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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 covenant with the cost assessment of a complex repairable system, consisting of two subsystems (Subsystem 1 and Subsystem 2) connected in series configuration and being operated by a human operator. Each subsystem has two identical units in parallel configuration and has different types of failure and two types of repairs (general repair and copula repair). Through the transition diagram, the system of first-order partial differential equations is derived and solved using a supplementary variable technique, Laplace transforms. All failures are assumed to follow exponential distribution, whereas repairs follow two types of distributions that are general and Gumbel–Hougaard family copula. In this paper, explicit expressions for reliability, availability, mean time to failure (MTTF) and cost analysis functions have been obtained. In this paper, two types of repairs (copula repair and general repair) have been studied, and it has been concluded that copula repair is more reliable as compared to general repair. Some computations are taken as particular case by evaluating: reliability, availability, MTTF and cost analysis, so as to capture the effect of both failure and repair rates to reliability measures. The results have been shown in tables and graphs. The convincing part has been discussed in last section of this study.

This paper is focused on the cost assessment of a system consisting two subsystem series configuration. Each subsystem has two identical units in parallel configuration. The performance of the system has been analyzed by supplementary variable techniques and Laplace transforms. Various measures of the reliability have been discussed by evaluations. Software called Maple 13 is used for computations.

In this research paper, the authors have evaluated the operational cost and incurred profit of the system together with other reliability measures for various situations and different types of failures and two types of repairs using Gumbel–Hougaard family copula distribution.

The present research focuses on the series and parallel configured complex systems that is used everywhere in industry and other sectors. The authors main aim is to claim that repair through the joint probability distribution copula is far better than general repair. Copula repair for a completely failed system is more beneficial for industrial system operations that will increase profit to the industrial sector.

The authors have observed that when repair follows general distribution the values of reliability obtained of the system are less compared to the those obtained when the authors apply copula repair, a joint probability distribution. It is a clear implication for industrial sector and organization to use the policy for a better generate revenue.

According to the best of authors’ knowledge, there is no social implication as this study is meant for reliability section. The study in management and case study matters is considered to have social implication.

This research is the original work of authors. Nothing has been copied from any paper or book. The references are cited according to the relevance of study.

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 various reliability measures like reliability, expected lifetime (mean time to failure), signature reliability and compare networks based on the different flows.

The reliability characteristics of complex bridge networks have been evaluated using different algorithms with the help of universal generating function (UGF). Further, the signature reliability of the considered networks has been determined using Owen’s method.

The present paper proposes an efficient algorithm to compute the reliability indices of complex bridge networks having i.i.d. lifetime components (nodes, edges) with the help of UGF and Owen’s method. This study reveals that a slight change in the complex bridge network affects the reliability significantly. Finally, by the reliability structure function, proposed algorithms are used to find the signature and MTTF. From signature, we have determined the different failure probabilities corresponding to edges of the network.

In this work, we have evaluated reliability characteristics and signature reliability of the complex bridge networks using UGF method and Owen’s method respectively unlike done in the past.

This study deals with the reliability analysis of a hybrid series–parallel system consisting of two subsystems A and B with two human operators. Subsystem A has two units in active parallel while subsystem B consists of two-out-of-four units. Both units have exponential failure and repair time. The system under consideration has two states: partial failure state and complete failure state. The mathematical equations associated with the transition diagram have been formulated using regenerative point techniques. The system is analysed using Laplace transforms to solve the mathematical equations. Some important measures of reliability such as availability of system, reliability of the system, mean time to failure (MTTF), sensitivity for MTTF and cost analysis have been discussed. Some particular cases have also been derived and examined to see the practical effect of the model. The computed results are demonstrated by tables and graphs. Furthermore, the results of the designed model are beneficial for system engineers and designers, reliability and maintenance managers.

This paper considered a hybrid series–parallel system consisting of two subsystems A and B with two human operators. The performance of the system is studied using the supplementary variable technique and Laplace transforms. The various measures of reliability such as availability, reliability, mean time to system failure (MTSF), sensitivity for MTTF and cost analysis have been computed for various values of failure and repair rates. Maple 13 software has been used for computations.

In this research paper, the authors have computed various measures of reliability such as availability, reliability, MTSF, sensitivity for MTTF and cost analysis for various values of failure and repair rates and find that failure due to human operators are more responsible for successful operation of the system and also regular repair should be invoked to improve system performance.

This research paper is the original work of authors. The references are well cited based on the importance of study. Nothing has been detached from any research paper or books.

The purpose of this paper is to find the reliability measures of Linux operating system connected in local area network (LAN).

The system has two different topologies, i.e. star topology (subsystem-1) and bus topology (subsystem-2), are placed at two different places, and connected to a server through a hub. Both the topologies have n clients. The system has partial failure and complete failure. The partial failure is of two type’s namely minor partial and major partial. The minor partial failure degrades the system whereas the major partial failure brings the system to a break down mode. The system can completely fail due to failure of server hacking and blocking.

By using supplementary variable technique and Laplace transformation, by taking different types of failure and two types of repairs the availability, non-availability, mean time to failure and cost analysis (expected profit) of the design system have been obtained.

