Gumbel-Hougaard Family Copula Research Articles

Reliability and performance analysis of a series- parallel Photovoltaic system with Human operators Using Gumbel Hougaard family copula

Reliability and performance analysis of a series- parallel Photovoltaic system with Human operators Using Gumbel Hougaard family copula

Reliability analysis of a complex repairable system in series configuration with switch and catastrophic failure using copula repair

This paper describes an analytical framework for in-depth investigation of a complex system consisting of two subsystems (namely L and M) in series configuration. Subsystem-L is composed of three identical units in parallel configuration that are working under 1-out-of-3: G policy, while subsystem-M has two non-identical units that are working under 1-out-of-2: G: policy. In subsystem-M, priority in operation is given to M1 unit whereas M2 unit put into cold standby mode if not in use. Moreover, both the subsystems are connected with controllers that may be perfect or imperfect at the time of need. We have considered a catastrophic failure due to frequent change in environmental conditions or man-made disruption. Failure rates of units in both the subsystems are constant and assumed to follow exponential distribution, but their repair supports two types of distributions namely general distribution and Gumbel-Hougaard family copula distribution. The system is studied by using the supplementary variable technique, Laplace transformation and Gumbel-Hougaard family of copula to derive differential equations and obtain important reliability indexes such as availability of the system, reliability of the system and profit analysis. The results have shown by tables and graphs. Conclusive part have been discussed in the last section of this study.

Performance Analysis of Multi-computer System Consisting of Three Subsystems in Series Configuration Using Copula Repair Policy

The present paper discuss the reliability characteristics of computer network system consisting of the devices load balancer, distributed database servers and a centralized server configured as series parallel system containing three subsystems. Subsystem 1: load balancer (LB) a device that act as a medium of channeling request to servers and receiving request or response from servers. Subsystem 2: identical distributed database servers (DDS) I, II and III connected in parallel, working under 2-out-of-3: G: policy, which manages and store some part of application data and Subsystem 3: centralized distributed database server (CDDS), which takes care of all the application data in DDS. Through the transition diagram, system of first-order partial differential equations are derived and solved using supplementary variable techniques, Laplace transforms and copula method. All failures are assumed to be exponentially distributed, whereas repairs follow two types of distributions; general distribution and Gumbel–Hougaard family copula, partial failures are repaired by general distribution while complete failures are repaired by copula distribution. The objective is to obtain the expressions for availability, reliability, mean time to failure (MTTF) and cost function. Computations for reliability measures 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 of the computations are presented in tables and graphs. The analysis of the results obtained with respect to the availability and expected profit indicates that copula repair policy is reliable than general repair policy.

Cost Benefit Analysis of a k-out-of-n: G Type Warm Standby Series System Under Catastrophic Failure Using Copula Linguistics

This paper deals with the study of reliability measures of a complex engineering system consisting three subsystems namely L, M, and N in series configuration. The subsystem-L has three units working under 1-out-of-3: G; policy, the subsystem-M has two units working under 1-out-of-2: G policy and the subsystem-N has one unit working under 1-out-of-1: G; policy. Moreover, the system may face catastrophic failure at any time t. The failure rates of units of all subsystems are constant and assumed to follow the exponential distribution however, their repair supports two types of distribution namely general distribution and Gumbel-Hougaard family copula distribution. The system is analyzed by using the supplementary variable technique, Laplace transformation and Gumbel-Hougaard family of copula to derive the differential equations and to obtain important reliability characteristics such as availability of the system, reliability of the system, MTTF, and profit analysis. The numerical results for reliability, availability, MTTF, and profit function are obtained by taking particular values of various parameters and repair cost using maple. Tables and figures demonstrate the computed results and conclude that copula repair is more effective repair policy for better performance of repairable systems. It gives a new aspect to scientific community to adopt multi-dimension repair in form of copula. Furthermore, the results of the model are beneficial for system engineers and designers, reliability and maintenance managers.

