摘要:

AbstractEstimation of the expected cost of a warranty for a stochastically failing unit is closely tied to estimation of the renewal function. The renewal function is a basic tool also used in probabilistic models arising in other areas such as reliability theory, inventory theory, and continuous sampling plans. In these other areas, estimation of a straight line approximation of the renewal function instead of direct estimation of the renewal function has proved successful. This approximation is based on a limit expression for large values of the argument, sayt, of the renewal function. However, in warranty analusis, typicallytis small compared to the mean failure time of the unit. Hence, alternative methods for renewal function estimation, both parametric and nonparametric, are presented and discussed. An important aspect of this paper is to discuss the performance of the renewal function estimators when only a small number of failed units is available. A Monte Carlo study is given which suggests guidelines for choosing an estimator under various circumstances.

ISSN:0028-1441    

DOI:10.1002/nav.3800330302

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

年代:1986

数据来源: WILEY

摘要:

AbstractCapacity expansion models are typically formulated in the context of some finite horizon. Because the firm lasts longer than the horizon, a bias can enter into the optimal solution from the model horizon chosen. Recently, Grinold [8] has proposed a “dual‐equilibrium method” for ameliorating possible distortions. Although the dual‐equilibrium method has superior analytical properties to other methods, it is conceptually more complex. In this paper it is shown that there are situations where the “primal‐equilibrium” approach of Manne [15]provides equivalent results and that the use of annualized capital costs in the objective function, although somewhat less efficient, results in a

ISSN:0028-1441    

DOI:10.1002/nav.3800330303

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

年代:1986

数据来源: WILEY

摘要:

AbstractAn alternating renewal process starts at time zero and visits states 1,2,…,r, 1,2, …,r1,2, …,r, … in sucession. The time spent in stateiduring any cycle has cumulative distribution functionFi, and the sojourn times in each state are mutually independent, positive and nondegenerate random variables. In the fixed time interval [0,T], letUi(T)denote the total amount of time spent in statei. In this note, a central limit theorem is proved for the random vector (Ui(T), 1 ≤i≤r) (properly normed and cente

ISSN:0028-1441    

DOI:10.1002/nav.3800330304

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

年代:1986

数据来源: WILEY

摘要:

AbstractWe consider the problem of schedulingnjobs with random processing times on a single machine in order to minimize the expected variance of the completion times. We prove a number of results, including one to the effect that the optimal schedule must beVshaped when the jobs have identical means or variances or have exponential processing times.

ISSN:0028-1441    

DOI:10.1002/nav.3800330305

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

年代:1986

数据来源: WILEY

摘要:

AbstractSimple criteria are found for reducing the computational effort in multistage Bayesian acceptance sampling. Regions of optimality are given for both terminal actions accept and reject. Also, criteria are presented for detecting nonoptimality of sets of sample sizes. Finally, nearly optimal (z,c−,c+)‐sampling plans are constructed by restricting attention to a small subset of sample si

ISSN:0028-1441    

DOI:10.1002/nav.3800330306

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

年代:1986

数据来源: WILEY

摘要:

AbstractDiscussed in this article are tests for the extreme‐value distribution, or, equivalently, for the two‐parameter Weibull distribution when parameters are unknown and the sample may be censored. The three tests investigated are based on the median, the mean, and the Anderson‐DarlingA2statistic calculated from a setziof values derived from the spacings of the sample. The median and the mean have previously been discussed by Mann, Scheuer, and Fertig [10] and by Tiku and Singh [14]. Asymptotic distributions and points are given for the test statistics, based on recently developed theory, and power studies are conducted to compare them with each other and with two other statistics suitable for the test. Of the normalized spacings tests,A2is recommended overall; the mean also gives good power in many situations, but can be nonconsi

ISSN:0028-1441    

DOI:10.1002/nav.3800330307

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

年代:1986

数据来源: WILEY

摘要:

AbstractAn approximation forP(X2+ Y2≤ K2σ21)based on an unpublished result of Kleinecke is derived, whereXandYare independent normal variables having zero means and variances σ21and σ22and σ1≥ σ2. Also, we provide asymptotic expressions for the probabilities for large values of β =K2(1 ‐c2)/4c2wherec= σ2/σ1. These are illustrated by comparing with values tabulated by Harter [6]. Solution ofKfor specifiedPandcis also considered. The main point of this note is that simple and easily calculable approximations forPandKcan be developed and there is no need for numerical evaluation

ISSN:0028-1441    

DOI:10.1002/nav.3800330308

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

年代:1986

数据来源: WILEY

摘要:

AbstractA network model incorporating stochastic features is considered. The model represents a complex sequential process where an object or system moves through a succession of states (nodes) and operating modes (classes) in the course of carrying out its function (fulfilling its purpose). Transitions between states and operating modes occur in a possibly random manner and require (consume) some resource in randomly varying amounts. We discuss the routing behavior and resource requirements of a typical object as it moves through (and eventually out of) the network. We then shift our focus from a single object and its odyssey to the network as a whole, where time is the resource and many objects are entering the network according to a possibly nonhomogeneous Poisson pattern; in this vein, we discuss the evolution of the network over time. Finally, we consider some applications of the formulation, and results.

ISSN:0028-1441    

DOI:10.1002/nav.3800330309

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

年代:1986

数据来源: WILEY

摘要:

AbstractAn optimization model which is frequently used to assist decision makers in the areas of resource scheduling, planning, and distribution is the minimum cost multiperiod network flow problem. This model describes network structure decision‐making problems over time. Such problems arise in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, as well as in many others. Although existing network solution techniques are efficient, there are still limitations to the size of problems that can be solved. To date, only a few researchers have taken the multiperiod structure into consideration in devising efficient solution methods. Standard network codes are usually used because of their availability and perceived efficiency. In this paper we discuss the development, implementation, and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method is a forward algorithm which exploits the natural decomposition of multiperiod network problems by limiting its pivoting activity. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for a large number of special structure models. Here we describe the specialization of the forward simplex method of Aronson, Morton, and Thompson to solving multiperiod network network flow problems. Computational results indicate that both the solution time and pivot count are linear in the number of periods. For standard network optimization codes, which do not exploit the multiperiod structure, the pivot count is linear in the number of periods; however, the solution time is quadrati

ISSN:0028-1441    

DOI:10.1002/nav.3800330310

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

年代:1986

数据来源: WILEY

摘要:

AbstractA system receives shocks at random points of time. Each shock causes a random amount of damage which accumulates over time. The system fails when the accumulated damage exceeds a fixed threshold. Upon failure the system is replaced by a new one. The damage process is controlled by means of a maintenance policy. There areMpossible maintenance actions. Given that a maintenance actionmis employed, then the cumulative damage decreases at raterm. Replacement costs and maintenance costs are considered. The objective is to determine an optimal maintenance policy under the following optimality criteria: (1) long‐run average cost; (2) total expected discounted cost over an infinite horizon. For a diffusion approximation, we show that the optimal maintenance expenditure rate is monotonically increasing in the cumulative damage leve

ISSN:0028-1441    

DOI:10.1002/nav.3800330311

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

年代:1986

数据来源: WILEY