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The purpose of this paper is to deal with a linear multi-state sliding window coherent system which generalizes the consecutive k-out-of-r-from-n:F system in the multi-state case. The system has n linearly ordered multi-state elements consisting of m parallel independent and identically distributed elements. Every element of the system can have two states: completely working or totally failed. The system fails if the sum of performance rate is lower than the given weight.

The authors proposed to compute the signature, MTTF and Barlow–Proschan index with the help of UGF technique of multi-state SWS which consists of m parallel i.i.d. components in each multi-state window.

In the present study, the authors have evaluated the signature reliability, expected lifetime, cost analysis and Barlow–Proschan index.

In this study, the authors have studied a linear multi-state sliding window system which consists of n ordered multi-state element, and each multi-state element also consists of m parallel windows. The focus of the present paper is to evaluate reliability metrices of the considered system with the help of signature from using the universal generating function.

Existing work on multi-level governance (MLG) has concentrated on decentring of the state (e.g., Rhodes, R. A. W. (1994). The hollowing out of the state: The changing nature of the public service in Britain. Political Quarterly, 65(2), 138–141; Rhodes, R. A. W. (1997). Understanding governance: Policy networks, governance, reflexivity and accountability. London: Open University Press; Rhodes, R. A. W. (2008). Understanding governance: Ten years on. Organisation Studies, 28(8), 1243–1264); growth of non-state actors in governing (e.g., Crouch, 2004; Jessop, B. (2004). Multi level governance and multi-level metagovernance-changes in the European Union as integral moments in the transformation and re-orientation of contemporary statehood. In I. Bache & M. Flinders (Eds.), Multi level governance. Oxford: Oxford University Press); classifying different types of governance (e.g., type 1 and type 2 MLG – see Hooghe & Marks, 2003; Ongaro, E., Massey, A., Holzer, M., & Wayenberg, E. (Eds.). (2010). Governance and intergovernmental relations in the European Union and the United States: Theoretical perspectives. Cheltenham: Edward Elgar). The purpose of the chapter is to complement these approaches by focusing on politics and political strategies in multi-level systems.

The chapter draws on an extensive literature in governance and political accountability and on political dynamics, management and strategies within multi-level state systems. Although in international context, particular accentuation is placed on the UK case.

There are three broad findings. First, while the growth of MLG and in particular supra state activities and institutions have undermined conventional conceptions of political accountability, more nuanced interpretations are provided; as are cases of successful popular challenge to a seemingly inevitable application of neo-liberal new public management driven approaches to public service provision, as witnessed in examples of public service de-privatisation and re-municipalisation. Second, as seen in the United Kingdom, political strategies in a multi-state system are presented in terms of zero sum or alternatively win-win scenarios. In Scotland, for example, though there have been difficulties for state wide parties in managing multi-level politics in the devolved arena, yet in that arena win-win strategies have been played out; and in Northern Ireland with a contextual backdrop of conflict, there is also evidence of win-win political actions. Third, some general findings are presented which outline a range of centrifugal and centripetal forces found in some European countries and how these affect the choice of political strategy.

A multi-state linear k-within-(r, s)-of-(m, n): F lattice system consists of m×n components arranged in m rows and n columns. The possible states of the system and its components are: 0, 1, 2, …, H. According to k values, the system can be categorized into three special cases: decreasing, increasing and constant. The system reliability of decreasing and constant cases exists. The purpose of this paper is to evaluate the system reliability in increasing case with i.i.d components, where there is no any algorithm for evaluating the system reliability in this case.

The Boole-Bonferroni bounds were applied for evaluating the reliability of many systems. In this paper, the author reformulated the second-order Boole-Bonferroni bounds to be suitable for the evaluation of the multi-state system reliability. And the author applied these bounds for deriving the lower bound and upper bound of increasing multi-state linear k-within-(r, s)-of-(m, n): F lattice system.

An illustrated example of the proposed bounds and many numerical examples are given. The author tested these examples and concluded the cases that make the new bounds are sharper.

In this paper, the author considered an important and complex system, the multi-state linear k-within-(r, s)-of-(m, n): F lattice system; it is a model for many applications, for example, telecommunication, radar detection, oil pipeline, mobile communications, inspection procedures and series of microwave towers systems.

