Series Repairable System Research Articles

Component-based perfect replacement optimizations for series and parallel systems consisting of repairable dependent components

In this paper, we consider the preventive perfect replacement and replacement by a new one policies for some arbitrary selected components in the repairable series and parallel systems with dependent components. These policies are also extended to other systems. In fact, regardless of the kind of system, the policies are applied to any system with a survival function that can be calculated as a known function of their component’s survival functions. The dependent structure of these components is formulated regarding copula frameworks. In addition, two optimal maintenance policies in accordance with the maximum expected life for a series and parallel system and minimum/maximum relative risk of a component for a series/parallel system have been provided. The problem issue of finding the optimal relative risk of a component is new and has not been proposed up to now. Although the optimal life extension of a system has been investigated previously, through a replacement policy of the whole system, in this study, the life of a series or parallel system is optimally extended through a replacement policy of some of its dependent components. The existence of the optimal solution has been shown for all copula functions and furthermore, some numerical results are detailed regarding the Gumbel, Frank, Joe, Clayton, FGM, Normal, and AMH copulas.

Maintenance decision of repairable series system with k-out-of-n: F subsystems

Maintenance decision of repairable series system with k-out-of-n: F subsystems

Estimation of the limiting availability of a repairable series system with stationary dependent sequences

The independence assumption would lead to poor estimation of the availability and even misleading conclusions when dependence actually exists. In this paper, we provide the estimation of the limiting availability of a repairable series system when the failure times and repair times are two independent sequences of stationary dependent random variables. Furthermore, consistency and asymptotic normality of the estimator of the limiting availability are derived under some regular conditions. Finally, we investigate the limiting availability for a first-order exponential moving average (EMA1) process and a first-order exponential autoregressive (EAR(1)) process. Simulations are presented to study the impact of dependence on the estimation of the limiting availability.

Optimal age replacement policy for parallel and series systems with dependent components

Maintenance plays a very vital role throughout the lifetime of a system and also in reality, the lifetime of components of a system may be dependent on each other that should be considered in a maintenance policy. This paper deals with age replacement policy for repairable series and parallel systems with n dependent components. We present two optimal age replacement policies based on the minimum expected cost function and maximum availability function. In this work, the copula framework is used to model the dependence structure for components and formulate the optimal decision problems. Therefore managers can use the results to decrease the cost imposed or increase the availability of their series or parallel systems with dependent components. The effects of the parameters of the model on the optimal solutions are studied and also the comparison of copulas is presented. An application on offshore wind turbine systems as a case study is discussed.

Reliability Modeling for Repairable Systems With Stochastic Lifetimes and Uncertain Repair Times

In actual industrial systems, there are often situations where the fault data are sufficient, whereas the repair data are insufficient. It is not appropriate to treat the system as a stochastic system or an uncertain system in this case. In this paper, the lifetimes of components are assumed to be random variables and the repair times of components are assumed to be uncertain variables. The entire system can be regarded as an uncertain random repairable system accordingly. Based on chance theory, some common reliability indexes of repairable system, such as availability, steady-state failure frequency, mean up time, and mean down time, are redefined and some properties are also presented. Then, the reliability mathematical models of repairable series systems, repairable parallel systems, repairable series-parallel systems, and repairable parallel-series systems are established, respectively. Furthermore, the formulas of reliability indexes of each repairable system are obtained. Finally, some numerical examples are presented to illustrate the calculation of the reliability indexes.

三部件串联可修系统的可靠性模型

三部件串联可修系统的可靠性模型

The Mathematical Model and Numerical Solution of Instantaneous Availabilities for the Two-Unit Series Repairable System and Parallel Repairable System with Three States

This paper is aimed to obtain the instantaneous availabilities (IAs) for the two-unit series system and parallel system with three states. By the compound S i m p s o n formula and the compound trapezoidal formula, we get the numerical solution of IA for the two-unit series system with three states based on the renewal process. With four-order R u n g e - K u t t a formula, the numerical solution of IA for the two-unit parallel system with three states is obtained based on the Markov process.

Reliability Mathematical Models of Repairable Systems With Uncertain Lifetimes and Repair Times

In system reliability problems, the lifetimes and the repair times are usually indeterministic. When insufficient samples are available to estimate distribution functions of the lifetimes and the repair times, it is rational to invite some experts to evaluate the belief degrees. Uncertainty theory is a branch of mathematics for modelling belief degrees. In this paper, the lifetimes and the repair times of typical repairable systems are assumed to be uncertain variables. Based on the above-mentioned assumptions, the uncertain reliability mathematical models of simple repairable series systems, simple repairable parallel systems, simple repairable series-parallel systems, and simple repairable parallel–series systems are established, respectively. The reliability indices, such as steady state availability, steady state failure frequency, mean up time, and mean down time, are proposed. Finally, some numerical examples are given for illustration.

A Generalized Signature of Repairable Coherent Systems

We present a generalized signature in repairable coherent systems resembling Samaniego's notion for statistically independent and identically distributed lifetimes. The repairable systems are made of different components which can individually fail, and be minimally repaired up to a fixed number of times. Failures occur according to Poisson processes, which might have either the same intensity function for each component, or different ones. The former case is similar to the notion of signature presented by Samaniego for i.i.d. random variables, whereas here statistically independent Poisson processes with identical intensity functions are considered. An explicit expression for computing the generalized signature of repairable series systems is obtained. It is shown that the reliability function of any repairable coherent system can be expressed as a generalized mixture of the probabilities of the number of repairs until system failure. We also establish that the stochastic ordering between the generalized signatures of two repairable systems is preserved by their lifetimes.

A new kind of repairable system with repairman vacations

In this paper, a new kind of series repairable system with repairman vacation is discussed, in which the failure rate functions of all the units and the delayed vacation rate function of the repairman are related to the working time of the system. The system model of a group of integro-differential equations is established by using probability analysis method, which then is translated into an initial value problem of a class of

Availability of Stochastic Degrading Systems Subject to Imperfect Repair

A series repairable system not only is one of the classical reliability models but is also the usually used model in practice. In this paper, a method for calculating system availability for series repairable system is studied. From the states of components, this methodology uses a gamma distribution to model the material degradation, and the impact of imperfect maintenance actions on the system reliability is investigated. The state of a degrading system immediately after the imperfect maintenance action is assumed as a random variable and the maintenance time follows a geometric process. At last, a numerical example is presented to demonstrate the use of the model.

Existence and Uniqueness of Solution of an N-unit Series Repairable System with a Repairman Doing Other Work

Weinvestigate an N-unit series repairable system with a repairman doing other work. By using the method of functional analysis, especially, 0 C -semigroup theory and

Developing a new model for availability of a series repairable system with multiple cold-standby subsystems and optimization using simulated annealing considering redundancy and repair facility allocation

Redundancy technique is considered as a way to enhance the reliability and availability of a system. This paper models availability of a repairable system with multiple subsystems in which the involved components follow cold-standby strategy. The goal is to find the optimal number of repairmen and redundant components in each subsystem for optimization of steady-state availability subject to weight, cost and volume constraints. Repairmen allocation is a new variable in redundancy allocation problem for repairable systems. This problem belongs to nonlinear programming. Due to complexity and time limitation, a simulated annealing algorithm is proposed to solve the problem. Finally, computational results of three cases with various subsystems are illustrated to prove the efficiency of the proposed algorithm.

Further research of a new kind of series repairable system

This paper is devoted to studying the uniqueness and existence of the system dynamic solution by using C0-semigroup theory and discussing its exponential stability by analyzing the spectral distribution of system operator and its quasi-compactness. Some primary reliability indices are discussed with the eigenfunction of system operator and the optimal vacation time to get the maximum system profit is analyzed at the end of paper.

A preventive maintenance and replacement policy of a series system with failure interaction

This article considers when preventive maintenance (PM) and replacement should be implemented for a repairable series system with failure interaction. Under the main assumption that the system gradually deteriorates with time, the modified sequential method is proposed to determine an optimal PM and replacement policy for the system based on minimizing expected cost per unit operation time. According to this method, PM epochs are determined one after the other, and consequently we can make use of all previous information on the system's operation process. Also, the replacement epoch depends on the PM's effective length. A property of the cost function with respect to both PM and replacement is discussed.

Stability analysis of a new kind n-unit series repairable system

In this paper, we deal with a new model of an n-unit series repairable system, in which a concept of a repairman with multiple-delayed vacation is introduced and the impact on the system reliability due to a replaceable facility is also considered. This paper is devoted to studying the unique existence and stability of the system solution. C 0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system in a special case. Some reliability indices of the system are also studied and the optimal vacation time is analyzed at the end of the paper.

Stability analysis of a new kind series system

An n-unit series repairable system with a repairman doing other work is discussed in this paper. We are devoted to studying the unique existence of the solution and the exponential stability of the system. Co-semigroup theory is used to prove the existence of a unique non-negative solution of the system. Then by analysing the spectra distribution of the system operator and the quasi-compactness of the system, we derive that the transient solution of the system exponentially converges to the non-negative steady-state solution, which is the eigenvector corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system and the strategy of the repairman doing other work in his idle time are presented at the end of the paper.

Optimal burn-in for maximizing reliability of repairable non-series systems

Burn-in is a manufacturing process applied to products to eliminate early failures in the factory before the products reach the customers. Various methods have been proposed for determining an optimal burn-in time of a non-repairable system or a repairable series system, assuming that system burn-in improves all components in the system. In this paper, we establish the trade-off between the component reliabilities during system burn-in and develop an optimal burn-in time for repairable non-series systems to maximize reliability. One impediment to expressing the reliability of a non-series system is in that successive failures during system burn-in cannot be described precisely because a failed component is not detected until the whole system fails. For approximating the successive failures of a non-series system during system burn-in, we considered two types of repair: minimal repair at the time of system failure, and repair at the time of component or connection failure. The two types of repair provide bounds on the optimal system burn-in time of non-series systems.

An N-Component Series Repairable System with Repairman Doing Other Work and Priority in Repair

In this paper, we discussed the reliability of an N-unit series repairable system with the repairman doing other work and priority in repair. In this system, it is assumed that the working time distributions of the n components and the arrival interval time distributions of the customers which are out of the system are both exponential and the components in system is given priority in repair. It is also assumed that the repair time distributions of the n components and the service time distributions of the customers are both general continuous distributions. After repair, components are “as good as new”. Under these assumptions, using a supplementary variable technique and Laplace transform technique, some important reliability indices such as the system availability, the idle probability of the repairman and the rate of service for customers are derived. Our problem is to determine whether or not given the priority to components in repairing such that the benefit of the system is maximized.

The Reliability Analysis of N-Unit Series Repairable System With One Replaceable Repair Facility and a Repairman Doing Other Work

A model of N-unit series repairable systems with a repairman doing other work is studied and the impact on the system reliability because of a replaceable facility is also considered. It is assumed that the life of each unit, the life of the facility are exponentially distributed, the repair time of the unit, the replace time of the facility and the work time of the repairman outside the system are all generally distributed. By using approach of supplementary variables and method of generalized Markov progress, some important reliability indicates of the system and the facility are obtained.