Under a free-replacement warranty of duration W, the customer is provided, for an initial cost of C, as many replacement items as needed to provide service for a period W. Payments of C are not made at fixed intervals of length W, but in random cycles of length Y = W + γ(W), where γ(W) is the (random) remaining life-time of the item in service W time units after the beginning of a cycle. The expected number of payments over the life cycle, L, of the item is given by MY(L), the renewal function for the random variable Y. We investigate this renewal function analytically and numerically and compare the latter with known asymptotic results. The distribution of Y, and hence the renewal function, depends on the underlying failure distribution of the items. Several choices for this distribution, including the exponential, uniform, gamma and Weibull, are considered. 相似文献
Suppose that a nonhomogeneous Poisson process is observed for a length of time T, say Let λ (t) denote the mean value function of the process. It is assumed that λ (t) is first increasing then decreasing inside the interval (0, T) with peak at t = t0, say. Three methods are given for estimating to. One of these methods is nonparametric, and the other two methods are based on the standard regression technique and the maximum likelihood principle The given resull has application in a problem of determining the azimuth of a target from the radar-impulse data. The time series of incoming signals may be approximated by the occurrence of a nonhomogeneous Poisson process with mean value function λ (t). The azimuth of the target is reasonably determined from the direction of the axis of the radar beam at the instant to, corresponding to the peak value of λ (t). 相似文献
Consider a system consisting of n separately maintained independent components where the components alternate between intervals in which they are “up” and in which they are “down”. When the ith component goes up [down] then, independent of the past, it remains up [down] for a random length of time, having distribution Fi[Gi], and then goes down [up]. We say that component i is failed at time t if it has been “down” at all time points s ?[t-A.t]: otherwise it is said to be working. Thus, a component is failed if it is down and has been down for the previous A time units. Assuming that all components initially start “up,” let T denote the first time they are all failed, at which point we say the system is failed. We obtain the moment-generating function of T when n = l, for general F and G, thus generalizing previous results which assumed that at least one of these distributions be exponential. In addition, we present a condition under which T is an NBU (new better than used) random variable. Finally we assume that all the up and down distributions Fi and Gii = l,….n, are exponential, and we obtain an exact expression for E(T) for general n; in addition we obtain bounds for all higher moments of T by showing that T is NBU. 相似文献
A dynamic version of the transportation (Hitchcock) problem occurs when there are demands at each of n sinks for T periods which can be fulfilled by shipments from m sources. A requirement in period t2 can be satisfied by a shipment in the same period (a linear shipping cost is incurred) or by a shipment in period t1 < t2 (in addition to the linear shipping cost a linear inventory cost is incurred for every period in which the commodity is stored). A well known method for solving this problem is to transform it into an equivalent single period transportation problem with mT sources and nT sinks. Our approach treats the model as a transshipment problem consisting of T, m source — n sink transportation problems linked together by inventory variables. Storage requirements are proportional to T2 for the single period equivalent transportation algorithm, proportional to T, for our algorithm without decomposition, and independent of T for our algorithm with decomposition. This storage saving feature enables much larger problems to be solved than were previously possible. Futhermore, we can easily incorporate upper bounds on inventories. This is not possible in the single period transportation equivalent. 相似文献
This paper develops a forward algorithm and planning horizon procedures for an important machine replacement model where it is assumed that the technological environment is improving over time and that the machine-in-use can be replaced by any of the several different kinds of machines available at that time. The set of replacement alternatives may include (i) new machines with different types of technologies such as labor- and capital- intensive, (ii) used machines, (iii) repairs and/or improvements which affect the performance characteristics of the existing machine, and so forth. The forward dynamic programming algorithm in the paper can be used to solve a finite horizon problem. The planning horizon results give a procedure to identify the forecast horizon T such that the optimal replacement decision for the first machine based on the forecast of machine technology until period T remains optimal for any problem with horizon longer than T and, for that matter, for the infinite horizon problem. A flow chart and a numerical example have been included to illustrate the algorithm. 相似文献
In this article an algorithm for computing upper and lower ? approximations of a (implicitly or explicitly) given convex function h defined on an interval of length T is developed. The approximations can be obtained under weak assumptions on h (in particular, no differentiability), and the error decreases quadratically with the number of iterations. To reach an absolute accuracy of ? the number of iterations is bounded by
This article deals with the M/G/1 queue with server vacations in which the return of the server to service depends on the number of customers present in the system. The main goal is optimization, which is done under the average cost criterion in the multiple- and single-vacation models as well as for the “total cost for one busy cycle” criterion in the multiple-vacation case. Expressions that characterize the optimal number of customers, below which the server should not start a new service period, are exhibited for the various cases. It is found that under the average cost criterion, the expression may be universal in the sense that it may hold for a general class of problems including such that arise in production planning and inventory theory (for the particular cost structure discussed). 相似文献
In this article an interactive method is developed to identify and rank a most preferred subset, T, of alternatives assuming that the decision maker has an implicit quasiconcave nondecreasing utility function. The method requires the decision maker to compare pairs of selected alternatives. Based on the responses of the decision maker, convex cones are constructed to eliminate alternatives that are proved to be inferior to alternatives in set T. The method aims at keeping the number of pairwise comparisons small. Computational experience with the method indicates that the required number of pairwise comparisons to form set T is usually small. However, the number of pairwise comparisons needed to confirm that this set is best may be large. 相似文献
A large population of independent identical units having finite mean lifetime T is observed. From the history A(y) of cumulative arrivals and the history B(y) of cumulative removals in the interval 0 ≦ y ≦ τ one must predict at time τ the desired T . Two lifetime predictors X(τ) and Y(τ) and related simple predictors obtained from A(y) and B(y) are shown to converge to T with a rate of convergence dependent on the structure of the failure rate function of the units. This dependence is studied theoretically and numerically. 相似文献