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1.
The reliability of the consecutive k-out-of-r-from-n:F system is studied. For k=2 an explicit solution is given for n components in line or in cycle in the i.i.d. case. For k⩾3 sharp lower and upper bounds are given for the reliability of the system and demonstrated for different values of n, k, r, p. These bounds are exact for r=n, n-1, n-2, n-3, and for these values the exact analytic solution is also given  相似文献   

2.
A system with n components in sequence is a consecutive- k-out-of-n:F system if it fails whenever k consecutive components are failed. Under the supposition that component failures need not be independent and that component failure probabilities need not be equal, a topological formula is presented for the exact system reliability of linear and circular consecutive-k -out-of-n:F networks. The number of terms in the reliability formula is O(n4) in the linear case and O(n5) in the circular case  相似文献   

3.
A linear (circular) consecutive-k-out-of-n:F system consists of n components ordered on a line (circle). Each component and the system have two states: good or failed. The system fails if and only if at least k consecutive components fail. The reliability of such systems is computed. The most general case is examined without any restriction on the components  相似文献   

4.
A consecutive-k-out-of-n:F line is a system of components in a sequence such that the system fails if and only if k consecutive components all fail. Relayed systems often quoted as examples of such systems differ from the definition by the fact that the first component must work to initiate the relay (in some cases the last component also must work). Such systems are differentiated from ordinary consecutive-k-out-of-n:F lines by adding the word `relayed'. It is shown that the main properties of the reliabilities of consecutive-k-out-of-n:F lines are preserved under this modification  相似文献   

5.
A consecutive-k-out-of-n:F (consecutive-k -out-of-n:G) system consists of an ordered sequence of n components such that the system is failed (good) if and only if at least k consecutive components in the system are failed (good). In the present work, the relationship between the consecutive- k-out-of-n:F system and the consecutive-k-out-of-n:G system is studied, theorems for such systems are developed, and available results for one type of system are applied to the other. The topics include system reliability, reliability bounds, component reliability importance, and optimal system design. A case study illustrates reliability analysis and optimal design of a train operation system. An optimal configuration rule is suggested by use of the Birnbaum importance index  相似文献   

6.
The authors examine: the determination of an optimal consecutive k-out-of-r-from-n:F system, under permutations of the components, and the Birnbaum-importance of components in the i.i.d. case. The authors first study (theorem 1) the optimality of a general system, with not necessarily s-identical components, under permutation of the components. Then they study (theorem 2) the importance of components in the i.i.d. case. Theorem 2 is readily derived from theorem 1. The main results are given in theorems 1 and 2, and proofs are given. The assumptions are: the system and each component are either good or failed: all binary component states are mutually statistically independent, and all n can be arranged in any linear order; and the system fails if and only if within r consecutive components, there are at least k failed ones  相似文献   

7.
The problem of achieving optimal system size (n) for {k,n-k+1}-out-of-n systems, assuming that failure may take either of two forms, is studied. It is assumed that components are independently identically distributed (i.i.d.) and that the two kinds of system failures can have different costs. The optimal k or n that maximizes mean system-profit is determined, and the effect of system parameters on the optimal k or n is studied. It is shown that there does not exist a pair (k,n) maximizing the mean system-profit  相似文献   

8.
An O(k×n) algorithm is described for evaluating the reliability of a circular consecutive-k-out- n:F system  相似文献   

9.
A linear (m, n)-lattice system consists of m ·n elements arranged like the elements of a (m ,n)-matrix, i.e. each of the m rows includes m elements, and each of the n columns includes m elements. A circular (m,n)-lattice system consists of m circles (centered at the same point) and n rays. The intersections of the circle and the rays represent the elements, i.e. each of the circles includes n elements and each of the rays has m elements. A (linear or circular) (m, n)-lattice system is a (linear or circular) connected-X-out-of-(m,n):F lattice system if it fails whenever at least one subset of connected failed components occurs which includes failed components connected in the meaning of connected-X. The paper presents some practical examples and the reliability formulas of simple systems using results of consecutive-k-out-of-n:F systems  相似文献   

10.
For a k-out-of-n:G subsystem, the mathematical determination of the most economical number of components in the subsystem is sought. Optimal values of k (for fixed n) and n (for fixed k), which minimize the mean total cost of k-out-of-n:G subsystems, are given. A numerical example illustrates the results  相似文献   

11.
A direct, exact method for computing the reliability for a consecutive-k-out-of-n:F system with homogeneous Markov dependence is presented. This method calculates the reliability for a consecutive-k-out-n:F system where the probability that any component i fails depends upon, and only upon, the state of the component (i-1)  相似文献   

