Reliability of weighted k-out-of-n: G systems consisting of two types of components and a cold standby component

In this article, the influence of a cold standby component to the reliability of weighted k-out-of-n: G systems consisting of two different types of components is studied. Weighted k-out-of-n: G systems are generalization of k-out-of-n systems that has attracted substantial interest in reliability theory because of their various applications in engineering. A method based on residual lifetimes of mixed components is presented for computing reliability of weighted k-out-of-n: G systems with two types of components and a cold standby component. Reliability and mean time to failure of different structured systems have been computed. Moreover, obtained results are used for defining optimal system configurations that can minimize the overall system costs.     

A geometric process repair model for a cold standby repairable system with imperfect delay repair and priority in use

In this article, a two-dissimilar-component cold standby repairable system with one repairman is studied. Assume that the repair after failure for each component is delayed or undelayed. Component 2 after repair is “as good as new” while Component 1 after repair is not, but Component 1 has priority in use. Under these assumptions, using a geometric process, we consider a replacement policy N based on the failure number of Component 1. An optimal replacement policy N* is determined by minimizing the average cost rate C(N) of the system. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.     

General standby allocation in series and parallel systems

Stochastic orders are very useful tools to compare the lifetimes of two systems. Optimum lifetime of a series (resp. parallel) system with general standby component(s) depends on the allocation strategy of standby component(s) into the system. Here, we discuss three different models of one or more standby components. In each model, we compare different series (resp. parallel) systems (which are formed through different allocation strategies of standby component(s)) with respect to the usual stochastic order and the stochastic precedence order. The results related to the cold as well as the hot standby models are obtained as particular cases of the results discussed in this article because the model considered here is a general one.     

An alternative approach to reliability analysis of cold standby systems

ABSTRACT

An alternative approach is applied for reliability analysis of standby systems on the basis of matrix renewal function. In this regard, a single-server, two identical unit cold standby systems with an imperfect switch is considered as a three-state semi-Markov process. Several important reliability measures such as availability, mean time to failure, expected number of failures, etc., are obtained for general lifetime distributions. Also, the main results have been treated to the case of exponential lifetimes and explicit formulas obtained for this case in addition of some numerical illustrations. This approach can easily be extended to more general standby systems with different configurations.     

Improving the bridge structure by using linear failure rate distribution

In this paper, a system of five components is studied; one of these components is a bridge network component. Each of these components has a non-constant failure rate. The system components have linear failure rate lifetime distribution. The given system is improved by using three methods: reduction, warm standby with perfect switch and warm standby with imperfect switch. The reliability equivalence factors of the bridge structure system are obtained. The γ-fractiles are obtained to compare the original system with these improved systems. Finally, we present numerical results to show the difference between these methods.     

Stochastic comparisons of two-unit repairable systems

Abstract

We consider two models of two-unit repairable systems: cold standby system and warm standby system. We suppose that the lifetimes and repair times of the units are all independent exponentially distributed random variables. Using stochastic orders we compare the lifetimes of systems under different assumptions on the parameters of exponential distributions. We also consider a cold standby system where the lifetimes and repair times of its units are not necessarily exponentially distributed.     

Standby redundancies at component level versus system level in series system

Abstract

It is known that the redundancy at the component level is better than the system level for the case of active redundancy. However, few results are available for standby redundancy due to the complexity of convolution. This note stochastically compares allocations of standby redundancies in series systems with exponential components at the component level versus the system level in sense of the likelihood ratio ordering. The established results strengthen and extend some known ones in the literature.     

On stochastic behaviors of load-sharing parallel systems

Abstract

This paper mainly investigates a general load-sharing parallel system having two units. First, we construct some comparisons among a load standby system, a warm standby system, a hot standby system and a cold standby system. Moreover, some stochastic comparisons between the load-sharing parallel system and one of its two components are obtained in the sense of the usual stochastic order. Finally, the residual life of this system and its properties are examined.     

Conditional k-out-of-n systems with a cold standby component

ABSTRACT

In this article, we consider a k-out-of-n system with a cold standby component under the general condition that lth (0 < l ? n ? k + 1) component is working at time t. The survival function and mean residual life function of such system are derived. Some stochastic monotonic properties of the system lifetimes are presented as well. Numeric results are provided to illustrate the results. The main results obtained in this article complement and generalize related ones in Eryilmaz (2012 Eryilmaz, S. (2012). On the mean residual life of a k-out-of-n: G system with a single cold standby component. Eur. J. Oper. Res. 222:273–277.[Crossref], [Web of Science ®] , [Google Scholar]).     

On the survival time of a repairable duplex system sustained by a cold standby unit subjected to a priority rule

We analyze the survival time of a general duplex system sustained by a cold standby unit subjected to a priority rule. The analysis is based on advanced complex function theory (sectionally holomorphic functions). As an example, we consider Weibull–Gnedenko and Erlang distributions for failure and repair. Several graphs are displaying the survival function.     

Discrete time cold standby repairable system: Combinatorial analysis

ABSTRACT

In this article, we obtain exact expression for the distribution of the time to failure of discrete time cold standby repairable system under the classical assumptions that both working time and repair time of components are geometric. Our method is based on alternative representation of lifetime as a waiting time random variable on a binary sequence, and combinatorial arguments. Such an exact expression for the time to failure distribution is new in the literature. Furthermore, we obtain the probability generating function and the first two moments of the lifetime random variable.     

