A tolerance interval based approach to address uncertainty for RAMS+C optimization

This paper proposes an approach based on tolerance intervals to address uncertainty for RAMS+C informed optimization of design and maintenance of safety-related systems using a combined Monte Carlo (MC) (simulation) and Genetic Algorithm (search) procedure. This approach is intended to keep control of the uncertainty effects on the decision criteria and reduce the computational effort in simulating RAMS+C using a MC procedure with simple random sampling. It exploits the advantages of order statistics to provide distribution free tolerance intervals for the RAMS+C estimation, which is based on the minimum number of runs necessary to guarantee a probability content or coverage with a confidence level. This approach has been implemented into a customization of the Multi-Objective Genetic Algorithm introduced by the authors in a previous work. For validation purposes, a simple application example regarding the testing and maintenance optimization of the High-Pressure Injection System of a nuclear power plant is also provided, which considers the effect of the epistemic uncertainty associated with the equipment reliability characteristics on the optimal testing and maintenance policy. This example proves that the new approach can provide a robust, fast and powerful tool for RAMS+C informed multi-objective optimization of testing and maintenance under uncertainty in objective and constraints. It is shown that the approach proposed performs very favourably in the face of noise in the output (i.e. uncertainty) and it is able to find the optimum over a complicated, high-dimensional non-linear space in a tiny fraction of the time required for enumeration of the decision space. In addition, a sensitivity study on the number of generations versus the number of trials (i.e. simulation runs) shows that overall computational resources must be assigned preferably to evolving a larger number of generations instead of being more precise in the quantification of the RAMS+C attributes for a candidate solution, i.e. evolution is preferred to accuracy.     

Optimization of imperfect preventive maintenance for multi-state systems

The paper generalizes a preventive maintenance optimization problem to multi-state systems, which have a range of performance levels. Multi-state system reliability is defined as the ability to satisfy given demand. The reliability of system elements is characterized by their hazard functions. The possible preventive maintenance actions are characterized by their ability to affect the effective age of equipment. An algorithm is developed which obtains the sequence of maintenance actions providing system functioning with the desired level of reliability during its lifetime by minimum maintenance cost.To evaluate multi-state system reliability, a universal generating function technique is applied. A genetic algorithm (GA) is used as an optimization technique. Basic GA procedures adapted to the given problem are presented. Examples of the determination of optimal preventive maintenance plans are demonstrated.     

A model for preventive maintenance planning by genetic algorithms based in cost and reliability

This work has two important goals. The first one is to present a novel methodology for preventive maintenance policy evaluation based upon a cost-reliability model, which allows the use of flexible intervals between maintenance interventions. Such innovative features represents an advantage over the traditional methodologies as it allows a continuous fitting of the schedules in order to better deal with the components failure rates. The second goal is to automatically optimize the preventive maintenance policies, considering the proposed methodology for systems evaluation.Due to the great amount of parameters to be analyzed and their strong and non-linear interdependencies, the search for the optimum combination of these parameters is a very hard task when dealing with optimizations schedules. For these reasons, genetic algorithms (GA) may be an appropriate optimization technique to be used. The GA will search for the optimum maintenance policy considering several relevant features such as: (i) the probability of needing a repair (corrective maintenance), (ii) the cost of such repair, (iii) typical outage times, (iv) preventive maintenance costs, (v) the impact of the maintenance in the systems reliability as a whole, (vi) probability of imperfect maintenance, etc. In order to evaluate the proposed methodology, the High Pressure Injection System (HPIS) of a typical 4-loop PWR was used as a case study. The results obtained by this methodology outline its good performance, allowing specific analysis on the weighting factors of the objective function.     

Optimal replacement and overhaul decisions with imperfect maintenance and warranty contracts

In this article, we develop a model to help a maintenance decision making situation of a given equipment. We propose a novel model to determine optimal life-cycle duration and intervals between overhauls by minimizing global maintenance costs. We consider a situation where the costumer, which owns the equipment, may negotiate a better warranty contract by offering an improved preventive maintenance program for the equipment. The equipment receives three kind of actions: repairs, overhauls, and replacement. An overhaul represents an imperfect maintenance action, that is, the failure rate is improved but not a point that the equipment is as good as new. Corrective maintenance actions are minimal, in the sense that the failure rate after each repair is the same as before the failure. The proposed strategy surpasses others seen in the literature since it considers at the same time the warranty negotiation situation and the optimal life-cycle duration under imperfect preventive actions. We also propose a simplified approach that facilitates the task of implementing the method in standard solvers.     