Reliability analysis of repairable network system of three computer labs connected with a server under 2- out- of- 3 G configuration

This paper presents the study of reliability measures of a complex system consisting of three computer labs connecting to a server in the parallel configuration under 2-out-of-3: G operation policy. The system is assumed to work if at least two labs are in good operative condition. The server failure brings the system to a complete failed state. The failure rates of all labs are different and assumed to follow an exponential distribution, but their repair supports two types of distribution, namely general distribution and Gumbel–Hougaard family copula distribution. The system of three labs with the server studied using the supplementary variable technique, laplace transform, expressions of reliability measures such as system availability, system reliability, MTTF, and cost analysis as incurred profit by operations have been computed. The numerical results for relevant measures like availability, reliability, MTTF, and profit function are also obtained by taking particular values of various failure and repair rate as stated. Tables and figures demonstrate the computed results.

Reliability analysis of communication network system with redundant relay station under partial and complete failure

The purpose of this paper is to study the performance of a communication network system consisting of a transmitter, two relay stations and a receiver arranged in series parallel. Through the transition diagram, the partial differential equations are derived, and Laplace transforms are then taken on these equations to derive system reliability, availability, the mean time to system failure (MTTF) and cost function. It is assumed that failure rates are constant and follows exponential distribution, repair rates of partial failure state are assumed to follow general distribution and complete failure states are repaired through Gumbel-Hougaard family copula. The system is analyzed through supplementary variable technique and Laplace transform. Different measures of testing system effectiveness which include reliability, availability, mean time to failure (MTTF) and profit function have been calculated for particular values of time, failure and repair rates. From the study, it is clear that time and failure rates of both transmitter, relay stations and receiver influence the reliability, availability, MTTF and profit function. Mathematical models developed in this paper can aid plant management for proper maintenance and system safety, avoiding incorrect reliability, availability and profit assessment and leading to inadequate maintenance decision making, which may result in unnecessary expenditures and reduction of safety standards.

Performance analysis of a complex repairable system with two subsystems in series configuration with an imperfect switch

This paper presents the study of reliability measures of a complex system consisting of two subsystems, subsystem-1, and subsystem-2, in a series configuration with switching device. The subsystem-1 has five units that are working under 2-out-of-5: G policy and the subsystem-2 has two units that are working under 1-out-of-2: G policy. Moreover, the switching device in the system is unreliable, and as long as the switch fails, the whole system fails immediately. Failure rates of units of subsystems are constant and assumed to follow the exponential distribution. Still, their repair supports two types of distribution, namely general distribution and Gumbel-Hougaard family copula distribution. Using the supplementary variable technique, Laplace transformations, and copula approach differential equations developed. Important reliability characteristics such as availability of the system, reliability of the system, MTTF, profit analysis, and sensitivity analysis for MTTF have computed for fixed values of failure and repair rates. Particular cases corresponding to the switching device have also considered. Graphs demonstrate results, and consequently, conclusions have done.

Safety Risk Management in Production Process: A case study in the automotive supplier industry

This paper deals with the study of reliability measures of a complex engineering system consisting three subsystems namely L, M, and N in series configuration. The subsystem-L has three units working under 1-out-of-3: G; policy, the subsystem-M has two units working under 1-out-of-2: G policy and the subsystem-N has one unit working under 1-out-of-1: G; policy. Moreover, the system may face catastrophic failure at any time t. The failure rates of units of all subsystems are constant and assumed to follow the exponential distribution however, their repair supports two types of distribution namely general distribution and Gumbel-Hougaard family copula distribution. The system is analyzed by using the supplementary variable technique, Laplace transformation and Gumbel-Hougaard family of copula to derive the differential equations and to obtain important reliability characteristics such as availability of the system, reliability of the system, MTTF, and profit analysis. The numerical results for reliability, availability, MTTF, and profit function are obtained by taking particular values of various parameters and repair cost using maple. Tables and figures demonstrate the computed results and conclude that copula repair is more effective repair policy for better performance of repairable systems. It gives a new aspect to scientific community to adopt multi-dimension repair in form of copula. Furthermore, the results of the model are beneficial for system engineers and designers, reliability and maintenance managers.

Stochastic analysis of a two units’ complex repairable system with switch and human failure using copula approach

This paper deals with the study of a complex system which consists of two subsystems in a series configuration (subsystem 1 and subsystem 2). The subsystem 2 is connected to subsystem 1 in a series configuration. The subsystem 1 has three identical units in parallel configuration and working under 2-out-of-3: G policy and its units are controlled by an instantaneous change over switch. Subsystem 2 has two identical units and uses 1-out-of-2: G scheme. A human operator operates the system, and human failure is considered to damage the entire system completely. All failure rates are assumed to follow exponential distribution and repairs follow two types of distribution (general distribution and Gumbel–Hougaard family copula) distribution. The system is analyzed using Supplementary variables technique, and the various measures of reliability have discussed. The computations for availability, reliability, MTTF, and profit benefit by operation of the system have done for different values of failure and repair rates. Graphs demonstrate results, and consequently, conclusions have done.

