims to present a case study where proportional hazards modeling software is used to evaluate the potential benefits of a condition‐based maintenance policy for military vehicle diesel engines.

Maintenance records for diesel engines were supplied by the UK Ministry of Defence. A proportional hazards model based on these data was created using EXAKT software. Covariate parameters were estimated using the maximum likelihood method and transition probabilities were established using a Markov Chain model. Finally, decision parameters were entered to create an optimal decision model.

Two significant covariates were identified as influencing the hazard rate of the engines. In addition, the optimal decision model indicated a potential economic saving of up to 30 per cent.

A model of this nature is particularly useful to predict failures, improve maintenance policies, and possibly reduce maintenance costs. In addition, the cost of implementing maintenance policies based on this model should be balanced with the potential to reduce the risk of danger to personnel.

The model presented provides military personnel with a decision tool that optimizes the maintenance policy for diesel engines installed in military vehicles.

Condition-based maintenance (CBM) has become a central maintenance approach because it performs more efficient diagnoses and prognoses based on equipment health condition compared to time-based methods. CBM models greatly inform maintenance decisions. This research examines three CBM fault prognostics models: logical analysis of data (LAD), artificial neural networks (ANNs) and proportional hazard models (PHM). A methodology, which involves data pre-processing, formulating the models and analyzing model outputs, is developed to apply and compare these models. The methodology is applied on NASA’s Turbofan Engine Degradation data set and the structural health monitoring (SHM) data set from a Nova Scotia Bridge. Results are evaluated using three metrics: error, half-life error and a cost score. This paper concludes that the LAD and feedforward ANN models compares favorably to the PHM model. However, the feedback ANN does not compare favorably, and its predictions show much larger variance than the predictions from the other three methods. Based on these conclusions, the purpose of this paper is to provide recommendations on the appropriate situations in which to apply these three prognostics models.

LAD, ANNs and PHM methods are adopted to perform prognostics and to calculate the mean residual life (MRL) of eqipment using NASA’s Turbofan Engine Degradation data set and the SHM data set from a Nova Scotia Bridge. Statistical testing was used to evaluate the statistical differences between the approaches based on these metrics. By considering the differences in these metrics between the models, it was possible to draw conclusions about how the models perform in specific cases.

Results were evaluated using three metrics: error, half-life error and a cost score. It was concluded that the LAD and feedforward ANN models compares favorably to the PHM model. However, the feedback ANN does not compare favorably and its predictions show much larger variance than the predictions from the other three methods. Overall the models predict failure after it has already occurred (negative error) when the residual life is large and vice versa.

It was concluded that a good CBM prognostics model for practical implications can be determined based on three main considerations: accuracy, run time and data type. When accuracy is a main concern, as in the case where impacts of failure are large, LAD and feedforward neural network are preferred. The preference changes when run time is considered. If data can be easily collected and updating the model is performed often, the ANNs and LAD are preferred. On the other hand, if CM data are not easily obtainable and existing data are not representative of the population’s behavior, data type comes into play. In this case, PHM is preferred.

Previous research in the literature performed reviews of multiple independent studies on CBM techniques performed on different data sets. They concluded that it is typically harder to implement artificial intelligence models, because of difficulties in data procurement, but these approaches offer improved performance as compared to more traditional model-based and statistical approaches. In this research, the authors further investigate and compare the performance and results from two major artificial intelligence models, namely, ANNs and LAD, and one pioneer statistical model, PHM over the same two real life prognostics data sets. Such in-depth comparison and review of major CBM techniques was missing in current literature of CBM field.

The control of an inventory where spare parts demand is infrequent has always been difficult to manage because of the randomness of the demand, as well as the existence of a large proportion of zero values in the demand pattern. The purpose of this paper is to propose a just-in-time (JIT) spare parts availability approach by integrating condition monitoring (CM) with spare parts management by means of proportional hazards models (PHM) to eliminate some of the shortcomings of the spare parts demand forecasting methods.