This paper suggests a method for the computation of the bounds of increasing multi-state linear k-within-(r,s)-of-(m,n): F lattice system. Furthermore, the author concluded that the cases that make these bounds are sharper.

The purpose of this paper is to evaluate the reliability indices such as reliability, mean time to failure and sensitivity analysis.

A non-repairable multi-state complex system with two subsystems, namely, S₁ and S₂, is studied. The subsystems S₁ and S₂ are multi-state weighted r-out-of-n: G and s-out-of-m: G systems, respectively. Every component of the sub-system S₁ consists of linear (f, l, k): G system, and the sub-system S₂ consists of circular (f, l, k): G system. The subsystems are connected in series arrangement and components of these subsystems are arranged in parallel.

Markov stochastic process has been applied to obtain probability of components of the subsystems and various results discuss such as reliability, mean time to failure and sensitivity analysis with the help of the universal generating function.

In this work, reliability measures of the purpose system can be enhanced under the high profit.

During the service period of communication satellite systems, their performance is often degraded due to the depletion mechanism. In this paper, the grey system theory is applied to the multi-state system effectiveness evaluation and the grey Lz-transformation ADC (availability, dependability and capability) effectiveness evaluation model is constructed to address the characteristics of the communication satellite system such as different constituent subsystems, numerous states and the inaccuracy and insufficiency of data.

The model is based on the ADC effectiveness evaluation method, combined with the Lz transformation and uses the definite weighted function of the three-parameter interval grey number as a bridge to incorporate the possibility of system performance being greater than the task demand into the effectiveness solution algorithm. At the same time, using MATLAB (Matrix laboratory) to solve each state probability, the same performance level in the Lz transform is combined. Then, the system effectiveness is obtained by Python.

The results show that the G-Lz-ADC model constructed in this paper can accurately evaluate the effectiveness of static/dynamic systems and certain/uncertain system and also has better applicability in evaluating the effectiveness of the multi-state complex system.

The G-Lz-ADC effectiveness evaluation model constructed in this paper can effectively reduce the complexity of traditional effectiveness evaluation models by combining the same performance levels in the Lz-transform and solving the effectiveness of the system with the help of computer programming, providing a new method for the effectiveness evaluation of the complex MSS. At the same time, the weaknesses of the system can be identified, providing a theoretical basis for improving the system’s effectiveness.

The possibility solution method based on the definite weighted function comparing the two three-parameter interval grey numbers is constructed, which compensates for the traditional calculation of the probability based on numerical values and subjective preferences of decision-makers. Meanwhile, the effectiveness evaluation model integrates the basic theories of three-parameter interval grey number and its definite weighted function, Grey−Markov, grey universal generating function (GUGF), grey multi-state system (GMSS), etc., which is an innovative method to solve the effectiveness of a multi-state instantaneous communication satellite system.

Renewable generation is a main component of most hybrid generation systems. However, randomness on its generation is a characteristic to be considered due to its direct impact on reliability and performance of these systems. For this reason, renewable generation usually is accompanied with other generation elements to improve their general performance. The purpose of this paper is to analyze the power generation system, composed of solar, wind and diesel generation and power outsourcing option from the grid as means of reserve source. A multi-objective optimization for the design of hybrid generation system is proposed, particularly using the cost of energy, two different reliability indexes and the percentage of renewable energy as objectives. Further, the uncertainty of renewable sources and demand is modeled with a new technique that permits to evaluate the reliability quickly.

The multi-state model of the generators and the load is modeled with the Universal Generating Function (UGF) to estimate the reliability indexes for the whole system. Then an evolutionary algorithm NSGA-II (Non-dominated Sorting Genetic Algorithm) is used to solve the multi-objective optimization model.

The use of UGF methodology reduces the computation time, providing effective results. The validation of reliability assessment of hybrid generation systems using the UGF is carried out taking as a benchmark the results obtained with the Monte Carlo simulation. The proposed multi-objective algorithm gives as a result different generators combinations that outline hybrid systems, where some of them could be preferred over others depending on its results for each independent objective. Also it allows us to observe the changes produced on the resulting solutions due to the impact of the power fluctuation of the renewable generators.

