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In this paper, a new general system consisted of l subsystems connected in series is introduced. Each subsystem connected in K-out-of-(n + m): G mixed standby configuration.

The lifetime of the system's units is assumed to be exponentially distributed and there is elapsed repair time with general distribution. The switch in each subsystem is assumed to be imperfect with the failure process follows an exponential distribution. A genetic algorithm is applied to the system to obtain the optimal solution of the system and solve the redundancy allocation problem.

Analysis of availability, reliability, mean time to failure and steady-state availability of the system is introduced. The measures of the system are discussed in special two cases when the elapsed repair time follows gamma and exponential distribution. An optimization problem with bi-objective functions is introduced to minimize the cost of the system and maximize the reliability function. A numeric application is introduced to show the implementation and effectiveness of the system and redundancy allocation problem.

A new general K-out-of-(n + m): G mixed standby model with elapsed repair time and imperfect switching is introduced.

The purpose of this paper is to introduce an efficient algorithm based on a non-linear accepting threshold to solve the redundancy allocation problem (RAP) considering multiple redundancy strategies. In addition to the components reliability, multiple redundancy strategies are simultaneously considered to vary the reliability of the system. The goal is to determine the optimal selection of elements, redundancy levels and redundancy strategy, which maximizes the system reliability under various system-level constraints.

The mixed RAP considering the use of active and standby components at the subsystem level belongs to the class of NP-hard problems involving selection of elements and redundancy levels, to maximize a specific system performance under a given set of physical and budget constraints. Generally, the authors recourse to meta-heuristic algorithms to solve this type of optimization problem in a reasonable computational time, especially for large-size problems. A non-linear threshold accepting algorithm (NTAA) is developed to solve the tackled optimization problem. Numerical results for test problems from previous research are reported and analyzed to assess the efficiency of the proposed algorithm.

The comparison with the best solutions obtained in previous studies, namely: genetic algorithm, simulated annealing, memetic algorithm and the particle swarm optimization for 33 different instances of the problem, demonstrated the superiority of the proposed algorithm in finding for all considered instances, a high-quality solution in a minimum computational time.

Considering multiple redundancy strategies helps to achieve higher reliability levels but increases the complexity of the obtained solution leading to infeasible systems in term of physical design. Technological constraints must be integrated into the model to provide a more comprehensive and realistic approach.

Designing high performant systems which meet customer requirements, under different economic and functional constraints is the main challenge faced by the manufacturers. The proposed algorithm aims to provide a superior solution of the reliability optimization problem by considering the possibility to adopt multiple redundancy strategies at the subsystem level in a minimum computational time.

A NTAA is expanded to the RAP considering multiple redundancy strategies at the subsystem level subject to weight and cost constraints. A procedure based on a penalized objective function is developed to encourage the algorithm to explore toward the feasible solutions area. By outperforming well-known solving technique, the NTAA provides a powerful tool to reliability designers of complex systems where different varieties of redundancies can be considered to achieve high-reliability systems.

One of the common approaches to improve systems reliability is using standby redundancy. Although many works are available in the literature on the applications of standby redundancy, the system components are assumed to be independent of each other. But, in reality, the system components can be dependent on one another, causing the failure of each component to affect the failure rate of the remaining active components. In this paper, a standby two-unit system is considered, assuming a dependency between the switch and its associated active component.

This paper assumes that the failures between the switch and its associated active component follow the Marshall–Olkin exponential bivariate exponential distribution. Then, the reliability analysis of the system is done using the continuous-time Markov chain method.

The derived equations application to determine the system steady-state availability, system reliability and sensitivity analysis on the mean time to failure is demonstrated using a numerical illustration.

All previous models assumed independency between the switch and the associated active unit in the standby redundancy approach. In this paper, the switch and its associated component are assumed to be dependent on each other.

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.

The purpose of this paper is to derive a closed-form expression for the steady-state availability of a cold standby repairable k-out-of-n system. This makes the availability calculation much easier and accurate.

Assuming exponential distributions for system failure and repair, the Markov method is employed to derive the formula.

The proposed formula establishes an easier and faster venue and provides accurate steady-state availability.

The formula is valid for the case when the probability density function of the component failure and the repair is exponential.

The Markov method has never been used in the literature to derive the steady-state availability of a cold standby repairable k-out-of-n: G system.

The purpose of this paper is to explore the reliability and sensitivity analysis of a system with M primary units, W standby units, and one repair facility when switching to primary units may fail.

Failure times of primary and standby units are assumed to have exponential distributions, and repair times of the failed units are also assumed to have an exponential distribution. Different failure rates and switching failure probabilities are given depending on the readiness states of standby units, designated hot, warm, or cold. The Laplace transform technique is used to transform a set of ordinary differential equations to a set of equations. After finding the solution, we can obtain the desired measures in the time domain by using the inverse Laplace transform.

Expressions for system reliability and mean time to failure (MTTF) are derived. Sensitivity analysis of the system reliability and the MTTF with respect to system parameters are investigated.