12.
Upper and lower bounds for the reliability of a (linear or circular) consecutive k-within-m-out-of-n:F system with unequal component-failure probabilities are provided. Numerical calculations indicate that, for systems with components of good enough reliability, these bounds quite adequately estimate system reliability. The estimate is easy to calculate, having computational complexity O(m2×n). For identically distributed components, a Weibull limit theorem for system time-to-failure is proved  相似文献   

13.
The authors study a discrete-time, infinite-horizon, dynamic programming model for the replacement of components in a binary k -out-of-n:F system. The goal is to trade off the component replacement and system failure costs. Under the criterion of minimizing the long-run average cost per period, it is optimal to follow a critical component policy (CCP), viz., a policy specified by a critical component set and the rule: replace a component if and only if it is failed and is in the critical component set. Computing an optimal CCP is a binary nonlinear programming problem, which can be solved by searching through a set with O(nk-1) points. This approach to finding an optimal CCP is practical when k is small. In particular, assuming s-independent components, it requires O(n2k-1) calculations. The authors analyze in detail the two most important cases with small k: the series (1-out-of-n:F) system and the 2-out-of-n:F system  相似文献   

14.
An m-consecutive-k-out-of-n:F system, consists of n components ordered on a line; the system fails if and only if there are at least m nonoverlapping runs of k consecutive failed components. Three theorems concerning such systems are stated and proved. Theorem one is a recursive formula to compute the failure probability of such a system. Theorem two is an exact formula for the failure probability. Theorem three is a limit theorem for the failure probability  相似文献   

15.
The authors discuss the preservation of certain partial orderings by a k-out-of-n:G system of i.i.d. components. If the lifetime of a component A is larger than that of a component B in the likelihood ratio, failure rate, or stochastic ordering, then a k-out-of-n:G system formed by n i.i.d. components of type A has a larger lifetime, in that ordering, than that of a similar system consisting of n i.i.d. components of type B. However, if the lifetime of a component A is larger than that of a component B in mean residual life, harmonic-average mean residual life, or variable orderings, it is not necessary that a k-out-of-n:G system formed by n i.i.d. components of type A has a larger lifetime, in that ordering, than that of a similar system consisting of n i.i.d. components of type B  相似文献   

16.
Pseudocyclic maximum-distance-separable codes   总被引:1,自引:0,他引:1  
The (n, k) pseudocyclic maximum-distance-separable (MDS) codes modulo (xn- a) over GF(q) are considered. Suppose that n is a divisor of q+1. If n is odd, pseudocyclic MDS codes exist for all k. However, if n is even, nontrivial pseudocyclic MDS codes exist for odd k (but not for even k) if a is a quadratic residue in GF(q), and they exist for even k (but not for odd k) if a is not a quadratic residue in GF(q). Also considered is the case when n is a divisor of q-1, and it is shown that pseudocyclic MDS codes exist if and only if the multiplicative order of a divides (q-1)/n, and that when this condition is satisfied, such codes exist for all k. If the condition is not satisfied, every pseudocyclic code of length n is the result of interleaving a shorter pseudocyclic code  相似文献   

17.
A consecutive-k cycle is a circular system such that the system fails if and only if any i consecutive components all fail. Reliabilities for consecutive-k cycles are usually computed by recursive equations. However, most recursive equations proposed so far for the cycle involve reliabilities for consecutive-k lines, requiring two passes where the first pass computes only the line reliabilities. A recursive equation involving cycles only is proposed that is simpler in form but much harder to understand on intuitive grounds. Another advantage is that the proposed cycle recursion has the same form as a line recursion previously proposed. Thus a uniform treatment of lines and cycles is possible. This uniform approach is used to obtain some explicit solutions of both line and cycle reliabilities for 2⩽k⩽4  相似文献   

18.
The authors provide a tool that an engineer designing a subsystem can use to decide between one subsystem and a more reliable but more costly one. The authors provide methods for selecting redundancy levels in k-out-of-n:G systems in order to minimize particular cost considerations where the k-out-of-n:G system is a subsystem of a major system. The n and k are chosen to minimize the total cost of the subsystem plus the average loss due to subsystem failure. A BASIC program is available to determine the n and k which find this minimum. Five loss functions are considered, and illustrations are given  相似文献   

19.
The authors consider a consecutive-k-out-n:F system consisting of identically distributed and statistically independent components, where the life distribution of an individual component is Weibull distributed with scale parameter 1/λ and shape parameter B. Let Tn be the life length of the consecutive-k-out-of-n:F system. The authors prove that for large values of n, the distribution of the n 1(ka)/Tn, is satisfactorily approximated by a Weibull distribution with the same scale parameter and shape parameter k times the original shape parameter  相似文献   

20.
A two-dimensional version of the consecutive-k-out-of-n:F model is considered. Bounds on system failure probabilities are determined by comparison with the usual one-dimensional model. Failure probabilities are determined by simulation for a variety of values of k and n  相似文献   

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