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The purpose of this paper is to deliberate the system reliability of a system in combination of three subsystems in a series configuration in which all three subsystems function under a k-out-of-n: G operational scheme. Based on computed results, it has been demonstrated that copula repair is better than general repair for system better performance. The supplementary variable approach with implications of copula distribution has been employed for assessing the system performance.

Probabilistic assessment of complex system consisting three subsystems, multi-failure threats and copula repair approach is used in this study. Abbas Jubrin Bin, V.V. Singh, D.K. Rawal, in this research paper, have analyzed a system consisting of three subsystems in a series configuration in which all three subsystems function under a k-out-of-n: G operational scheme. The supplementary variable approach with implications of copula distribution has been employed for assessing the system performance. Based on computed results, it has been demonstrated that copula repair is better than general repair for system better performance.

In this analysis, four different cases of availability are analysed for Gumbel–Hougaard family copula and also four cases for general repair with similar failure rates are studied. The authors found that when failure rates increase, the system availability decreases, and when the system follows copula repair distribution, the system availability is better than general repair.

This research may be implemented in various industrial systems where the subsystems are configured under k-out-of-n: G working policy. It is also advisable that copula repair is highly recommended for best performances from the system. On the basis of mean time to system failure (MTSF) computations, the failure rate which affects system failure more needs to be controlled by monitoring, servicing and replacing stratagem.

This research work has great implications in various industrial systems like power plant systems, nuclear power plant, electricity distributions system, etc. where the k-out-of-n-type of system operation scheme is validated for system operations with the multi-repair.

This work is a new work by authors. In the previously available technical analysis of the system, the researchers have analyzed the repairable system either supplementary variable approach, supplementary variable and system which have two subsystems in a series configuration. This research work analyzed a system with three subsystems with a multi-repair approach and supplementary variables.

The purpose of this paper is to develop a preventive maintenance policy with continuous monitoring for a circular consecutive-k-out-of-n: F systems. A preventive maintenance policy is developed based on the system critical condition which is related to the number of working components in the minimal cut sets of the system. If there is at least one minimal cut set which consists of only one working component, the system is maintained preventively (PM) after a certain time interval and the failed components are replaced with the new ones to prevent the system failures. If the system fails prior to the preventive maintenance, the system is correctively maintained (CM) immediately by replacing the failed components.

The mathematical function of the expected cost rate for the proposed maintenance policy is derived. The costs of PM, CM, and replacement per component are considered. The optimal maintenance parameter, which is the PM interval, is obtained by enumeration, and the numerical studies are shown with various system and cost parameters. The performance of the proposed policy is evaluated by comparing its expected cost rate to those of the no-PM and age-PM policies. The percentage of cost increase from the no-PM and age-PM policies to the proposed PM policy is calculated and this value can represents how important the continuous monitoring in this policy.

The proposed policy outperforms other policies. When the cost of CM is high and the cost of PM is low, the proposed PM policy is more suitable.

The system consists of identical components and the component failure times follow an exponential distribution. Continuous monitoring is considered, which means that the component states can be known at any time. Three cost parameters, cost of PM, CM, and replacement per component, are considered.

This paper shows a maintenance problem for circular consecutive-k-out-of-n: F systems. Many studies on this system type focused on the reliability estimation or system design problem. Previous study with this policy (Endharta and Yun, 2015) has been developed for linear systems, although the study used a simulation approach to estimate the expected cost rate. Also, Endharta et al. (2016) considered a similar method for the different types of system, which is linear consecutive-k-out-of-n: F system.

This paper analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The computed results are more supportable for repairable system performability analysis.

In this paper, the authors have analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The supplementary variable technique has employed for analyzing the performance of the system.

Reliability measures have been computed for different types of configuration. It generalized the results for purely series and purely parallel configurations.

This research may be beneficial for industrial system performances whereas a k-out-of-n-type configuration exists.

Not sure as it is a theoretical assessment.

This research may not have social implications.

This work is the sole work of authors that have not been communicated to any other journal before.

The purpose of this paper is to evaluate the reliability and signature reliability of solar panel k-out-of-n-multiplex system with the help of universal generating function.

Energy scarcity and global warming issues have become important concerns for humanity in recent decades. To solve these problems, various nations work for renewable energy sources (RESs), including sun, breeze, geothermal, wave, radioactive and biofuels. Solar energy is absorbed by solar panels, referred to as photovoltaic panels, which then transform it into electricity that can be used to power buildings or residences. Remote places can be supplied with electricity using these panels. Solar energy is often generated using a solar panel that is connected to an inverter for power supply. As a result, a converter reliability evaluation is frequently required. This paper presents a study on the reliability analysis of k-out-of-n systems with heterogeneous components. In this research, the universal generating function methodology is used to identify the reliability function and signature reliability of the solar array components. This method is commonly used to assess the tail signature and Barlow-Proschan index with independent and identically distributed components.