RAMS+C informed decision-making with application to multi-objective optimization of technical specifications and maintenance using genetic algorithms

The role of technical specifications and maintenance (TSM) activities at nuclear power plants (NPP) aims to increase reliability, availability and maintainability (RAM) of Safety-Related Equipment, which, in turn, must yield to an improved level of plant safety. However, more resources (e.g. costs, task force, etc.) have to be assigned in above areas to achieve better scores in reliability, availability, maintainability and safety (RAMS). Current situation at NPP shows different programs implemented at the plant that aim to the improvement of particular TSM-related parameters where the decision-making process is based on the assessment of the impact of the change proposed on a subgroup of RAMS+C attributes.This paper briefly reviews the role of TSM and two main groups of improvement programs at NPP, which suggest the convenience of considering the approach proposed in this paper for the Integrated Multi-Criteria Decision-Making on changes to TSM-related parameters based on RAMS+C criteria as a whole, as it can be seem as a decision-making process more consistent with the role and synergic effects of TSM and the objectives and goals of current improvement programs at NPP. The case of application to the Emergency Diesel Generator system demonstrates the viability and significance of the proposed approach for the Multi-objective Optimization of TSM-related parameters using a Genetic Algorithm.     

Control-limit preventive maintenance policies for components subject to imperfect preventive maintenance and variable operational conditions

This paper develops two component-level control-limit preventive maintenance (PM) policies for systems subject to the joint effect of partial recovery PM acts (imperfect PM acts) and variable operational conditions, and investigates the properties of the proposed policies. The extended proportional hazards model (EPHM) is used to model the system failure likelihood influenced by both factors. Several numerical experiments are conducted for policy property analysis, using real lifetime and operational condition data and typical characterization of imperfect PM acts and maintenance durations. The experimental results demonstrate the necessity of considering both factors when they do exist, characterize the joint effect of the two factors on the performance of an optimized PM policy, and explore the influence of the loading sequence of time-varying operational conditions on the performance of an optimized PM policy. The proposed policies extend the applicability of PM optimization techniques.     

Modelling and optimizing sequential imperfect preventive maintenance

This paper deals with the problem of scheduling imperfect preventive maintenance (PM) of some equipment. It uses a model due to Kijima in which each application of PM reduces the equipment's effective age (but without making it as good as new). The approach presented here involves minimizing a performance function which allows for the costs of minimal repair and eventual system replacement as well as for the costs of PM during the equipment's operating lifetime. The paper describes a numerical investigation into the sensitivity of optimum schedules to different aspects of an age-reduction model (including the situation when parts of a system are non-maintainable—i.e., unaffected by PM).     

Inverse modelling of multi-objective thermodynamically optimized turbojet engines using GMDH-type neural networks and evolutionary algorithms

A novel approach is presented in this article for obtaining inverse mapping of thermodynamically Pareto-optimized ideal turbojet engines using group method of data handling (GMDH)-type neural networks and evolutionary algorithms (EAs). EAs are used in two different aspects. Firstly, multi-objective EAs (non–dominated sorting genetic algorithm-II) with a new diversity preserving mechanism are used for Pareto-based optimization of the thermodynamic cycle of ideal turbojet engines considering four important conflicting thermodynamic objectives, namely, specific thrust ({ST}), specific fuel consumption ({SFC}), propulsive efficiency (η_p), and thermal efficiency (η_t). The best obtained Pareto front, as a result, is a data table representing data pairs of non-dominated vectors of design variables, which are Mach number and pressure ratio, and the corresponding four objective functions. Secondly, EAs and singular value decomposition are deployed simultaneously for optimal design of both connectivity configuration and the values of coefficients, respectively, involved in GMDH-type neural networks which are used for the inverse modelling of the input–output data table obtained as the best Pareto front. Therefore, two different polynomial relations among the four thermo-mechanical objectives and both Mach number and pressure ratio are searched using that Pareto front. The results obtained in this paper are very promising and show that such important relationships may exist and could be discovered using both multi-objective EAs and evolutionarily designed GMDH-type neural networks.     

Modelling imperfect maintenance and the reliability of complex systems using superposed renewal processes

In problems of maintenance optimization, it is convenient to assume that repairs are equivalent to replacements and that systems or objects are, therefore, brought back into an as good as new state after each repair. Standard results in renewal theory may then be applied for determining optimal maintenance policies. In practice, there are many situations in which this assumption cannot be made. The quintessential problem with imperfect maintenance is how to model it. In many cases it is very difficult to assess by how much a partial repair will improve the condition of a system or object and it is equally difficult to assess how such a repair influences the rate of deterioration. In this paper, a superposition of renewal process is used to model the effect of imperfect maintenance. It constitutes a different modelling approach than the more common use of a virtual age process.     

