A geometric-process maintenance model for a deteriorating system under a random environment

This paper studies a geometric-process maintenance-model for a deteriorating system under a random environment. Assume that the number of random shocks, up to time t, produced by the random environment forms a counting process. Whenever a random shock arrives, the system operating time is reduced. The successive reductions in the system operating time are statistically independent and identically distributed random variables. Assume that the consecutive repair times of the system after failures, form an increasing geometric process; under the condition that the system suffers no random shock, the successive operating times of the system after repairs constitute a decreasing geometric process. A replacement policy N, by which the system is replaced at the time of the failure N, is adopted. An explicit expression for the average cost rate (long-run average cost per unit time) is derived. Then, an optimal replacement policy is determined analytically. As a particular case, a compound Poisson process model is also studied.published_or_final_versio

A maintenance model for a deteriorating system under random environment using partial product process

In this paper, deteriorating system maintenance model under random environment using partial product process is studied. Up to time t, assume that the number of random shocks generated by the random environment is a counting process. Whenever a random shock occurs, the operating time of the system is reduced. The successive reductions in the operating time of the system are statistically independent and identically distributed random variables. Assume that the system’s successive operating times after repairs form a decreasing partial product process. Assume that the system’s consecutive repair times after failures constitute an increasing partial product process provided that the system suffers no random shock. A replacement policy N is applied. Afterwards, for minimizing the mean cost per unit time in long-run, an optimal policy N*is determined analytically. A numerical illustration is provided to strengthen the theoretical results.Publisher's Versiio

Structural reliability prediction of a steel bridge element using dynamic object oriented Bayesian Network (DOOBN)

Different from conventional methods for structural reliability evaluation, such as, first/second-order reliability methods (FORM/SORM) or Monte Carlo simulation based on corresponding limit state functions, a novel approach based on dynamic objective oriented Bayesian network (DOOBN) for prediction of structural reliability of a steel bridge element has been proposed in this paper. The DOOBN approach can effectively model the deterioration processes of a steel bridge element and predict their structural reliability over time. This approach is also able to achieve Bayesian updating with observed information from measurements, monitoring and visual inspection. Moreover, the computational capacity embedded in the approach can be used to facilitate integrated management and maintenance optimization in a bridge system. A steel bridge girder is used to validate the proposed approach. The predicted results are compared with those evaluated by FORM method

Optimum maintenance strategy for deteriorating bridge structures based on lifetime functions

The highway networks of most European and North American countries are completed or close to completion. However, many of their bridges are aging, and in the United States alone a very significant part of the about 600,000 existing bridges is considered to be deficient and must be replaced, repaired or upgraded in the short term. The funds available for the maintenance of existing highway bridges are extremely limited when compared with the huge investment necessary, and must, therefore, be spent wisely. In this paper, a model based on lifetime functions for predicting the evolution in time of the reliability of deteriorating bridges under maintenance is presented. This model uses the probability of satisfactory system performance during a specified time interval as a measure of reliability and treats each bridge structure as a system composed of several components. In this manner, it is possible to predict the structural performance of deteriorating structures in a probabilistic framework. In addition, the optimum maintenance strategy is identified using as objective the minimization of the present value of the life-cycle maintenance cost. An existing bridge is analyzed using lifetime functions and its optimum maintenance strategy is found.U.S. National Science Foundation - CMS-9912525; CMS-0217290.Colorado Department of TransportationDutch Ministry of Transportation, Public Works, and Water Management

Decline and repair, and covariate effects

The failure processes of repairable systems may be impacted by operational and environmental stress factors. To accommodate such factors, reliability can be modelled using a multiplicative intensity function. In the proportional intensity model, the failure intensity is the product of the failure intensity function of the baseline system that quantifies intrinsic factors and a function of covariates that quantify extrinsic factors. The existing literature has extensively studied the failure processes of repairable systems using general repair concepts such as age-reduction when no covariate effects are considered. This paper investigates different approaches for modelling the failure and repair process of repairable systems in the presence of time-dependent covariates. We derive statistical properties of the failure processes for such systems

Production Systems with Deteriorating Product Quality : System-Theoretic Approach

Manufacturing systems with perishable products are widely seen in practice (e.g., food, metal processing, etc.). In such systems, the quality of a part is highly dependent on its residence time within the system. However, the behavior and properties of these systems have not been studied systematically, and, therefore, is carried out in this dissertation. Specifically, it was assumed that the probability that each unfinished part is of good quality is a decreasing function of its residence time in the preceding buffer. Then, in the framework of serial production lines with machines having Bernoulli and geometric reliability models, closed-form formulas for performance evaluation in the two-machine line case were derived, and develop an aggregation-based procedure to approximate the performance measures in M\u3e2-machine lines. In addition, the monotonicity properties of these production lines using numerical experiments were studied. A case study in an automotive stamping plant is described to illustrate the theoretical results obtained. Also, Bernoulli serial lines with controlled parts released was analyzed for both deterministic and stochastic releases. Finally, bottleneck analysis in Bernoulli serial lines with deteriorating product quality were studied

Selective maintenance optimisation for series-parallel systems alternating missions and scheduled breaks with stochastic durations

This paper deals with the selective maintenance problem for a multi-component system performing consecutive missions separated by scheduled breaks. To increase the probability of successfully completing its next mission, the system components are maintained during the break. A list of potential imperfect maintenance actions on each component, ranging from minimal repair to replacement is available. The general hybrid hazard rate approach is used to model the reliability improvement of the system components. Durations of the maintenance actions, the mission and the breaks are stochastic with known probability distributions. The resulting optimisation problem is modelled as a non-linear stochastic programme. Its objective is to determine a cost-optimal subset of maintenance actions to be performed on the components given the limited stochastic duration of the break and the minimum system reliability level required to complete the next mission. The fundamental concepts and relevant parameters of this decision-making problem are developed and discussed. Numerical experiments are provided to demonstrate the added value of solving this selective maintenance problem as a stochastic optimisation programme

Inference and dynamic decision-making for deteriorating systems with probabilistic dependencies through Bayesian networks and deep reinforcement learning

In the context of modern environmental and societal concerns, there is an increasing demand for methods able to identify management strategies for civil engineering systems, minimizing structural failure risks while optimally planning inspection and maintenance (I&M) processes. Most available methods simplify the I&M decision problem to the component level due to the computational complexity associated with global optimization methodologies under joint system-level state descriptions. In this paper, we propose an efficient algorithmic framework for inference and decision-making under uncertainty for engineering systems exposed to deteriorating environments, providing optimal management strategies directly at the system level. In our approach, the decision problem is formulated as a factored partially observable Markov decision process, whose dynamics are encoded in Bayesian network conditional structures. The methodology can handle environments under equal or general, unequal deterioration correlations among components, through Gaussian hierarchical structures and dynamic Bayesian networks. In terms of policy optimization, we adopt a deep decentralized multi-agent actor-critic (DDMAC) reinforcement learning approach, in which the policies are approximated by actor neural networks guided by a critic network. By including deterioration dependence in the simulated environment, and by formulating the cost model at the system level, DDMAC policies intrinsically consider the underlying system-effects. This is demonstrated through numerical experiments conducted for both a 9-out-of-10 system and a steel frame under fatigue deterioration. Results demonstrate that DDMAC policies offer substantial benefits when compared to state-of-the-art heuristic approaches. The inherent consideration of system-effects by DDMAC strategies is also interpreted based on the learned policies