摘要:

AbstractIn two earlier papers, we proposed algorithms for finding an optimal sequence of processingmitems onqmachines, by finding a minimaximal path in a disjunctive network. In a third paper, this latter model was generalized (from 2‐state to 3‐state disjunctive graphs) so as to accommodate project scheduling with resource constraints. In this paper, we discuss another algorithm for the (2‐state) disjunctive network problem, closely related to those mentioned above. To make the paper self‐contained, section 2 briefly describes the problem. Section 3 introduces a class of constraints which forms the basis of the algorithm discussed in section 4. The constraints have only 1, −1, or 0 as coefficients on the left‐hand side, integers on the right‐hand side. The whole procedure of generating these constraints and finding a feasible solution whenever a new constraint is added, can be interpreted (section 5) as a process of generating a graph with degree‐constraints on its nodes, and then finding a subgraph satisfying the degree‐constraints. The nodes of the graph are generated by solving a critical‐path‐problem, the feasible subgraphs are found by

ISSN:0028-1441    

DOI:10.1002/nav.3800170102

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

年代:1970

数据来源: WILEY

ISSN:0028-1441    

DOI:10.1002/nav.3800170103

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

年代:1970

数据来源: WILEY

摘要:

AbstractA description is given of results of preliminary investigations (by a group at North American Rockwell Corporation) related to the Monte Carlo generation of lower Confidence bounds on the reliability of a logically complex system. In calculating system confidence bounds by use of a Monte Carlo procedure, one must generate the distribution of each independent subsystem reliability, given the life‐test failure data for that subsystem. Therefore, an assumption of a specified a priori distribution for each subsystem reliability is implicit in the procedure.In order that clues may be obtained as to optimum prior assumptions to be used in calculating Monte Carlo bounds for a complex system, the model has been restricted to a series system wherein each independent subsystem has exponentially distributed failure time and prototypes of each subsystem are tested until a fixed (but not necessarily the same for each subsystem) number of failures occurs. For this model, optimum (uniformly most accurate unbiased) exact classical confidence bounds on the reliabilityR(tm) at a specified mission time,tm, are available, although not easily calculated (El Mawaziny [12] and Lenter and Buehler [27]). Computer programs for calculating the optimum classical bounds and the Bayesian Monte Carlo bounds were written, and a means of numerically comparing various forms of prior distributions against an optimum standard was thus provided. One prior distribution widely used in obtaining Monte Carlo and general Bayesian exact lower confidence bounds on system reliability is thereby shown numerically to yield bounds which are conservative in the classical sense for this series‐system model. Another suggested prior distribution is shown to give bounds which are usually conservative but under certain conditions are liberal, and hence not truly confidence bounds. Moreover, it is demonstrated by a combination of numerical and analytical results, that for a series system containing more than one independent subsystem there exists no prior distribution for subsystem reliability which is independent of the data and which yields the optimum lower bounds. Other numerical results related to the selection of optimum methods for generating the bounds and evaluation of certain approximate methods are descri

ISSN:0028-1441    

DOI:10.1002/nav.3800170104

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

年代:1970

数据来源: WILEY

摘要:

AbstractA common problem in life testing is to demonstrate that the mean time to failure, θ, exceeds some minimum acceptable value, say θ1, with a given confidence coefficient γ. When this is true, it is said that “θ1has been demonstrated with a confidence γ”. In this paper a Sequential Bayes Procedure (SBP) for demonstrating (by means of. a probability statement) that θ exceeds θ1is presented. The SBP differs from the classical procedure in the sense that a prior distribution is assumed on the parameter θ, calling for a Bayesian approach. The procedure is based on the sequence of

ISSN:0028-1441    

DOI:10.1002/nav.3800170105

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

年代:1970

数据来源: WILEY

摘要:

