A dynamic auto-adaptive predictive maintenance policy for degradation with unknown parameters

International audienceWith the development of monitoring equipment, research on condition-based maintenance (CBM) is rapidly growing. CBM optimization aims to find an optimal CBM policy which minimizes the average cost of the system over a specified duration of time. This paper proposes a dynamic auto-adaptive predictive maintenance policy for single-unit systems whose gradual deterioration is governed by an increasing stochastic process. The parameters of the degradation process are assumed to be unknown and Bayes' theorem is used to update the prior information. The time interval between two successive inspections is scheduled based on the remaining useful life (RUL) of the system and is updated along with the degradation parameters. A procedure is proposed to dynamically adapt the maintenance decision variables accordingly. Finally, different possible maintenance policies are considered and compared to illustrate their performance

Virtual series-system models of imperfect repair

Novel models of imperfect repair are fitted to classic reliability datasets. The models suppose that a virtual system comprises a component and a remainder in series. On failure of the component, the component is renewed, and on failure of the remainder, the component is renewed and the remainder is minimally repaired. It follows that the repair process is a counting process that is the superposition of a renewal process and a Poisson process. The repair effect, that is, the extent to the system is repaired by renewal of the component, depends on the relative intensities of the superposed processes. The repair effect may be negative, when the intensity of the part that is a renewal process is a decreasing function. Other special cases of the model exist (renewal process, Poisson process, superposed renewal process and homogeneous Poisson process). Model fit is important because the nature of the model and corresponding parameter values determine the effectiveness of maintenance, which we also consider. A cost-minimizing repair policy may be determined provided the cost of preventive-repair is less than the cost of corrective-repair and the repairable part is ageing. If the remainder is ageing, then policy needs to be adapted as it ages

Integrated production quality and condition-based maintenance optimisation for a stochastically deteriorating manufacturing system

This paper investigates the problem of optimally integrating production quality and condition-based maintenance in a stochastically deteriorating single- product, single-machine production system. Inspections are periodically performed on the system to assess its actual degradation status. The system is considered to be in ‘fail mode’ whenever its degradation level exceeds a predetermined threshold. The proportion of non-conforming items, those that are produced during the time interval where the degradation is beyond the specification threshold, are replaced either via overtime production or spot market purchases. To optimise preventive maintenance costs and at the same time reduce production of non-conforming items, the degradation of the system must be optimally monitored so that preventive maintenance is carried out at appropriate time intervals. In this paper, an integrated optimisation model is developed to determine the optimal inspection cycle and the degradation threshold level, beyond which preventive maintenance should be carried out, while minimising the sum of inspection and maintenance costs, in addition to the production of non-conforming items and inventory costs. An expression for the total expected cost rate over an infinite time horizon is developed and solution method for the resulting model is discussed. Numerical experiments are provided to illustrate the proposed approach

Semiparametric estimate of the efficiency of imperfect maintenance actions for a gamma deteriorating system

International audienceA system is considered, which is deteriorating over time according to a non homogeneous gamma process with unknown parameters. The system is subject to periodic and instantaneous imperfect maintenance actions (repairs). Each imperfect repair removes a proportion ρ of the accumulated degradation since the previous repair. The parameter ρ hence appears as a measure for the maintenance efficiency. This model is called arithmetic reduction of degradation of order 1. The system is inspected right before each maintenance action, thus providing some multivariate measurement of the successively observed deterioration levels. Based on these data, a semiparametric estimator of ρ is proposed, considering the parameters of the underlying gamma process as nuisance parameters. This estimator is mainly based on the range of admissible ρ's, which depends on the data. Under technical assumptions, consistency results are obtained, with surprisingly high convergence rates (up to exponential). The case where several i.i.d. systems are observed is next envisioned. Consistency results are obtained for the efficiency estimator, as the number of systems tends to infinity, with a convergence rate that can be higher or lower than the classical square root rate. Finally, the performances of the estimators are illustrated on a few numerical examples

A condition-based maintenance policy for degrading systems with age- and state-dependent operating cost

