Recurrence relations between moments of order statistics

A general result for obtaining recurrence relations between single moments of order statistics is obtained and has been used to establish the recurrence relations between moments of some doubly truncated distributions. The examples considered are Weibull, exponential, Pareto, power function, Cauchy, and logistic. Recurrence relations are also obtained for nontruncated gamma and beta distributions.     

The effect of stochastic time delays on the reliability of isolated impulse systems

This article concerns the effect of stochastic time delays in the operation of components upon system reliability for isolated impulse systems, for which component delays have hitherto been treated as deterministic. These are systems, such as automatic protective devices, which remain idle for most of their lives but which are required to respond with the utmost speed to input signals arising at arbitrary isolated time instants. System failure can arise from components failing to operate, or from being too slow to operate so that the systems operation is too slow to meet requirements. During operation components are usually subjected to greater stresses than during idling, so that it is assumed that components are subjected to increased failure tendencies during the time it takes them to perform their functions. The effect of stochastic time delays on the evaluation of systems reliability is considered, and a hierarchy of complexity associated with the physical nature of the delays in series and redundant configurations is exposed. Some simple exponential illustrations are presented.     

A nonlinear approach to the multiorigin,multidestination fleet deployment problem

The problem of minimal-cost operation of a fleet of ships carrying a specific amount of bulk cargo from several origin ports to several destination ports during a specified time interval is examined. The fuel oil cost, a major component of the total operating cost, is realistically modeled as a nonlinear function of the vessels' operating speeds. Introduction of both full load and ballast speeds as independent variables results in a nonlinear optimization problem in which the vessels' allocation to the available routes and the optimal speed selection problem are coupled. Within the framework of our model, each vessel of the fleet may load at any origin, unload at a destination and return to the same origin. The solution method developed utilizes specific features of the above fleet deployment model, and may reduce substantially the dimensionality of the problem. Under certain conditions, decoupling of the speed selection from the vessel allocation problem can be achieved, and linear programming can be used to obtain an optimal solution. In the general case, a projected Lagrangian method appears to be more appropriate for the problem under consideration.     

Some experiences using MIL-STD-105 in the united states air force

The historical and, to some extent, the current role of attribute inspection sampling in the United States Air Force is described. Some insight into consideration culminating in revisions made to the original MIL-STD-105 sampling plans is provided. These revisions were motivated from a practitioner's perspective rather than that of a statistical expert. Some significant administrative applications within the Air Force are described, and a practical method, based on the total amount of inspection, is given for distinguishing between sampling plans that have a fixed risk level (i.e., common value on the OC curves).     

On the bivariate negative binomial distribution of mitchell and paulson

The bivariate negative binomial distribution of Mitchell and Paulson [17] for the case b = c = 0 is shown to be equivalent to the accident proneness model of Edwards and Gurland [4] and Subrahmaniam [19,20]. The diagonal series expansion of its joint probability function is then derived. Two other formulations of this distribution are also considered: (i) as a mixture model, which showed how it arises as the discrete analogue to the Wicksell-Kibble bivariate gamma distribution, and (ii) as a consequence of the linear birth-and-death process with immigration.     

A reliability model with states of partial operation

This article generalizes the classical dichotomic reliability model to include states of partial operation. The generalized model can be considered as a special case of a general jump process. Both continuous and discrete state spaces are included. The relationship to cumulative damage shock models is discussed. Properties of the model are investigated and these are illustrated via examples. The equivalence of three forms of component independence is proved, but this equivalence does not generalize to the property of zero covariance. Alternative forms of series and parallel connections and the effect of component replacement are discussed.     

The validity of assumptions underlying current uses of Lanchester attrition rates

This study examines critically the various assumptions, results, and concepts that exist to date in the literature and scientific community concerning the relationships among the Lanchester, stochastic Lanchester, and the general renewal models of combat. Many of the prevailing understandings are shown to be erroneous.     

Forecast horizons for the discounted dynamic lot-size problem allowing speculative motive

This article considers the dynamic lot-size problem under discounting, allowing speculative motive for holding inventory. A variable rolling-horizon procedure is presented, which, under certain regularity conditions, is guaranteed to generate an infinite-horizon optimal-production plan. We also discuss a fixed rolling-horizon procedure which provides a production plan that achieves an infinite-horizon cost within a user-specified tolerance ϵ of optimality. The fixed-horizon length T* needed in this procedure is given in terms of a closed-form formula that is independent of specific forecasted demands. We also present computational results for problems with a range of cost parameters and demand characteristics.     

Optimal inventory policies for substitutable commodities with stochastic demand

In this article we consider a stochastic model for two products which have a single-period inventory structure and which can be used as substitutes for each other should the need arise. Substitution will occur with probability one, but at perhaps a different revenue level. We prove that the expected profit function is concave, allowing us to find optimal stocking levels for the two products. We compare optimum inventory levels for the case of single substitution with that where there is no substitution. It is demonstrated for the case of single substitution that total optimum order quantities can actually increase or decrease with the substitution revenue.