Cost assessment of complex repairable system consisting two subsystems in series configuration using Gumbel Hougaard family copula

Purpose 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. Design/methodology/approach 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. Findings 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. Research limitations/implications 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. Practical implications 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. Social implications 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. Originality/value 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.

Reliability Measures of Two Dissimilar Units Parallel System Using Gumbel-Hougaard Family Copula

The goal of the present study is to investigate the availability and the reliability of the system, which has two dissimilar units in the parallel network under copula. Other key parameters, such as mean time to failure (MTTF) and expected profit are also evaluated. Simultaneous malfunctioning of units, common cause failure and human fault are the causes of system breakdown. The present mathematical model is examined under the assumption that each failure rate is constant and is exponentially distributed. The system undergoes repair in the completely failed state as well as in degraded state. In the case of complete failure, the system is repaired by two repair facilities and that are tackled by utilizing Gumbel-Hougaard family copula. The present system has been studied by applying the concepts of probability theory, supplementary variable technique and Laplace transformation.

Stochastic Design Exploration with Rework of Flexible Manufacturing System Under Copula-Coverage Approach

Manufacturing systems are increasingly becoming automated and complex in nature. Highly reliable and flexible manufacturing systems (FMSs) are the necessity of manufacturing industries to fulfill the increasing customized demands. Worldwide, FMSs are used in industries to attain high productivity in production environments with rapidly and continuously changing manufactured goods structures and demands. Reliability prediction plays a very significant role in system design in the manufacturing industry, and two crucial issues in the prediction of system reliability are failures of equipment and system configuration. This novel work presents a stochastic model to analyze the performance of an FMS through its reliability characteristics, in the concern of its equipment. To improve the reliability of FMS, determine the sensitivity of the reliability measures of FMS. FMS consists of many components such as machine tools like CNC, automatic handling and material storage, controller and robot for serving load. The designed system is studied by using the Markov process, supplementary variable technique, Laplace transformation, coverage factor and Gumbel–Hougaard family copula to obtain various reliability measures. For some realistic approach, particular cases and graphical illustrations are also obtained.

Stochastic analysis of a complex system under preemptive resume repair policy using Gumbel-Hougaard family copula

The present paper focuses on the study of complex system consisting of three units super priority, priority and ordinary unit under preemptive resume repair policy. Three units connected with an automatic changeover switch and human operator is handling the system. Together with the failure in super priority, priority and ordinary unit, the other important failures like deliberate failure and switch failure have been considered for study of mathematical model. All failure rates are assumed constant and follow exponential distribution however, the repair rate for partially failed state follow general distribution and complete failed states are repaired using Gumbel-Hougaard family copula (a joint probability distribution of general distribution and negative exponential distribution). The system is analysed using supplementary variable technique and Laplace transform. The various popular measures of reliability such as availability, reliability, mean time to failure (MTTF) and profit function has been calculated for particular values of failure and repair rates. Sensitivity analysis for different traditional measures has also been done. Computed results have been highlighted by tables and graphs.

Stochastic analysis of a complex system under preemptive resume repair policy using Gumbel-Hougaard family copula

Stochastic analysis of a complex system under preemptive resume repair policy using Gumbel-Hougaard family copula

Performance assessment of repairable system in series configuration under different types of failure and repair policies using copula linguistics

This paper deals with the study of reliability measures of a complex system consisting two subsystems, subsystem-1 and subsystem-2 in a series configuration. The subsystem-1 has three units that are working under the policy 2-out-of-3: F; policy, and the subsystem-2 has two units that are working under 1-out-of-2: G; policy. Failure rates of units of subsystems are constant and assumed to follow an exponential distribution, but their repair supports two types of distribution, general distribution, and Gumbel-Hougaard family copula distribution. Two types of repair (general repair and copula repair) have been employed for partially failed and completely failed states. The system is analysed using the supplementary variable technique. Some important measures of reliability such as availability of system, reliability of the system, MTTF and profit analysis have been discussed. Computations have taken a particular case by evaluating availability, reliability, MTTF and profit of operation of the system.

