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The effect of adding cold standby redundancy to a system at system and component levels provides a useful information in reliability design. For a series (parallel) system adding cold standby redundancy at the component (system) level yields longer system lifetime. In this paper, the effect of adding cold standby redundancy to a general coherent structure at system and component levels is studied. In particular, signature-based expressions for the survival function of the system after standby redundancy at system and component levels are obtained. Thus for a given coherent structure with known signature, the survival functions and mean time to failure of new systems can be easily calculated and comparisons can be done in terms of stochastic ordering, and mean time to failure ordering. As a case study, circular consecutive- k -out-of- n :G system which can be used to analyze activities in a nuclear accelerator is considered. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Birnbaum importance measure of a component in a binary coherent system. A representation for the Birnbaum importance of a component is obtained when the system consists of exchangeable dependent components. The results are closely related to the concept of the signature of a coherent system. Some examples are presented to illustrate the results. [ABSTRACT FROM AUTHOR]

A coherent system of order n that consists two different types of dependent components is considered. The lifetimes of the components in each group are assumed to follow an exchangeable joint distribution, and the two random vectors, which represent the lifetimes of the components in each group are also assumed to be dependent. Under this particular form of dependence, all components are assumed to be dependent but they are categorized with respect to their reliability functions. Mixture representation is obtained for the survival function of the system's lifetime. Mixture representations are also obtained for the series and parallel systems consisting of disjoint modules such that all components of Type I are involved in one module (subsystem) and all components of Type II are placed in the other module. The theoretical results are illustrated with examples. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 388-394, 2015 [ABSTRACT FROM AUTHOR]

The signature of a system is a useful concept not only in the analysis of binary coherent systems but also in network reliability. Computation of system signature is a well-defined combinatorial problem. This article is concerned with the computation of signature vectors of series and parallel systems consisting of modules. We derive simple formulas for the signature and minimal signature of series and parallel systems based on signatures and minimal signatures of modules with given structures. We present computational results to illustrate the findings. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this paper is to show the usefulness of system signature for computing some important reliability indices of repairable systems. In particular, we obtain signature-based expressions for stationary availability, rate of occurrence of failure, and mean time to the first failure of repairable systems. Using these expressions we compute corresponding reliability indices of all systems with three and four components. Computational results are also presented for consecutive- -within- -out-of- :F and -consecutive- -out-of- :F systems. [Copyright &y& Elsevier]

The consecutive k-out-of-n systems are important structures in reliability engineering due to their applications in various real life situations. In this paper, we study the residual lifetime of these systems under the condition that the total number of failed components at time t1 is r, and at time t2 (t2 >t1) the system is still working. We obtain explicit expressions for the survival function of the corresponding residual life when the components are exchangeably dependent. We also obtain a signature-based mixture representation for a coherent system satisfying a certain property. [ABSTRACT FROM PUBLISHER]

A combined m-consecutive-k-out-of-n:F & consecutive-kc-out-of-n :F system consists of n linearly ordered components, and fails iff there exist at least kc consecutive failed components, or at least m non-overlapping runs of k consecutive failed components. This structure has applications for modeling systems such as infrared detecting and signal processing, and bank automatic payment systems. In this paper, we derive a combinatorial equation for the number of path sets of this structure including a specified number of working components. This number is used to derive a reliability function, and a signature based survival function formulae, for the system consisting of i.i.d. components. We also obtain a combinatorial equation for the reliability of a system with Markov dependent components. [ABSTRACT FROM PUBLISHER]

A consecutive k-within-m-out-of-n:F system consists of n linearly ordered components and fails if and only if there are m consecutive components which include among them at least k failed components. This system model generalizes both consecutive k-out-of-n:F and k-out-of-n:F systems. In this article, we study the dynamic reliability properties of consecutive k-within-m-out-of-n:F system consisting of exchangeable dependent components. We also obtain some stochastic ordering results and use them to get simple approximation formulae for the survival function and mean time to failure of this system. [ABSTRACT FROM AUTHOR]

The signature of a system is a useful tool in a variety of applications including the evaluation of the reliability characteristics of systems, and the comparison of the performance of competing systems. We study the evaluation and application of signatures of systems involving two common failure criteria which are common in real life applications. The failure or survival of these systems generally depends on the number of consecutively failed or working components, or total number of failed or working components in the whole system. We provide a method for obtaining the signatures of such systems. Applications of the results are also presented. [ABSTRACT FROM AUTHOR]

• Preventive and corrective maintenance policies. • Signature based results. • Illustrations for consecutive- k systems. This article presents a signature-based representation for the expected cost rate of age-based preventive maintenance policy for a binary coherent system consisting of independent exponential components, and then specializes the method to consecutive k -out-of- n system and its generalizations. According to the age-based preventive maintenance policy, the system is replaced at failure or before failure. For an arbitrary coherent system, the number of failed components at replacement time is a random variable. Thus, the expected cost per unit of time involves the mean number of failed components at replacement time. This mean is represented in terms of signature. Extensive numerical and graphical examples are presented for m -consecutive k -out-of- n :F and consecutive- k -within- m -out-of- n :F systems. [ABSTRACT FROM AUTHOR]

According to the well-known age replacement policy, the system is replaced preventively at time t or correctively at system failure, whichever occurs first. For a coherent system consisting of components having common failure time distribution which has increasing failure rate, we present necessary conditions for the existence of the unique optimal value which minimizes the mean cost rate. The conditions are mainly based on the signature which only depends on the system's structure. The results are illustrated for linear and circular consecutive type systems. [ABSTRACT FROM AUTHOR]