In order to obtain the event data (lifetime) and CM data (first natural frequency) required to build the PHM for the spares demand forecasting, a series of fatigue tests were conducted on a group of turbomachinery blades that were systematically fatigued on an electrodynamic shaker in the laboratory, through base excitation. The process of data generation in the numerical as well as experimental approaches comprised introducing an initial crack in each of the blades and subjecting the blades to base excitation on the shaker and then propagating the crack. The blade fatigue life was estimated from monitoring the first natural frequency of each blade while the crack was propagating. The numerical investigation was performed using the MSC.MARC/2016 software package.

After building the PHM using the data obtained during the fatigue tests, a blending of the PHM with economic considerations allowed determining the optimal risk level, which minimizes the cost. The optimal risk point was then used to estimate the JIT spare parts demand and define a component replacement policy. The outcome from the PHM and economical approach allowed proposing development of an integrated forecasting methodology based not only on failure information, but also on condition information.

The research is simplified by not considering all the elements usually forming part of the spare parts management study, such as lead time, stock holding, etc. This is done to focus the attention on component replacement, so that a just-in-time spare parts availability approach can be implemented. Another feature of the work relates to the decision making using PHM. The approach adopted here does not consider the use of the transition probability matrix as addressed by Jardine and Makis (2013). Instead, a simulation method is used to determine the optimal risk point which minimizes the cost.

This paper presents a way to address some existing shortcomings of traditional spare parts demand forecasting methods, by introducing the PHM as a tool to forecast spare parts demand, not considering the previous demand as is the case for most of the traditional spare parts forecasting methods, but the condition of the parts in operation. In this paper, the blade bending first mode natural frequency is used as the covariate in the PHM in a laboratory experiment. The choice of natural frequency as covariate is justified by its relationship with structural stiffness (and hence damage), as well as being a global parameter that could be measured anywhere on the blade without affecting the results.

Cox’s proportional hazards model (PHM) has been widely applied to the analysis of lifetime data. It involves covariates influencing the failure of products. Regarding the covariates as discrete random variables, the probability model is reduced to a mixture of PHM. This article presents a statistical procedure to estimate model parameters in the mixture of PHM. The estimation procedure is developed in a parametric framework when not only complete sets of field data but also incomplete ones are given. The expectation‐maximization algorithm is employed to handle the incomplete data problem. Simulation results are presented to illustrate the accuracy and some properties of the estimation results.

This paper aims to discuss and bring to the attention of researchers and practitioners the data management issues relating to condition‐based maintenance (CBM) optimization.

The common data quality problems encountered in CBM decision analyses are investigated with a view to suggesting methods to resolve these problems. In particular, the approaches for handling missing data in the decision analysis are reviewed.

This paper proposes a data structure for managing the asset‐related maintenance data that support CBM decision analysis. It also presents a procedure for data‐driven CBM optimization comprising the steps of data preparation, model construction and validation, decision‐making, and sensitivity analysis.

Analysis of condition monitoring data using the proportional hazards modeling (PHM) approach has been proved to be successful in optimizing CBM decisions relating to motor transmission equipment, power transformers and manufacturing processes. However, on many occasions, asset managers still make sub‐optimal decisions because of data quality problems. Thus, mathematical models by themselves do not guarantee that correct decisions will be made if the raw data do not have the required quality. This paper examines the significant issues of data management in CBM decision analysis. In particular, the requirements of data captured from two common condition monitoring techniques – namely vibration monitoring and oil analysis – are discussed.

This paper offers advice to asset managers on ways to avoid capturing poor data and the procedure for manipulating imperfect data, so that they can assess equipment conditions and predict failures more accurately. This way, the useful life of physical assets can be extended and the related maintenance costs minimized. It also proposes a research agenda on CBM optimization and associated data management issues.

