Probabilistic assessment of complex system consisting three subsystems, multi-failure threats and copula repair approach

PurposeThe 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.Design/methodology/approachProbabilistic 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.FindingsIn 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.Research limitations/implicationsThis 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.Practical implicationsThis 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.Originality/valueThis 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.

Chimera state in coupled map lattice of matrices

In recent years, a lot of research has focused on understanding the behavior of when synchronous and asynchronous phases occur, that is, the existence of chimera states in various networks. Chimera states have wide-range applications in many disciplines including biology, chemistry, physics, or engineering. The object of research in this paper is a coupled map lattice of matrices when each node is described by an iterative map of matrices of order two. A regular topology network of iterative maps of matrices was formed by replacing the scalar iterative map with the iterative map of matrices in each node. The coupled map of matrices is special in a way where we can observe the effect of divergence. This effect can be observed when the matrix of initial conditions is a nilpotent matrix. Also, the evolution of the derived network is investigated. It is found that the network of the supplementary variable $\mu$ can evolve into three different modes: the quiet state, the state of divergence, and the formation of divergence chimeras. The space of parameters of node coupling including coupling strength $\varepsilon$ and coupling range $r$ is also analyzed in this study. Image entropy is applied in order to identify chimera state parameter zones.

Copula based Measures of Repairable Parallel System with Fault Coverage

The main objective of this study is to analyse the reliability behaviour of parallel systems with three types of failure, namely unit failure, human failure and major failure. For this purpose, we apply three different statistical techniques, namely copula, coverage and copula-coverage. More precisely, this study presents a stochastic model for analysing the behaviour of a multi-state system consisting of two non-identical units by incorporating the concept of coverage factor and two types of repair facilities between failed state to a normal state. The system could be characterized as being in a failed state due to unit failures, human failure and major failures, such as catastrophic and environmental failure. All failure rates are constant and it is assumed that these are exponentially distributed whereas, repair rates follow the Gumbel-Hougaard copula distribution. The entire system is modelled as a finite-state Markov process. Time-dependent reliability measures like availability, reliability and mean time to failure (MTTF) are obtained by supplementary variable techniques and Laplace transformations. The present study provides a comparative analysis for reliability measures among the aforementioned techniques, while a discussion referring to which technique makes the system more reliable is also developed. Furthermore, numerical simulations are presented to validate the analytical results.

Optimization Analysis of the N Policy M/G/1 Queue with Working Breakdowns

This paper deals with the N policy M/G/1 queue with working breakdowns. The supplementary variable and probability generating function techniques are implemented to develop the steady-state results. The stability condition of a stable queue, as well as several system performance measures, are also derived. A two-stage optimization method is employed to determine the optimal threshold N and the optimal joint values of two mean service rates until the stability constraint is satisfied. To demonstrate the effectiveness of two-stage optimization method, some numerical results are presented. Finally, we carry out sensitivity analysis for the expected cost function with numerical illustrations.

Queuing system in E- Commerce

This paper explores an investigation on Queuing framework in E-trade. Online business (electronic trade) is the acquiring and selling of product and adventures, or the transmitting of benefits or data, over an electronic system, basically the web. It is the trading of things or administrations using PC systems like Internet or online casual networks. Here the Business is led utilizing PCs, phones, fax machines, standardized tag per users, Visas, ATM or other electronic apparatuses without the trading of paper-based records or physically moving to a strip mall. It incorporates exercises, for instance, acquirement, request passage, trade handling, online installment, verification, stock control, request satisfaction, shipment, and client support. In the Queuing arrangement of E trade, the clients touches base in Batch with Reneging happens at the set-up time organize and Optional second stage where breakdown happens just as fix procedure will be done. Moreover, we accept that the clients may renege amid the Initial stage because of eagerness (Slow server) or Non-Satisfaction in acquiring the items from the specific site. At the season of Repair process, Strictly Non-acceptability of the clients is executed. The model is well analyzed and solved by supplementary variable method .The system performance measures are derived. Numerical analysis and graphical representation of the model clearly justifies the model to a fullest satisfaction.

Queuing System Modeling for Supermarkets

Supermarkets may not have the IT needs that service-oriented businesses do, but that does not mean they cannot use computers in their day-to-day operations. Many supermarkets are adopting complex computer systems that allow them to regulate many of their practices, providing business leaders with more information to make decisions with and making some processes automatic, saving supermarkets both time and money. For the complete satisfaction of the customers, in system modeling, various queuing system is followed by the super markets. In all those queuing system, various queuing issue have to be dealt with. Among those, on of the Queuing problem is inspected and it is considered as a Non Markovian Queuing issues. For the above portrayed Queuing problem, by the usage of supplementary variable method, performance measures like number of customers in the system, average length of the queue, waiting time of the customers in the system as well as in the queue are derived. In addition, idle time of the server and the time spent by the server for each service are determined. The model is well justified by means of a Numerical portrayal and a grow graphical examination is done toward the end to favour the model