The main contributions of this paper are: an extended multi state model that includes different types of renewable energies, with emphasis on modeling of solar energy; demonstrate the performance improvement of UGF against SMC regarding the computational time required for this case; test the impact of different multi-states numbers for the representation of the elements; depict through multi-objective optimization, the impact of combining different energies on the cost and reliability of the resultant systems.

The purpose of this paper is to introduce a method for modelling the multi-state repairable systems subject to stochastic degradation processes by using the coloured stochastic Petri nets (CSPN). The method is a compact and flexible Petri nets model for multi-state repairable systems and offers an alternative to the combinatory of Markov graphs.

The method is grounded on specific theorems used to design an algorithm for systematic construction of multi-state repairable systems models, whatever is their size.

Stop and constraint functions were derived from these theorems and allow to considering k-out-of-n structure systems and to identifying the minimal cut sets, useful to monitoring the states evolution of the system.

The properties of this model will be studied, and new investigations will help to demonstrate the feasibility of the approach in real world, and more complex structure will be considered.

The simulation models based on CSPN can be used as a tool by maintenance decision makers, for prediction of the effectiveness of maintenance strategies.

The proposed approach and model provide an efficient tool for advanced investigations on the development and implementation of maintenance policies and strategies in real life.

The main purpose of the expert system presented in the paper is to support proper decision-making to perform the operation of the complex and crucial technical system in a rational way.

The proposed system was developed using the universal concepts of a semi-Markov process, quality space and a multi-objective analysis. The maintenance and operation processes of a machine were modelled in the form of a semi-Markov process, the quality space was used to exclude the operation and maintenance process of critical quality and finally, thanks to implementation of a multi-objective analysis, the assessment system was build.

By generating each flow of the process, the expert system supports optimization of a technical system operation to choose the best maintenance strategy. Application of the expert system created based on a real industrial system is presented at the end of the paper.

The limitations of the proposed approach can be found in the parts of simulation and assessment. As the number of states to be taken into consideration increases, the time of calculation gets longer as well. As regards the assessment, ranges of the criteria argument have to be determined. Unfortunately, in some industrial systems, they are difficult to define or they are infinite and should be artificially limited.

The system provides three most important benefits as compared to other solutions. The first benefit is the system ability to make a choice of the best strategy from the perspective of the accepted criteria. The second advantage is the ability to choose the best operation and maintenance strategy from the point of view of a decision-maker. And the third is that the decision-maker can be completely sure that the chosen way of operation is not of critical quality.

The novelty of the proposed solution involves the system approach to the expert system design, thanks to the described procedure which is flexible and can be easily implemented in different technical systems which have a crucial impact on reliability and safety of their operation. It is the unique combination of probability-based simulation, multi-dimensional quality considerations and multi-objective analysis.

The purpose of this paper is to investigate the reliability analysis of a multi-state manufacturing system with different performance levels. In, fact, reliability assessment of manufacturing systems gives a reasonable demonstration of system performance.

This research utilizes a multi-state system reliability analysis to develop a new metric for evaluating production systems.

The proposed model provides a sensible measure to assess the system situation against the best-case scenario of a production line.

The proposed model incorporates not only failures that stop production but also deals with partial failures where the system continues to operate at reduced performance rates. The analyses are represented in a best-case vs worst-case situation. Each of these cases provides insight for managers with respect to planning operation and maintenance activities.

In some environments, the failure rate of a system depends not only on time but also on the system condition, such as vibrational level, efficiency and the number of random shocks, each of which causes failure. In this situation, systems can keep working, though they fail gradually. So, the purpose of this paper is modeling multi-state system reliability analysis in capacitor bank under fatal and nonfatal shocks by a simulation approach.

In some situations, there may be several levels of failure where the system performance diminishes gradually. However, if the level of failure is beyond a certain threshold, the system may stop working. Transition from one faulty stage to the next can lead the system to more rapid degradation. Thus, in failure analysis, the authors need to consider the transition rate from these stages in order to model the failure process.

This study aims to perform multi-state system reliability analysis in energy storage facilities of SAIPA Corporation. This is performed to extract a predictive model for failure behavior as well as to analyze the effect of shocks on deterioration. The results indicate that the reliability of the system improved by 6%.

The results of this study can provide more confidence for critical system designers who are engaged on the proper system performance beyond economic design.