Stochastic analysis of k-out-of-n: G type of repairable system in combination of subsystems with controllers and multi repair approach

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.

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.

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.

Strategy for Synthesis of Flexible Heat Exchanger Networks Embedded with System Reliability Analysis

Reliability analysis of a series repairable system with multiple failures

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.

The High voltage static converter systems are deployed at different military and DoD assets in which power electronics is used for the isolated and stabilized AC or DC voltage/frequency conversion process and the Insulated Gate Bipolar Transistor (IGBT) triggering system plays crucial role in such systems. Such type of systems and equipments are being operated by the combat deployed personnel and they rely upon in order to complete their critical missions. Therefore, it is evident that reliability and availability during the mission and maintainability of the system before and after the mission is paramount. The objective of this paper is to present the predicted Reliability, Maintainability, Availability and Failure rate analysis of the IGBT triggering system. The analysis is made in the marine environment by defining specific parameters. The method used to calculate the reliability prediction of the IGBT triggering system is based on the calculation of Mean Time Between Failure (MTBF), which is obtained from the calculation of Failure rate of individual components used in the system. The maintainability analysis is done based on the length of the time required by the repairable components, repair through replaceable components or replacing the whole system. Therefore, this analysis will use the Mean Time To Repair (MTTR). MTBF and MTTR are used as key elements in the availability analysis of the system. Pareto analysis is presented in order to show the individual components failure rate contribution used in the system. The presented analysis shows the relationship between reliability, maintainability and availability of a system and also shows how the reliability and maintainability analysis improves the availability of the designed system. The presented analysis can be viewed with reference to system lifetime calculation as it will help in investment plan of designed system in marine environment.

Reliability of systems by mixture forms of uncertainty

This paper deals with the study of reliability measures of a system, which is a combination of two subsystems, each of them having two units in parallel configuration. The subsystem-1 is having two parallel units and working under the 1-out-of-2: G policy and the subsystem-2 is connected with subsystem-1 in a series configuration is also working under the same policy 1-out-of-2:G. The units of subsystem-1 & subsystem -2 have different types of failure and two type of repairs namely general repair and Gumbel-Hougaard family copula distribution. The important reliability measures of system are calculated by using the supplementary variable technique and Laplace transform.

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.

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.

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.

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.

System reliability depends not only on the reliabilities of components in the system but also on their interactions. Generally, in a system, not only s-independent failures but also s-dependent failures among components can occur; thus there are many studies where the s-dependencies among components are taken into account in system reliability and availability analysis, but in which the failure and repair rates were assumed constant. Whereas, from a practical viewpoint, the constant failure rate assumption for components has been, and is repeatedly challenged by knowledgeable reliability practitioners. Therefore, there are other studies which handled the problem of time-varying failure rates, among which all concerned repairable systems did not involve s-dependent failures. In most cases, however, to combine s-dependent failures and time-varying failure and repair rates in system reliability and availability analysis is the most appropriate for real systems. But it is very difficult to obtain the analytic solution and, in most cases, the closed-form solution for system reliability and availability does not exist, so that numerical or simulation methods must be used. This paper studies one kind of system that endures environmental shocks, and where one or more components can fail simultaneously due to a cumulative shock-damage process. An approach for reliability and availability analysis of such kinds of repairable systems is presented, where failure and repair rates of components can be varied with time. One type of special vehicle with such mechanical systems illustrates system reliability and availability solutions.

PurposeDegraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems where the degradation process follows Weibull distribution and critical failures follow exponential distribution.Design/methodology/approachThe research uses Semi-Markov modeling using the approach of method of stages which is suitable when the failure processes follow Weibull distribution. The paper considers various states of the system and uses state transition diagram to present the transition of the system among good state, degraded state and failed state. Method of stages is used to convert the semi-Markov model to Markov model. The number of stages calculated in Method of stages is usually not an integer value which needs to be round off. Method of stages thus suffers from the rounding off error. A unique approach is proposed to arrive at failure rates to reduce the error in method of stages. Periodic inspection and repairs of systems are commonly followed in industries to take care of system degradation. This paper presents models to carry out reliability and availability analysis of the systems including the case where degraded failures can be arrested by appropriate inspection and repair.FindingsThe proposed method for estimating the degraded failure rate can be used to reduce the error in method of stages. The models and the methodology are suitable for reliability and availability analysis of systems involving degradation which is very common in systems involving moving parts. These models are very suitable in accurately estimating the system reliability and availability which is very important in industry. The models conveniently cover the cases of degraded systems for which the model proposed by Hokstad and Frovig is not suitable.Research limitations/implicationsThe models developed consider the systems where the repair phenomenon follows exponential and the failure mechanism follows Weibull with shape parameter greater than 1.Practical implicationsThese models can be suitably used to deal with reliability and availability analysis of systems where the degradation process is non-exponential. Thus, the models can be practically used to meet the industrial requirement of accurately estimating the reliability and availability of degradable systems.Originality/valueA unique approach is presented in this paper for estimating degraded failure rate in the method of stages which reduces the rounding error. The models presented for reliability and availability analyses can deal with degradable systems where the degradation process follows Weibull distribution, which is not possible with the model presented by Hokstad and Frovig.