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The purpose of this paper is to develop novel preventive maintenance (PM) modeling methods for a cold standby system subject to two types of failures: random failure and deterioration failure.

The system consists of two components and a single repair shop, assuming that the repair shop can only service for one component at a time. Based on semi-Markov theory, transition probabilities between all possible system states are discussed. With the transition probabilities, Markov renewal equations are established at regenerative points. By solving the Markov regenerative equations, the mean time from the initial state to system failure (MTSF) and the steady state availability (SSA) are formulated as two reliability measures for different reliability requirements of systems. The optimal PM policies are obtained when MTSF and SSA are maximized.

The result of simulation experiments verifies that the derived maintenance models are effective. Sensitivity analysis revealed the significant influencing factors for optimal PM policy for cold standby systems when different system reliability indexes (i.e. MTSF and SSA) are considered. Furthermore, the results show that the repair for random failure has a tremendous impact on prolonging the MTSF of cold standby system and PM plays a greater role in promoting the system availability of a cold standby system than it does in prolonging the MTSF of system.

In practical situations, system not only suffers normal deterioration caused by internal factors, but also undergoes random failures influenced by random shocks. Therefore, multiple failure types are needed to be considered in maintenance modeling. The result of the sensitivity analysis has an instructional role in making maintenance decisions by different system reliability indexes (i.e. MTSF and SSA).

This paper presents novel PM modeling methods for a cold standby system subject to two types of failures: random failure and deterioration failure. The sensitivity analysis identifies the significant influencing factors for optimal maintenance policy by different system reliability indexes which are useful for the managers for further decision making.

Profit analysis of a two non‐identical unit cold standby system model with mutual changeover of the units is carried out in this paper. With mutual changeover of the unit, the operating unit, after functioning for some random amount of time, becomes standby to take rest, and the standby unit becomes operative. The failure and repair times of each unit are jointly distributed as bivariate exponential (BVE) with different parameters. Various measures of system effectiveness useful to system engineers and designers are obtained by using the regenerative point technique. Behaviour of the mean time to system failure (MTSF) and availability have also been studied graphically.

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 present study is to carry out stochastic analysis of some important reliability measures of a three-unit system where there are two types of units called type-I and type-II. In type-II, two identical units work simultaneously to meet the system requirements while in type-I, a single unit is kept in spare and can be used to work whenever required at the failure of either of the units of type-II. The system starts its operation with type-II units and thus priority is given to the operation of type-II units. The type II units are different to type-I unit but can perform the same task. There is a single server who handles repair activities of both type of units and the units are assumed to be in pristine condition after every repair. Failures of both types of units are independent and constant. The system can fail at the failure of either of the type-II units and type-I unit.

Semi-Markov process and regenerative point technique are used to study the behaviour of different reliability measures of the system.

In this paper, a three-unit non-identical repairable system is analysed stochastically and its reliability characteristics such as transition probabilities (TP), mean sojourn time (MST), MTSF, steady state availability, expected number of repairs of units, expected number of visits of the repairman and expected busy period of repairman are derived to carry out profit analysis.

The direct application of the present study can be seen is case of a power distribution system where solar panels may be considered as type-II units and transformer as the type-I unit. Here, the case study is carried out by using approximate data from some old studies; however, a study with accurate data would be more preferable.

This paper is one of the few reliability studies conducted on a system with simultaneous working units. Also, the comparative study of the profit of the present system model has been done with that of the model Kadyan et al. (2020a).

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.

This study deals with the Bayesian analysis of the reliability characteristics of some static system models. Recognizing the fact that overestimation (underestimation) of reliability function or mean time to system failure (MTSF), hazard rate is more serious than that resulting due to its underestimation (overestimation), an asymmetric loss function, called the linear exponential (LINEX), has been used in the analysis. The results are also given for the squared error loss function (SELF).

Investigates a stochastic model of a two identical unit cold standby system. Assumes that, if repair of the failed unit is not completed within a specified time, then an order is placed to replace the failed unit by the new one. The specified time is also known as the maximum repair time limit which may change from user to user of the system, so that it is assumed as a random variable. Joint distribution of failure and repair times is bivariate exponential whereas the distributions of lead time (difference between order and delivery time for a new unit) and replacement time of the new unit are negative exponential. Obtains various reliability characteristics of the system under study by using regenerative point technique. Also studied characteristics through graphs.

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 consider a General System Configuration (GSC), whose particular cases are all the popular system configurations. In reliability engineering one comes across various system configurations, for example, series, parallel and k‐out of‐m system models, which consist of a number of components.

The paper gives a general approach to express the reliability properties of the whole system in terms of component parameters. The reliability of a GSC is expressed as a polynomial of the component reliability. Lifetime data on components have been used to estimate the system reliability characteristics through classical and Bayes estimation procedures.

The paper finds that the underlying distribution is assumed to be Weibull and, in view of cost constraints, Type‐II censored information has been used.

The paper is useful for reliability practitioners as well as theoreticians. It provides an easy method to estimate the reliability of any system configuration.

Three types of estimation procedures for a general system configuration have been developed for the first time. The lifetimes of components are assumed to follow widely used Weibull distribution, whose particular case is the most popular exponential distribution.

Deals with the stochastic analysis of a two identical unit cold standby system model with repair and replacement policies. Taking the bivariate exponential distribution of failure and repair times and using the regenerative point technique, various measures of system effectiveness are obtained.