Reliability Evaluation for A Class of Multi-Unit Cold Standby Systems under Poisson Shocks

The reliability evaluation for a multi-units cold standby system with a switch-over under Poisson shocks is investigated. The random value of each shock is assumed to be i.i.d. with some known distribution. Each arrival of a shock has a random effect on the operating unit and on the switch-over. When the operating unit fails while the switch-over is normal, the next cold standby unit will start to operate immediately. The system fails only when all the units have failed or both the operating unit and the switch-over have failed. The reliability function and the mean time to the failure (MTTF) of the system are obtained.     

Copula-based reliability analysis for a parallel system with a cold standby

The traditional reliability models cannot well reflect the effect of performance dependence of subsystems on the reliability of system, and neglect the problems of initial reliability and standby redundancy. In this paper, the reliability of a parallel system with active multicomponents and a single cold-standby unit has been investigated. The simultaneously working components are dependent and the dependence is expressed by a copula function. Based on the theories of conditional probability, the explicit expressions for the reliability and the MTTF of the system, in terms of the copula function and marginal lifetime distributions, are obtained. Let the copula function be the FGM copula and the marginal lifetime distribution be exponential distribution, a system with two parallel dependent units and a single cold-standby unit is taken as an example. The effect of different degrees of dependence among components on system reliability is analyzed, and the system reliability can be expressed as the linear combination of exponential reliability functions with different failure rates. For investigating how the degree of dependence affects the mean lifetime, furthermore, the parallel system with a single cold standby, comprising different number of active components, is also presented. The effectiveness of the modeling method is verified, and the method presented provides a theoretical basis for reliability design of engineering systems and physics of failure.     

A model for k-out-of-m load-sharing systems

ABSTRACT

In a load-sharing system, the failure of a component affects the residual lifetime of the surviving components. We propose a model for the load-sharing phenomenon in k-out-of-m systems. The model is based on exponentiated conditional distributions of the order statistics formed by the failure times of the components. For an illustration, we consider two component parallel systems with the initial lifetimes of the components having Weibull and linear failure rate distributions. We analyze one data set to show that the proposed model may be a better fit than the model based on sequential order statistics.     

Allocating Redundancies to k-out-of-n Systems with Independent and Heterogeneous Components

This paper studies the allocation of independent redundancies with a common life distribution to k-out-of-n systems of independent components with non identical life distributions. A sufficient condition is found for allocating more active redundancies to the weaker component to gain a larger lifetime for k-out-of-n systems, and assigning more standby redundancies to the weaker (stronger) components is proved to yield larger lifetime for series (parallel) systems in the sense of the increasing concave (convex) order. Also, the optimal policy is proved to be majorized by all other policies when the system’s components are stochastically ordered.     

Stochastic properties and parameter estimation for a general load-sharing system

We study here a general load-sharing parallel system in which the lifetimes of the components of the system are arbitrary continuous random variables. The system functions if at least one component in the system functions and the surviving unit shares the whole load. Some sufficient conditions are obtained for the usual stochastic order between two different load-sharing systems. We then consider the optimal allocation problem of one load standby in a series system with two independent components. Finally, the maximum likelihood estimation of the parameters for some specific systems is discussed.     

Importance of Components for a System

Which component is most important for a system's survival? We answer this question by ranking the information relationship between a system and its components. The mutual information (M) measures dependence between the operational states of the system and a component for a mission time as well as between their life lengths. This measure ranks each component in terms of its expected utility for predicting the system's survival. We explore some relationships between the ordering of importance of components by M and by Zellner's Maximal Data Information (MDIP) criterion. For many systems the bivariate distribution of the component and system lifetimes does not have a density with respect to the two-dimensional Lebesgue measure. For these systems, M is not defined, so we use a modification of a mutual information index to cover such situations. Our results for ordering dependence are general in terms of binary structures, sum of random variables, and order statistics.     

A Study on Reliability for A Two-Item Cold Standby Markov Repairable System with Neglected Failures

This article studies reliability for a Markov repairable two-item cold standby system with neglected failures. In the system, if a failed time of the system is too short (less than a given critical value) to cause the system to fail, then the failed time may be omitted from the downtime record, i.e., the failure effect could be neglected. In ion-channel modeling, this situation is called the time interval omission problem. The availability indices and the mean downtime are presented as two measures of reliability for this repairable system. Some numerical examples are shown to illustrate the results obtained in this article.     

Bayesian Analysis for a Redundant Repairable System with Imperfect Coverage

System characteristics of a redundant repairable system with two primary units and one standby are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the coverage factor is the same for an operating unit failure as that for a standby unit failure. Times to failure and times to repair of the operating and standby units are assumed to follow exponential distributions. When times to failure and times to repair with uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper.     

Reliability Properties of Systems with Two Exchangeable Log-Logistic Components

In this article, we study the reliability properties of systems under bivariate log-logistic model which comes out from a particular stress-strength analysis. For this model, we obtain basic reliability characteristics of series and parallel systems and investigate their properties. We also derive distribution and moments of cold standby system under the abovementioned exchangeable model.