Most of the maintenance policies in existing publications assume that no cost is incurred as long as the system can undertake missions while little consideration has been devoted to the operating cost during system operation. However, in practice, the operating cost increases while the system ages and degrades even if a system is in a functioning state. This paper proposes a maintenance policy for a degrading system with age- and state-dependent operating cost, which increases with system age and degradation levels. Under such a setting, a replacement model is first developed to investigate the optimal preventive replacement policy. The replacement model is then extended to a repair-replacement model, in which imperfect repair is assumed to restore the system to the operating condition. Particularly, the repair model with controllable and uncontrollable repair levels is considered separately. The paper proves that the optimal maintenance policy is actually a monotone control limit policy, where the optimal control limits decrease monotonically with system age. Finally, a numerical example along with sensitivity analysis is presented to illustrate the optimal maintenance policy. The proposed model implies a more conservative maintenance policy, compared with the traditional model without the age- and state-dependent operating cost

Continuous-observation partially observable semi-Markov decision processes for machine maintenance

Partially observable semi-Markov decision processes (POSMDPs) provide a rich framework for planning under both state transition uncertainty and observation uncertainty. In this paper, we widen the literature on POSMDP by studying discrete-state, discrete-action yet continuous-observation POSMDPs. We prove that the resultant α-vector set is continuous and therefore propose a point-based value iteration algorithm. This paper also bridges the gap between POSMDP and machine maintenance by incorporating various types of maintenance actions, such as actions changing machine state, actions changing degradation rate, and the temporally extended action "do nothing''. Both finite and infinite planning horizons are reviewed, and the solution methodology for each type of planning horizon is given. We illustrate the maintenance decision process via a real industrial problem and demonstrate that the developed framework can be readily applied to solve relevant maintenance problems

Maintenance scheduling for multicomponent systems with hidden failures

This paper develops a maintenance policy for a multicomponent system subject to hidden failures. Components of the system are assumed to suffer from hidden failures, which can only be detected at inspection. The objective of the maintenance policy is to determine the inspection intervals for each component such that the long-run cost rate is minimized. Due to the dependence among components, an exact optimal solution is difficult to obtain. Concerned with the intractability of the problem, a heuristic method named “base interval approach” is adopted to reduce the computational complexity. Performance of the base interval approach is analyzed, and the result shows that the proposed policy can approximate the optimal policy within a small factor. Two numerical examples are presented to illustrate the effectiveness of the policy

Modeling multivariate degradation processes with time‐variant covariates and imperfect maintenance effects

International audienceThis article proposes two types of degradation models that are suitable for describing multivariate degrading systems subject to time‐variant covariates and imperfect maintenance activities. A multivariate Wiener process is constructed as a baseline model, on top of which two types of models are developed to meaningfully characterize the time‐variant covariates and imperfect maintenance effects. The underlying difference between the two models lies in the way of capturing the influences of covariates and maintenance: The first model reflects these impacts in the degradation rates/paths directly, whereas the second one describes the impacts by modifying the time scales governing the degradation processes. In each model, two particular imperfect maintenance models are presented, which differ in the extent of reduction in degradation level or virtual age. The two degradation models are then compared in certain special cases. The proposed multivariate degradation models pertain to complex industrial systems whose health deterioration can be characterized by multiple performance characteristics and can be altered or affected by maintenance activities and operating/environmental conditions

Degradation-based maintenance decision using stochastic filtering for systems under imperfect maintenance

International audienceThe notion of imperfect maintenance has spawned a large body of literature, and many imperfect maintenance models have been developed. However, there is very little work on developing suitable imperfect maintenance models for systems outfitted with sensors. Motivated by the practical need of such imperfect maintenance models, the broad objective of this paper is to propose an imperfect maintenance model that is applicable to systems whose sensor information can be modeled by stochastic processes. The proposed imperfect maintenance model is founded on the intuition that maintenance actions will change the rate of deterioration of a system, and that each maintenance action should have a different degree of impact on the rate of deterioration. The corresponding parameter-estimation problem can be divided into two parts: the estimation of fixed model parameters and the estimation of the impact of each maintenance action on the rate of deterioration. The quasi-Monte Carlo method is utilized for estimating fixed model parameters, and the filtering technique is utilized for dynamically estimating the impact from each maintenance action. The competence and robustness of the developed methods are evidenced via simulated data, and the utility of the proposed imperfect maintenance model is revealed via a real data set

Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen