摘要:

AbstractA machine or production system is subject to random failure. Upon failure the system is replaced by a new one, and the process repeats. A cost is associated with each replacement, and an additional cost is incurred at each failure in service. Thus, there is an incentive for a controller to attempt to replace before failure occurs. The problem is to find an optimal control strategy that balances the cost of replacement with the cost of failure and results in a minimum total long‐run average cost per unit time. We attack this problem under the cumulative damage model for system failure. In this failure model, shocks occur to the system in accordance with a Poisson process. Each shock causes a random amount of damage or wear and these damages accumulate additively. At any given shock, the system fails with a known probability that depends on the total damage accumulated to date. We assume that the cumulative damage is observable by the controller and that his decisions may be based on its current value. Supposing that the shock failure probability is an increasing function of the cumulative damage, we show that an optimal policy is to replace either upon failure or when this damage first exceeds a critical control level, and we give an equation which implicitly defines the optimal control level in terms of the cost and other system parameters. Also treated are some more general models that allow for income lost during repair time and other extension

ISSN:0028-1441    

DOI:10.1002/nav.3800220102

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1975

数据来源: WILEY

摘要:

AbstractLower confidence limits are derived for the impact probability within a circle of fixed radius. The bivariate normal distribution with zero means, unequal variances, and zero correlation is the probability model for impacts. A new representation of the impact probability function is offered. This presentation is valid also for the dependent case, where the eigenvalues of the covariance matrix replace the variances. When the ratio of variances is known the lower confidence limits are uniformly most accurate (UMA). A few alternative approaches are compared by simulation when the ratio of variances is unknown.

ISSN:0028-1441    

DOI:10.1002/nav.3800220103

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1975

数据来源: WILEY

摘要:

AbstractThis paper is concerned with estimating p = P(X1

ISSN:0028-1441    

DOI:10.1002/nav.3800220104

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1975

数据来源: WILEY

摘要:

AbstractThe calculation of the exact reliability of complex systems is a difficult and tedious task. Consequently simple approximating techniques have great practical value.The hazard transform of a system is an invertible transformation of its reliability function which is convenient and useful in both applied and theoretical reliability work. A simple calculus for finding an approximate hazard transform for systems formed by series and parallel combinations of components is extended so that it can be used for any coherent system. The extended calculus is shown to lead to conservative approximations.A first order version of the extended calculus is also discussed. This method of approximation is even more simple to use, but is not always conservative. Examples of its application indicate that it is capable of giving quite accurate results.

ISSN:0028-1441    

DOI:10.1002/nav.3800220105

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1975

数据来源: WILEY

摘要:

AbstractFor eachn,X1(n),…,Xn(n) are independent and identically distributed random variables, each with cumulative distribution functionF(x) which is known to be absolutely continuous but is otherwise unknown. The problem is to test the hypothesis that\documentclass{article}\pagestyle{empty}\begin{document}$ F(x) = G\left( {{\textstyle{{x - \theta _1 } \over {\theta _2 }}}} \right) $\end{document}, where the cumulative distribution functionGxis completely specified and satisfies certain regularity conditions, and the parameters θ1, θ2are unknown and unspecified, except that the scale parameter θ2, is positive.Y1(n) ≦Y2(n) ≦ … ≦Yn(n)are the ordered values ofX1(n),…,Xn(n). A test based on a certain subset of {Yi(n)} is proposed, is shown to have asymptotically a normal distribution when the hypothesis is true, and is shown to be consistent against all alternatives satisfying a mild regula

ISSN:0028-1441    

DOI:10.1002/nav.3800220106

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1975

数据来源: WILEY

摘要:

AbstractExact expressions for the first and second order moments of order statistics from the truncated exponential distribution, when the proportion 1–Pof truncation is known in advance, are presented in this paper. Tables of expected values and variances‐covariances are given forP= 0.5 (0.1) 0.9 andn= 1 (1)

ISSN:0028-1441    

DOI:10.1002/nav.3800220107

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1975

数据来源: WILEY

摘要:

AbstractThis paper gives a new organization of the theoretical results of the Generalized Transportation Problem with capacity constraints. A graph‐theoretic approach is utilized to define the basis as a one‐forest consisting of one‐trees (a tree with an extra edge). Algorithmic development of the pivot‐step is presented by the representation of a two‐tree (a tree with two extra edges). Constructive procedures and proofs leading to an efficient computer code are provided. The basic definition of an operator theory which leads to the discussion of various operators is also given. In later papers we will present additional results on the operator theory for the generalized transportation problem based on the results in the pres

ISSN:0028-1441    

DOI:10.1002/nav.3800220108

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1975

数据来源: WILEY

摘要:

AbstractThis paper investigates the effect on the optimum solution of a capacitated generalized transportation problem when certain data of the problem are continuously varied as a linear function of a single parameter. First the rim conditions, then the cost coefficients, and finally the cell upper bounds are varied parametrically and the effect on the optimal solution, the associated change in costs and the dual changes are derived. Finally the effect of simultaneous changes in both cost coefficients and rim conditions are investigated. Bound operators that effect changes in upper bounds are shown to be equivalent to rim operators. The discussion in this paper is limited to basis preserving operators for which the changes in the data are such that the optimum bases are preserved.

ISSN:0028-1441    

DOI:10.1002/nav.3800220109

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1975

数据来源: WILEY

摘要:

AbstractA unifying survey of the literature related to the knapsack problem; that is, maximize\documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_i {v_i x_{i,} } $\end{document}, subject to\documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_j {w_i x_i W} $\end{document}andxi⩾ 0, integer; wherevi,wiandWare known integers, andwi(i= 1, 2, …,N) andWare positive. Various uses, including those in group theory and in other integer programming algorithms, as well as applications from the literature, are discussed. Dynamic programming, branch and bound, search enumeration, heuristic methods, and other solution techniques are presented. Computational experience, and extensions of the knapsack problem, such as to the multi‐dimensional case, are also consi

ISSN:0028-1441    

DOI:10.1002/nav.3800220110

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1975

数据来源: WILEY

摘要:

AbstractA modified generalized programming procedure is presented for solving concave programming problems with equality constraints. The procedure constructs convenient linear approximations of the gradient of the dual and finds points where the approximating functions vanish. In the quadratic programming case, the procedure is finitely convergent. Global convergence is established for the non‐quadratic case. Illustrative numerical examples are include

ISSN:0028-1441    

DOI:10.1002/nav.3800220111

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1975

数据来源: WILEY