Performance Analysis of Complex System in Series Configuration Under Different Failure and Repair Discipline Using Copula

This paper deal with the study of reliability of a complex system consists of three subsystems, (subsystem-1, subsystem-2 and subsystem-3) connected in series configuration. The subsystem-1 has three units and working under the policy 2-out-of-3: F policy, subsystem-2 has two units in parallel configuration and is working under 1-out-of-2: G policy and subsystem-3 is connected with subsystem-2. All three subsystems are connected in series configuration. The system has two types of failure, partial failure and completely failure. It is assumed that the partial failure bring the system to degraded state, while the complete failure stop functioning in the system. All failure rates are constant and assumed to follow exponential time distribution, but the repair follow two types of distribution, i.e., general distribution and exponential distribution. It is assumed that the system in partially failed/degraded states are repaired by employing general time distribution but the completely failed states are repaired by Gumbel–Hougaard family copula distribution. The system is analyzed by supplementary variable technique. Some crucial measures of reliability such as Availability, mean-time-to-failure (MTTF) and profit analysis have been discussed. Some computations are taken as special case by evaluating Availability, MTTF and profit by taking different failure rates.

Availability,MTTF and Cost analysis of complex system under Preemptive resume repair policy using copula distribution

In the present paper authors have focused on the study of complex system consisting two subsystems, in series configuration and handling by a human operator. The subsystem (1) has three units at super priority, priority and ordinary & the subsystem (2) has one unit in series configuration with the subsystem-1. The whole system is operated by a human operator and human failure can also appear at different state where system is in operational mode. Initially super priority unit starts function and failure during of super priority unit the priority unit start functioning and super priority unit goes under repair. The primitive resume repair policy is employed for repair of subsystem-1. The all failure rates are assumed to constants and follow exponential distribution but repair follow general and Gumbel-Hougaard family copula distribution. The system is studied by supplementary variable technique and Laplace transform. Various measure of reliability such as availability, state transition probabilities, mean time to system failure(M.T.T.F) and profit function has been discussed for available maintenance cost for all time and profit incurred by unit time for given interval. Some particular cases have been discussed for different values of different rates .

Modeling and Availability Analysis of Internet Data Center with various Maintenance Policies

In this paper, the authors have focused on the stochastic analysis of an internet data center (IDC), which consists of a database main server connected to a redundant server. Observing the different possibilities of functioning of the system, analysis has been done to evaluate the various reliability characteristics of the system. The system can completely fail due to failure of redundant server before repair of database server, router failure and switch failure. The system can also fail completely due to a cooling failure or some natural calamity like earthquake, fire etc. All the failure rates are assumed constant while the repairs follow two types of distributions namely general and Gumbel-Hougaard family copula.

Stochastic Analysis of a Standby System With Waiting Repair Strategy

This paper investigates the reliability of a standby system incorporating waiting time to repair. The considered system consists of two units, namely, the main unit and the standby unit. Whenever the main unit fails, the whole load is transferred to the standby unit instantaneously by a switching-over device. As regards to the repairing of the main unit, it has to wait for repair whenever it fails due to unavailability of repair facility. When both the main and standby units fail, then the system goes to the complete failure mode. The system may also fail due to incorrect start of the system, which can occur due to an untrained and inexperience operator. The repair of the main and standby units follows general distribution, whereas repair due to human error is obtained with the help of Gumbel-Hougaard family copula. The system is analyzed by supplementary variable technique and Laplace transformation. Various reliability measures like availability, mean time to failure, and profit function have been evaluated for the considered system. A numerical example with a way to illustrate the utility of the model has also been presented.

Analysis of a complex system with common cause failure and two types of repair facilities with different distributions in failure

This paper through a systematic view presents a mathematical model of a complex system that can fail in n-mutually exclusive ways of total failure or due to common cause failure. The system has two modes, namely normal and failed, with two types of repair facility. Repair rates are arbitrary functions of the time spent. All transition rates are assumed to be constant except at one where two types of failure, namely logarithmic and constant are possible. By employing a supplementary variable technique, Laplace transformation and Gumbel-Hougaard family copula, various transition state probabilities, availability and cost analysis (expected profit) are obtained along with steady-state behaviour of the system. Time-dependent probabilities and availability are also obtained by evaluating inversions. Finally, some special cases of the system and their plots are also appended.