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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.

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.

This paper aims to deal with the estimation of the empirical Bayesian exact confidence limits of reliability indexes of a cold standby series system with (n+k−1) units under the general progressive Type II censoring scheme.

Assuming that the lifetime of each unit in the system is identical and independent random variable with exponential distribution, the exact confidence limits of the reliability indexes are derived by using an empirical Bayes approach when an exponential prior distribution of the failure rate parameter is considered. The accuracy of these confidence limits is examined in terms of their coverage probabilities by means of Monte-Carlo simulations.

The simulation results show that accuracy of exact confidence limits of reliability indexes of a cold standby series system is efficient. Therefore, this approach is good enough to use for reliability practitioners in order to improve the system reliability.

When items are costly, the general progressive Type II censoring scheme is used to reduce the total test time and the associated cost of an experiment. The proposed method provides the means to estimate the exact confidence limits of reliability indexes of the proposed cold standby series system under this scheme.

The application of the proposed technique will help the reliability engineers/managers/system engineers in various industrial and other setups where a cold standby series system is widely used.

The main objective of this paper is to study the optimal system for series systems with mixed standby (including cold standby, warm standby and hot standby) components.

The paper deals with the reliability and availability characteristics of four different series system configurations. The failure time of the operative, hot standby and warm standby are assumed to be exponentially distributed with parameters λ, λ, and α respectively. The repair time distribution of each server is also exponentially distributed with parameter μ.

The mean time to failure, MTTF_i, and the steady‐state availability A_i(∞) for four configurations are examined and comparisons made. For all four configurations, the configurations are ranked based on: MTTF_i, A_i(∞), and C_i/B_i where B_i is either MTTF_i or A_i(∞). Obviously, the system with height MTTF_i and A_i(∞), do not need frequent maintenance, i.e. less maintenance.

Numerical results for the cost/benefit measure have been obtained for all configurations. It is interesting to note first that the optimal configuration using the cost/MTTF_i measure is configuration 4. Next the optimal configuration using the cost/A_i(∞) measure is configuration 2.

The purpose of this paper is to estimate the required number of robots consisting of some non-repairable components, by employing a renewal model. Considering the importance of the availability of standby autonomous robots for reducing and preventing down-times of advanced production systems, which imposes a considerable loss, the present research tries to introduce a practical model for the determination of the required number of autonomous robots.

Most of the available research on the estimation of the required standby components based on the reliability characteristics of components has not considered the environmental factors influencing the reliability characteristics. Therefore, such estimations are not accurate enough. In contrast, this paper focuses on the influence of the environmental and human factors (e.g. the operators’ skill) on the robot reliability characteristics.

A model based on the Weibull renewal process combined with the cold standby strategy is developed for reliability evaluation of the system. The effectiveness of the proposed integrated reliability evaluation model is worked out in some cases.

Determining a required number of robots is an important issue in availability and utilization of a complex robotic production system. In an advanced production system, while the estimation process of a required number of robots can be performed through different approaches, one of the realistic estimation methods is based on the system’s reliability that takes into consideration the system operating environment. To forecast the required number of robots for an existing production system, in some cases, the assumption of a constant failure rate does not differ much from the assumption of a non-constant failure rate and can be made with an acceptable error.

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 analyze a parallel system consisting of n dependent components with lifetimes following Weibull distribution. FGM Copula in multivariate case is used to generate the reliability function of the original system. A reduction method is introduced to improve system reliability. Other methods of hot, cold and warm duplication are established to improve system reliability. An application is introduced to show the results and compare between different improvement methods.

In this paper, a study of a parallel system consisting of n dependent and non-identical components is introduced. Reliability function of the original system is derived by using the concepts of copula, subject to Weibull distribution. Reliability function of the original system is improved according to reduction, hot duplication, warm and cold duplication methods. Reliability equivalence factors are introduced to compare between different system designs. Numerical illustration and real-time data application are discussed to show the results obtained in this paper.

Copulas can be used to model the reliability of systems with dependent units.

This paper is original. Improvement of the reliability of dependent systems is not discussed in literature. Copula is a useful tool to analyze the reliability of dependent systems. The introduced model is considered as a generalization of the models discussed in literature.

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.

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.

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.