AbstractSuppose that observations from populations π1, …, πk(k≥ 1) are normally distributed with unknown means μ1., μk, respectively, and a common known variance σ2. Let μ[1]μ … ≤ μ[k]denote the ranked means. We takenindependent observations from each population, denote the sample mean of thenobservation from π1byXi(i= 1, …,k), and define the ranked sample meansX[1]≤ … ≤X[k]. The problem of confidence interval estimation of μ(1), …,μ[k]is stated and related to previous work (Section 1). The following results are obtained (Section 2). Fori= 1, …,kand any γ(0<γ<1) an upper confidence interval for μ[i]with minimal probability of coverage γ is (− ∞,X[i]+h i*) withh i*= (σ/n1/2) Φ−1(γ1/k‐i+1), where Φ(·) is the standard normal cdf. A lower confidence interval for μ[i]with minimal probability of coverage γ is (Xi[i]–g i*, + ∞) withg i*= (σ/n1/2) Φ−1(γ1/i). For the upper confidence interval on μ[i]the maximal probability of coverage is 1– [1 – γ1/k‐i+1]i, while for the lower confidence interval on μ[i]the maximal probability of coverage is 1–[1– γ1/i]k‐i+1. Thus the maximal overprotection can always be calculated. The overprotection is tabled fork= 2, 3. These results extend to certain translation parameter families. It is proven that, under a bounded completeness condition, a monotone upper confidence intervalh(X1, …,Xk) for

ISSN:0028-1441    

DOI:10.1002/nav.3800170106

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

年代:1970

数据来源: WILEY

摘要:

AbstractThe two inventory echelons under consideration are the depot,D, andktender shipsE1, …,Ek. The tender ships supply the demand for certain parts of operational boats (the customers). The statistical model assumes that the total monthly demands at thektenders are stationary independent Poisson random variables, with unknown means λ1, …, λk. The stock levels on the tenders, at the heginning of each month, can be adjusted either by ordering more units from the depot, or by shipping bach to the depot an excess stock. There is no traffic of stock between tenders which is not via the depot. The lead time from the depot to the tenders is at most 1 month. The lead time for orders of the depot from the manufacturer isLmonths. The loss function due to erroneous decision js comprised of linear functions of the extra monthly stocks, and linear functions of shortages at the tenders and at the depot over theNmonths. A Bayes sequential decision process is set up for the optimal adjustment levels and orders of the two echelons. The Dynamic Programming recursive functions are given for a planning horizon ofNm

ISSN:0028-1441    

DOI:10.1002/nav.3800170107

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

年代:1970

数据来源: WILEY

摘要:

AbstractA simple model containing elements common to all logistics pipeline allocations is presented. This model is based on a two‐sided gam

ISSN:0028-1441    

DOI:10.1002/nav.3800170108

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

年代:1970

数据来源: WILEY

摘要:

AbstractAn optimal policy is characterized for operating the following system. Customers arrive in [O,T] according to a homogeneous Poisson process. Instantaneous services are provided at timesOandT. Additional instantaneous services can be provided atNintermediate stop ping times. These times must be chosen to minimize the total expected customer‐hours in [O,T] spent waiting for servic

ISSN:0028-1441    

DOI:10.1002/nav.3800170109

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

年代:1970

数据来源: WILEY

摘要:

AbstractThis paper deals with techniques applicable to predicting spare parts demand for military helicopters. The military helicopter is a distinct weapons system, whose unique configuration may preclude the direct application of forecasting techniques which have proved successful for other weapon systems. Furthermore, although the military helicopter has become extremely important tactically in modern warfare, it has received scant attention in terms of research concerning its supply support.Specifically, this paper summarizes research done to measure and compare the forecasting accuracy of six mathematical models, as they were applied to three prominent military helicopters. In addition, the paper describes attempts that were made to define, where possible, the conditions under which a specific forecasting technique might be applicable. In general, it is shown that the most accurate set of helicopter spare parts demand forecasts are produced by a second order polynomial exponential smoothing model. This model is observed to have most accurately described the highly volatile, and upward‐trended demand time series which were the subject of the stud

ISSN:0028-1441    

DOI:10.1002/nav.3800170110

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

年代:1970

数据来源: WILEY

摘要:

AbstractThis paper examines the effect of limitation, regarding weapons that are likely to fail during the period of deployment, on the final outcome in a stochastic duel model. Inter‐firing times as well as inter‐failure times have been assumed to be exponentially distribu

ISSN:0028-1441    

DOI:10.1002/nav.3800170111

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

年代:1970

数据来源: WILEY