A hybrid genetic based optimization procedure for aircraft conceptual analysis

The problem to define a methodology for the analysis of aircraft performances, in the phase of conceptual design, is addressed. The proposed approach is based on a numerical optimization procedure where a scalar objective function, the take-off weight, is minimized. Deterministic and stochastic approaches as well as hybridizations between these two search techniques are considered. More precisely, we consider two-stage strategies where the optimum localization is performed by a genetic algorithm, while a gradient-based method is used to terminate the optimization process. Also, another type of hybridization strategy is investigated where a partially converged gradient-based method is incorporated in the genetic algorithm as a new operator. A detailed discussion is made and various different solutions are critically compared. The proposed methodology is consistent and capable of giving fundamental information to the designer for further investigating towards the directions identified by the procedure. A basic example is described, and the use of the methodology to establish the effects of different geometrical and technological parameters is discussed.     

A novel evolutionary meta-heuristic for the multi-objective optimization of real-world water distribution networks

Genetic algorithms are currently one of the state-of-the-art meta-heuristic techniques for the optimization of large engineering systems such as the design and rehabilitation of water distribution networks. They are capable of finding near-optimal cost solutions to these problems given certain cost and hydraulic parameters. Recently, multi-objective genetic algorithms have become prevalent in the water industry due to the conflicting nature of these hydraulic and cost objectives. The Pareto-front of solutions can aid decision makers in the water industry as it provides a set of design solutions which can be examined by experienced engineers. However, multi-objective genetic algorithms tend to require a large number of objective function evaluations to arrive at an acceptable Pareto-front. This article investigates a novel hybrid cellular automaton and genetic approach to multi-objective optimization (known as CAMOGA). The proposed method is applied to two large, real-world networks taken from the UK water industry. The results show that the proposed cellular automaton approach can provide a good approximation of the Pareto-front with very few network simulations, and that CAMOGA outperforms the standard multi-objective genetic algorithm in terms of efficiency in discovering similar Pareto-fronts.     

Determination of Pareto frontier in multi-objective maintenance optimization

The objective of a maintenance policy generally is the global maintenance cost minimization that involves not only the direct costs for both the maintenance actions and the spare parts, but also those ones due to the system stop for preventive maintenance and the downtime for failure. For some operating systems, the failure event can be dangerous so that they are asked to operate assuring a very high reliability level between two consecutive fixed stops. The present paper attempts to individuate the set of elements on which performing maintenance actions so that the system can assure the required reliability level until the next fixed stop for maintenance, minimizing both the global maintenance cost and the total maintenance time. In order to solve the previous constrained multi-objective optimization problem, an effective approach is proposed to obtain the best solutions (that is the Pareto optimal frontier) among which the decision maker will choose the more suitable one. As well known, describing the whole Pareto optimal frontier generally is a troublesome task. The paper proposes an algorithm able to rapidly overcome this problem and its effectiveness is shown by an application to a case study regarding a complex series-parallel system.     

Risk based maintenance optimization: foundational issues

Lately there has been an increasing focus on risk based maintenance optimization in the offshore industry prompted by new functional regulations on risk. In this paper we present alternative probabilistic frameworks for this optimization, using a Bayesian approach. Some key features of the frameworks are discussed, including uncertainty treatment and type of performance measures to be used.     

Combining iterative heuristic optimization and uncertainty analysis methods for robust parameter design

A number of investigators have pointed out that products and processes lack quality because of performance inconsistency, which is often due to uncontrollable parameters in the manufacturing process or product usage. Robust design methods are aimed at finding product/process designs that are less sensitive to parameter variation. Robust design of computer simulations requires a large number of runs, which are very time consuming. A novel methodology for robust design is presented in this article. It integrates an iterative heuristic optimization method with uncertainty analysis to achieve effective variability reductions, exploring a large parameter domain with an accessible number of simulations. To demonstrate the effectiveness of this methodology, the robust design of a 0.15 μm CMOS device is shown.     

A new multi-objective optimization model for preventive maintenance and replacement scheduling of multi-component systems

In this article, a new multi-objective optimization model is developed to determine the optimal preventive maintenance and replacement schedules in a repairable and maintainable multi-component system. In this model, the planning horizon is divided into discrete and equally-sized periods in which three possible actions must be planned for each component, namely maintenance, replacement, or do nothing. The objective is to determine a plan of actions for each component in the system while minimizing the total cost and maximizing overall system reliability simultaneously over the planning horizon. Because of the complexity, combinatorial and highly nonlinear structure of the mathematical model, two metaheuristic solution methods, generational genetic algorithm, and a simulated annealing are applied to tackle the problem. The Pareto optimal solutions that provide good tradeoffs between the total cost and the overall reliability of the system can be obtained by the solution approach. Such a modeling approach should be useful for maintenance planners and engineers tasked with the problem of developing recommended maintenance plans for complex systems of components.     