This paper presents the first time that a contour of the MTTF with respect to standby states has been obtained, which is quite useful for the decision makers.

This paper aims to study the reliability of the high-speed train operation control system in the Chinese Train Control System Level 3 (CTCS-3) operating mode.

Dynamic fault tree and Bayesian network method are adopted to analyze the reliability and weakness of the CTCS-3 system.

First, a physical architecture and data flow diagram of the CTCS-3 system are established according to the typical structure and functions of the CTCS-3 system. Second, the dynamic fault tree of the CTCS-3 system is constructed. Considering the prior probability of the bottom event and the existence of dynamic redundancy, the dynamic fault tree is transformed into a Bayesian net. The reliability of the CTCS-3 system is carried out based on the prior probability and the weakness that affects the reliability of the system based on the posterior probability is also analyzed by the Bayesian network. Finally, it is disclosed that the impact of the on-board subsystem on the reliability of the CTCS-3 system is generally greater than that of the ground subsystem. The two weakest modules in the onboard subsystem are the driver-machine interface (DMI) and balise transmission module (BTM) and the weakest one in the ground subsystem is Balise. The analysis results are generally consistent with the malfunctions in the field operation of China’s high-speed railway.

(1) By reasoning, the reliability of the train operation control system in the CTCS-3 operating mode meets the standard requirements.

(2) Through backward reasoning, it is found that the failure of the onboard subsystem leads to a greater probability of failure of the train control system.

(3) The DMI, BTM and automatic train protection computer unit modules are weak components in the onboard subsystem. Vital digit input&output, train interface unit and train security gateway are rarely involved in previous research, the result in this paper shows that these three modules are also weak components in the subsystem, which requires attention.

In this paper, the objective is to perform mathematical modeling to optimize the steady-state availability of a multi-state repairable crushing system of a sugar plant using the evolutionary algorithm of Particle Swarm Optimization (PSO). The system availability is optimized by evaluating the optimal values of failure and repair rate parameters concerned with the subsystem of the system.

Mathematical modeling of the multi-state repairable system is performed to develop the first-order differential equations based on the exponential distribution of the failure and repair rates. These differential equations are recursively solved to obtain the availability under normalizing conditions. The availability of the system is optimized by using the PSO algorithm. The results obtained by PSO are validated by using the Genetic Algorithm (GA).

The availability analysis of the system concludes that the cane preparation (F1) is critical of the crushing system and the optimized availability of the system using PSO is achieved as high as 87.12%.

A crushing system of the sugar plant is evaluated as it is the main system of the sugar plant. The maintenance data associated with failure and repair rate parameters were analyzed with the help of maintenance records/logbook and by conducting personal meetings with maintenance executives of the plant. The results obtained in the paper helped them to plan maintenance strategies accordingly to get optimal system availability.

The analysis of the optimal production and preventive maintenance with lockout/tagout planning problem for a manufacturing system is presented in this paper. The considered manufacturing system consists of two non-identical machines in passive redundancy producing one type of part. These machines are subject to random breakdowns and repairs. The purpose of this paper is to minimize production, inventory, backlog and maintenance costs over an infinite planning horizon; in addition, it aims to verify the influence of human reliability on the inventory levels for illustrating the importance of human error during the maintenance and lockout/tagout activities.

This paper is different compared to other research projects on preventive maintenance and lockout/tagout. The influence of human error on lockout/tagout as well as on preventive maintenance activities are presented in this paper. The preventive maintenance policy depends on the machine age. For the considered manufacturing system the optimality conditions are provided, and numerical methods are used to obtain machine age-dependent optimal control policies (production and preventive maintenance rates with lockout/tagout). Numerical examples and sensitivity analysis are presented to illustrate the usefulness of the proposed approach. The system capacity is described by a finite-state Markov chain.

The proposed model taking into account the preventive maintenance activities with lockout/tagout and human error jointly, instead of taking into account separately. It verifies the influence of human error during preventive maintenance and lockout/tagout activities on the optimal safety stock levels using an extension of the hedging point structure.

The model proposed in this paper might be extended to manufacturing systems, but a number of conditions must be met to make effective use of it.

The originality of this paper is to consider the preventive maintenance activities with lockout/tagout and human error simultaneously. The control policy is obtained in order to find the solution for the considered manufacturing system. This paper also brings a new vision on the importance of human reliability during preventive maintenance and lockout/tagout activities.

Most methods of reliability analysis of cold standby systems assume that the precise probability distributions of the component times to failure are available. However, this assumption may be unreasonable in a wide scope of cases (software, human‐machine systems). Therefore, the imprecise reliability models of cold standby systems are proposed in the paper. These models suppose that arbitrary probability distributions of the component time to failure are possible and they are restricted only by available information in the form of lower and upper probabilities of some events. It is shown how the reliability assessments may vary with a type of available information. The impact of the independence condition on reliability of systems is studied. Numerical examples illustrate the proposed models.