The Barlow-Proschan index, tail signature, signature, expected lifetime, expected cost and minimal signature of independent identically distributed are all computed.

This is the first study of solar panel k-out-of-n-multiplex systems to examine the signature reliability with the help of universal generating function techniques with various measures.

The purpose of this paper is to compute the signature reliability of the coherent systems.

The considered k-out-of-n coherent system consists of n number of elements connected in series. With the help of these systems, the authors have evaluated a mathematical structure using universal generating function.

Using the universal generating function technique, the authors evaluate tail signature, Barlow-Proschan index, expected lifetime and expected cost.

In this paper, the authors have developed a coherent systems based on the universal generating function technique.

The purpose of this paper is to derive a closed-form expression for the steady-state availability of a cold standby repairable k-out-of-n system. This makes the availability calculation much easier and accurate.

Assuming exponential distributions for system failure and repair, the Markov method is employed to derive the formula.

The proposed formula establishes an easier and faster venue and provides accurate steady-state availability.

The formula is valid for the case when the probability density function of the component failure and the repair is exponential.

The Markov method has never been used in the literature to derive the steady-state availability of a cold standby repairable k-out-of-n: G system.

The purpose of this paper is to propose a condition-based opportunistic maintenance policy considering economic dependence for a series–parallel hybrid system with a K-out-of-N redundant structure, where a single component in series is denoted as subsystem1, and K-out-of-N redundant structure is denoted as subsystem2.

Based on the theory of Residual Useful Life (RUL), inspection points are determined, and then different maintenance actions are adopted in the purpose of minimizing the cost rate. Both perfect and imperfect maintenance actions are carried out for subsystem1. More significantly, regarding economic dependence, condition-based opportunistic maintenance is designed for the series–parallel hybrid system: preemptive maintenance for subsystem1, and both preemptive and postponed maintenance for subsystem2.

The sensitivity analysis indicates that the proposed policy outperforms two classical maintenance policies, incurring the lowest total cost rate under the context of both heterogeneous and quasi-homogeneous K-out-of-N subsystems.

This model can be applied in series–parallel systems with redundant structures that are widely used in power transmission systems in electric power plants, manufacturing systems in textile factories and sewerage systems. Considering inconvenience and high cost incurred in the inspection of hybrid systems, this model helps production managers better maintain these systems.

In maintenance literature, much attention has been received in repairing strategies on hybrid systems with economic dependence considering preemptive maintenance. Limited work has considered postponed maintenance. However, this paper uses both condition-based preemptive and postponed maintenance on the issue of economic dependence bringing opportunities for grouping maintenance activities for a series–parallel hybrid system.

The purpose of this paper is to investigate the reliability measures, namely, availability, reliability, mean time to failure and expected profit. The authors also analyse the sensitivity of these reliability measures.

Depending upon the real industrial relevance, a generalized system which is easily repairable, extremely reliable and of high quality is expected by the rapid growth of the digital economy. Considering reliability, as one of the performance measure, the authors have designed a complex system which consists of three subsystems, namely, A, B and C in series configuration. The subsystem A consists of n numbers of units which are arranged in parallel configuration, subsystem B consists of two sub-subsystems X and Y align parallel to one another, where X is a type of 1-out-of-n:F. Failure and repair rates are assumed to be follow the general distribution.

The system is deeply studied by the usage of the supplementary variable technique, Laplace transformation and Markov’s law. Various conclusive results such as availability and reliability of the system, mean time to failure, cost and sensitivity analysis have been discussed further.

Through the systematic view of reliability measures of the proposed system, performance of the system can be enhanced under high profit.

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.

In this paper, a new general system consisted of l subsystems connected in series is introduced. Each subsystem connected in K-out-of-(n + m): G mixed standby configuration.

The lifetime of the system's units is assumed to be exponentially distributed and there is elapsed repair time with general distribution. The switch in each subsystem is assumed to be imperfect with the failure process follows an exponential distribution. A genetic algorithm is applied to the system to obtain the optimal solution of the system and solve the redundancy allocation problem.

Analysis of availability, reliability, mean time to failure and steady-state availability of the system is introduced. The measures of the system are discussed in special two cases when the elapsed repair time follows gamma and exponential distribution. An optimization problem with bi-objective functions is introduced to minimize the cost of the system and maximize the reliability function. A numeric application is introduced to show the implementation and effectiveness of the system and redundancy allocation problem.

A new general K-out-of-(n + m): G mixed standby model with elapsed repair time and imperfect switching is introduced.