In this research, a mathematical model of Linux operating system has been discussed from which one can check the behavioral analysis of the designed system.

The purpose of this paper is to evaluate various reliability measures like availability, reliability, mean time to failure and profit function.

The authors present a novel method for availability analysis of an engineering system incorporating waiting time to repair. The considered system consists of two subsystems, namely, A and B connected in series. The subsystem B has two identical units in standby arrangement. Each unit of the subsystem has two modes, i.e. normal efficiency or failed. The two standby units of the subsystem B are connected by an imperfect switching. The system is analyzed by supplementary variable technique, Laplace transformation and Gumbel-Hougaard family of copula.

Numerical examples with a way to highlight the important results have been appended at last. Numerical calculation shows that availability and reliability of the system is decreasing with respect to time when failure rates are fixed at different values. Finally, cost analysis of system reveals that the expected profit decreases with increase in service cost.

This paper presents a mathematical model in which an important aspect of switching has been taken into consideration, which is consistent with actual failures of switching by assuming two different types of failure between adjacent transition. It is evaluated with the help of the Gumbel-Hougaard family of copula.

The purpose of this paper is to analyse the performance of a wind electric generating power plant through the study of reliability measures. The enhancement of the performance of the wind power plant using various approaches is also an objective of this paper.

This paper describes two models of a wind electric generating power plant using the Markov process and supplementary variable technique and solved with the help of Laplace transformation. The first model has been analyzed without fault coverage and Gumbel-Hougaard family of copula, while the second model of the wind power plant employs fault coverage and Gumbel-Hougaard family of copula which are used to enhance the performance. The proposed methodology is then illustrated in detail considering numerical examples.

Numerous reliability characteristics such as availability, reliability and mean time to failure to examine the performance of the wind power plant have been investigated. Through the comparative study of both the models, the authors concluded that the plant can generate electricity over long periods of time by covering more and more detected faults, which is made possible with two types of repair facility.

In this work, the authors have developed a mathematical model based on a wind electric generating power plant. This work incorporates not only the component failures that stop or degrade the working of the plant but also deals with the catastrophic and repair strategy of the plant.

The purpose of this paper is to model and to improve the stability and long-lasting operation of the small home solar system configuration regarding the reliability, availability, sensitivity, cost analysis and mean time to failure (MTTF).

A model of a small home solar system is designed in this write up. It is designed in a series–parallel configuration, such that four panels are arranged in parallel, working under 1-out-of-4: G; policy and two batteries configured in parallel also, working under 1-out-of-2: G; policy. The panels are connected to a charge controller, then to the batteries and lastly to an inverter, all connected together in series configuration. Different types of system reliability such as reliability, sensitivity, availability, MTTF and cost analysis for particular values of the failure and repair rates have been evaluated by using a supplementary variable and Laplace transforms and demonstrated the computed results on tables and graphs. The main objective here is to improve the stability and long-lasting operation of the small solar system configuration regarding the reliability, availability, sensitivity, cost analysis and MTTF.

The future behavior of the small solar system and similar systems can be easily predicted at any given time for any parametric values, it is also better to provide repair than replacements in the system for better availability and reliability, it signifies that γp, γb, γc and γi are responsible for the better performance of the system, the variation of sensitivity together with the parametric values variations and lastly deduced that the profit will decrease whenever service cost increase.

This paper provides a model of small home solar system and its reliability analysis.

Solar photovoltaic (PV) is commonly used as a renewable energy source to provide electrical power to customers. This research establishes a method for testing the performance reliability of large grid-connected PV power systems. Solar PV can turn unrestricted amounts of sunlight into energy without releasing carbon dioxide or other contaminants into the atmosphere. Because of these advantages, large-scale solar PV generation has been increasingly incorporated into power grids to meet energy demand. The capability of the installation and the position of the PV are the most important considerations for a utility company when installing solar PV generation in their system. Because of the unpredictability of sunlight, the amount of solar penetration in a device is generally restricted by reliability constraints. PV power systems are made up of five PV modules, with three of them needing to be operational at the same time. In other words, three out of five. Then there is a charge controller and a battery bank with three batteries, two of which must be consecutively be in operation. i.e. two out of three. Inverter and two distributors, all of which were involved at the same time. i.e. two out of two. In order to evaluate real-world grid-connected PV networks, state enumeration is used. To measure the reliability of PV systems, a collection of reliability indices has been created. Furthermore, detailed sensitivity tests are carried out to examine the effect of various factors on the efficiency of PV power systems. Every module's test results on a realistic 10-kW PV system. To see how the model works in practice, many scenarios are considered. Tables and graphs are used to show the findings.

The system of first-order differential equations is formulated and solved using Laplace transforms using regenerative point techniques. Several scenarios were examined to determine the impact of the model under consideration. The calculations were done with Maple 13 software.

The authors get availability, reliability, mean time to failure (MTTF), MTTF sensitivity and gain feature in this research. To measure the reliability of PV systems, a collection of reliability indices has been created. Furthermore, detailed sensitivity tests are carried out to examine the effect of various factors on the efficiency of PV power systems.

This is the authors' original copy of the paper. Because of the importance of the study, the references are well-cited. Nothing from any previously published articles or textbooks has been withdrawn.