Search

An optimal allocation problem for a monotonic failure rate repairable system under some resource constraints is studied. In the first model, the numbers of minimal and perfect repairs are fixed and in the second model, the total amount of repair resource is fixed.

We propose the consecutive-$k_r $-out-of- $n_r $:F linear zigzag structure and circular polygon structure, which extend the consecutive-k-out-of-n:F system model. By employing the finite Markov chain imbedding approach, we have proven the equations for calculating the reliability of consecutive-k-out-of-n:F system with different patterns given the state of the first and(or) the last component(s). Based on those reliability equations, we provide the rules for obtaining the reliability of the linear zigzag structure and circular polygon structure. Numerical examples are presented as an illustration of our new system model and demonstrate the use of the equations and rules proposed in this paper. [ABSTRACT FROM AUTHOR]

A consecutive-k-out-of- n : F ( G ) system with sparse d consists of n components ordered in a line or a circle, while the system fails (works) iff, there exist at least k consecutive failed (working) components with sparse d for 0 \le d \le n - k . In this paper, a circular consecutive- k -out-of- n system with sparse d is considered. Some equations for system reliability and Birnbaum importance are derived by means of the finite Markov chain imbedding approach. Then the Birnbaum importance of components is compared in the situations where the system is under an IID model, and where one of the components is known to be failed, respectively. Finally, some numerical examples are followed to illustrate the results obtained in the paper. [ABSTRACT FROM PUBLISHER]

Since Birnbaum importance was introduced in 1969, there have been more than twenty kinds of importance measures so far. Among the various measures, Birnbaum importance plays an extremely important role because many importance measures have been defined under its illumination and have relationships with it. A lot of work has been done for Birnbaum importance in consecutive-k systems since the systems were introduced. Because the problems in practice are increasingly complicated, in 2007, Zhao proposed consecutive-k systems with sparse d, which is an extension of the current consecutive-k systems. In this paper, we study Birnbaum importance for linear consecutive-k-out-of-n systems with sparse d. Some equations on Birnbaum importance are proposed. With these equations, the ranking of components in the system on the basis of Birnbaum importance is given; and then some patterns of ranking are presented. Finally, two numerical examples are given to illustrate the results obtained in this paper. [ABSTRACT FROM PUBLISHER]

Here we present the structure functions for the linear and circular m-consecutive-k, l-out-of- n:F (G) systems, which consists of n linearly or circularly ordered components such that the system fails (works) iff there are at least m times l-overlapping runs of consecutive k failed (working) components. The duality of these F and G systems is obtained, and the proofs are given. The generalized reliability formulae for the systems are obtained by using the finite Markov chain imbedding approach for statistically independent and Markov-dependent cases. Some miscellaneous results on the reliability of these systems and numerical examples are provided to illustrate the results obtained in the paper. [ABSTRACT FROM PUBLISHER]

A linear connected-(r,s)-out-of-(m,n):F system consists of m\times n components arranged in m rows by n columns, and it fails iff there exists a r\times s subsystem in which all components are failed. The linear connected-(r,s)-out-of-(m,n):F system can be used for modeling engineering systems such as temperature feeler systems, supervision systems, etc. In this paper, a general method is proposed based on the finite Markov chain imbedding approach to study the exact reliability of a linear connected-(r,s)-out-of-(m,n):F system. Then a new more efficient method, which reduces the size of the state space by combining some states into one state, is presented to reduce the computing time. Furthermore, three numerical examples are given. The first two numerical examples show that the proposed algorithm is efficient not only when the component states are i.i.d., but also when the component states are statistically independent and non-identically distributed. And the last numerical example shows that our method can be used to compute not only the reliability, but also the component importance. [ABSTRACT FROM AUTHOR]