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In this paper, new procedures for a fuzzy Markov reward model are introduced to find the reliability measures.

It is supposed that the introduced system consisted of n identical units connected in parallel and each unit has m different types of failures. Also, each unit of the system is allowed to have d levels of degradation from a working state to complete failure. Non-homogeneous Markov reward model is used to construct the system of differential equations of the model. Procedures are proposed to obtain reliability measures of the model under considering that the failure and repair rates of the systems unit are fuzzy. An application is constructed to analyze a system of 2-unit, and results are shown graphically.

Non-homogeneous Markov reward model is used to construct the system of differential equations of the model.

All papers in literature assumed Markov reward model with deterministic parameters. In this paper, a generalization of classical Markov reward model is introduced.

The present paper analyzed a model consisting of one unit with a warm standby unit where the main unit has three states: up, degraded and down.

The semi-Markov model under the regenerative method is used to construct the mathematical model for the system.

The effectiveness measures of the system are discussed such as availability, reliability, steady-state availability and mean time to system failure. The life and repair times of the system units are assumed to be discrete follow discrete Weibull distribution. Also, the parameters of the discrete Weibull distribution are assumed to be fuzzy with bell-shaped membership function. An application is introduced to show the results obtained for the system and the profit of the presented model.

Rarely papers in literature treated the topic of the discrete-time semi-Markov process using a regenerative point technique.

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.

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.