Discusses work completed at Cardinal River Coals in Canada to improve the existing oil analysis condition monitoring program being undertaken for wheel motors. Oil analysis results from a fleet of 55 haul truck wheel motors were analyzed along with their respective failures and repairs over a nine‐year period. Detailed data cleaning procedures were applied to prepare data for modeling. In addition, definitions of failure and suspension were clarified depending on equipment condition at replacement. Using the proportional hazards model approach, the key condition variables relating to failures were found from among the 19 elements monitored, plus sediment and viscosity. Those key variables were then incorporated into a decision model that provided an unambiguous and optimal recommendation on whether to continue operating a wheel motor or to remove it for overhaul on the basis of data obtained from an oil sample. Wheel motor failure implied extensive planetary gear or sun gear damage necessitating the replacement of one or more major internal components in a general overhaul. The decision model, when triggered by incoming data, provided both a recommendation based on an optimal decision policy as well as an estimate of the unit’s remaining useful life. By optimizing the times of repair as a function both of age and condition data a 20‐30 percent potential savings in overhaul costs over existing practice was identified.

The purpose of this paper is to propose a novel condition-based maintenance (CBM) policy with two sampling intervals for a system subject to stochastic deterioration described by the Cox’s proportional hazards model (PHM).

In this paper, the new or renewed system is monitored using a longer sampling interval. When the estimated hazard function of the system exceeds a warning limit, the observations are taken more frequently, i.e., the sampling interval changes to a shorter one. Preventive maintenance is performed when either the hazard function exceeds a maintenance threshold or the system age exceeds a pre-determined age. A more expensive corrective maintenance is performed upon system failure. The proposed model is formulated in the semi-Markov decision process (SMDP) framework.

The optimal maintenance policy is found and a computational algorithm based on policy iteration for SMDP is developed to obtain the control thresholds as well as the sampling intervals minimizing the long-run expected average cost per unit time.

A numerical example is presented to illustrate the whole procedure. The newly proposed maintenance policy with two sampling intervals outperforms previously developed maintenance policies using PHM. The paper compares the proposed model with a single sampling interval CBM model and well-known age-based model. Formulas for the conditional reliability function and the mean residual life are also derived for the proposed model. Sensitivity analysis has been performed to study the effect of the changes in the Weibull parameters on the average cost.

The results show that considerable cost savings can be obtained by implementing the maintenance policy developed in this paper.

Unlike the previous CBM policies widely discussed in the literature which use sequential or periodic monitoring, the authors propose a new sampling strategy based on two sampling intervals. From the economic point of view, when the sampling is costly, it is advantageous to monitor the system less frequently when it is in a healthy state and more frequently when it deteriorates and enters the unhealthy state.

The purpose of this paper is the simultaneous determination of optimal replacement threshold and inspection scheme for a system within condition-based maintenance (CBM) framework.

A proportional hazards model (PHM) is used for risk of failure and a Markovian process to model the system covariates. Total expected long-run cost (including replacement, inspection and downtime costs) is formulated in terms of replacement threshold and inspection scheme. Through an iterative procedure, for all different values of replacement thresholds, their associated optimal inspection scheme is determined using an effective search algorithm. By evaluating the corresponding costs, the optimal replacement threshold and its associated optimal inspection scheme are, then, identified.

The mathematical formulation, that takes into account all different costs, required for the simultaneous determination of optimal replacement threshold and optimal inspection scheme for an item subjected to CBM using PHM is provided. The proposed approach is compared against classical age policy and one state-of-the-art policy through a numerical example. The results show that the proposed approach outperforms other comparing policies.

In practical situations where CBM is implemented, inspections and downtime often incur cost. Under such circumstances, findings of this paper can be utilized for the determination of optimal replacement threshold and optimal inspection scheme so that the CBM cost is minimized.

In most of the reported researches, it is often assumed that inspections have no cost and/or that the time for replacements (either preventive or at failure) is negligible. In the contrary, in this paper the author takes all cost factors including inspection costs, replacement time(s) and their associated downtime costs into account in the simultaneous determination of optimal replacement threshold and optimal inspection scheme.