A new modeling approach to the safety evaluation of N-modular redundant computer systems in presence of imperfect maintenance

A large number of safety-critical control systems are based on N-modular redundant architectures, using majority voters on the outputs of independent computation units. In order to assess the compliance of these architectures with international safety standards, the frequency of hazardous failures must be analyzed by developing and solving proper formal models. Furthermore, the impact of maintenance faults has to be considered, since imperfect maintenance may degrade the safety integrity level of the system. In this paper, we present both a failure model for voting architectures based on Bayesian networks and a maintenance model based on continuous time Markov chains, and we propose to combine them according to a compositional multiformalism modeling approach in order to analyze the impact of imperfect maintenance on the system safety. We also show how the proposed approach promotes the reuse and the interchange of models as well the interchange of solving tools.     

Multi-objective optimization of generalized reliability design problems using feature models—A concept for early design stages

Reliability optimization problems such as the redundancy allocation problem (RAP) have been of considerable interest in the past. However, due to the restrictions of the design space formulation, they may not be applicable in all practical design problems. A method with high modelling freedom for rapid design screening is desirable, especially in early design stages. This work presents a novel approach to reliability optimization. Feature modelling, a specification method originating from software engineering, is applied for the fast specification and enumeration of complex design spaces. It is shown how feature models can not only describe arbitrary RAPs but also much more complex design problems. The design screening is accomplished by a multi-objective evolutionary algorithm for probabilistic objectives. Comparing averages or medians may hide the true characteristics of this distributions. Therefore the algorithm uses solely the probability of a system dominating another to achieve the Pareto optimal set. We illustrate the approach by specifying a RAP and a more complex design space and screening them with the evolutionary algorithm.     

Alternatives and challenges in optimizing industrial safety using genetic algorithms

Safety (S) improvement of industrial installations leans on the optimal allocation of designs that use more reliable equipment and testing and maintenance activities to assure a high level of reliability, availability and maintainability (RAM) for their safety-related systems. However, this also requires assigning a certain amount of resources (C) that are usually limited. Therefore, the decision-maker in this context faces in general a multiple-objective optimization problem (MOP) based on RAMS+C criteria where the parameters of design, testing and maintenance act as decision variables. Solutions to the MOP can be obtained by solving the problem directly, or by transforming it into several single-objective problems. A general framework for such MOP based on RAMS+C criteria is proposed in this paper. Then, problem formulation and fundamentals of two major groups of resolution alternatives are presented. Next, both alternatives are implemented in this paper using genetic algorithms (GAs), named single-objective GA and multi-objective GA, respectively, which are then used in the case of application to solve the problem of testing and maintenance optimization based on unavailability and cost criteria. The results show the capabilities and limitations of both approaches. Based on them, future challenges are identified in this field and guidelines provided for further research.     

Comparing effectiveness and efficiency in technical specifications and maintenance optimization

Optimization of technical specification requirements and maintenance (TS&M) has been found interesting from the very beginning at Nuclear Power Plants (NPPs). However, the resolution of such a kind of optimization problem has been limited often to focus only on individual TS&M-related parameters (STI, AOT, PM frequency, etc.) and/or adopting an individual optimization criterion (availability, costs, plant risks, etc.). Nevertheless, a number of reasons exist (e.g. interaction, similar scope, etc.) that justify the interest to focus on the coordinated optimization of all of the relevant TS&M-related parameters based on multiple criteria.The purpose of this paper is on signifying benefits and improvement areas in performing the coordinated optimization of TS&M through reviewing the effectiveness and efficiency of common strategies for optimizing TS&M at system level. A case of application is provided for a stand-by safety-related system to demonstrate the basic procedure and to extract a number of conclusions and recommendations from the results achieved. Thus, it is concluded that the optimized values depend on the particular TS&M-related parameters being involved and the solutions with the largest benefit (minimum risk or minimum cost) are achieved when considering the simultaneous optimization of all of them, although increased computational resources are also required. Consequently, it is necessary to analyze not only the value reached but also the performance of the optimization procedure through effectiveness and efficiency measures which lead to recommendations on potential improvement areas.     

Sensitivity and uncertainty analysis in optimization programs using an evolutionary approach: a maintenance application

Indirect-Grouping Maintenance Strategy requires the calculation of an optimum (global) according to a minimization program P. However the model on which the optimal is based may be incomplete in the sense that important uncertainties have not been considered. In order to evaluate the effects of the uncertainty of the parameters or how the uncertainty is propagated in the optimization program, the decision-maker needs to evaluate the range of variation of program P.In this work an innovative two step evolutionary approach to analyze uncertainties in Indirect-Grouping Maintenance Strategies is presented. The proposed approach combines the two proven techniques of Cellular Evolutionary Strategies (CES) and Evolutionary Strategies (ES) for the optimization problem. The approach does not guarantee the global optimum, but the experiments show that the results are very close to the real one. The examples presented confirm that the approach produces very good approximations for the range of the minimum when there is uncertainty in the model parameters and can be used as a tool for uncertainty/sensitivity analysis in other areas.