Statistical analysis of a conventional fuze timer

In this paper, a statistical analytic model for evaluation of the performance of a standard electric bomb fuze timer is presented. The model is based on what is called a selective design assembly, where one item, namely, a resistor, is used to time the circuit. In such an assembly, the remaining components are chosen a priori from predetermined distributions. Based on the analysis, a general numerical integration scheme is utilized for assessing performance of the timer. The results of a computer simulation are also given. In the last section of the paper, a theory for evaluation of the yield of two or more timers designed to operate in sequence is derived. To appraise such a scheme, a numerical quadrature routine is developed.     

Storage problems when demand is “all or nothing”

An inventory of physical goods or storage space (in a communications system buffer, for instance) often experiences “all or nothing” demand: if a demand of random size D can be immediately and entirely filled from stock it is satisfied, but otherwise it vanishes. Probabilistic properties of the resulting inventory level are discussed analytically, both for the single buffer and for multiple buffer problems. Numerical results are presented.     

Test selection for a mass screeening program

Periodic mass screening is the scheduled application of a test to all members of a population to provide early detection of a randomly occurring defect or disease. This paper considers periodic mass screening with particular reference to the imperfect capacity of the test to detect an existing defect and the associated problem of selecting the kind of test to use. Alternative kinds of tests differ with respect to their reliability characteristics and their cost per application. Two kinds of imperfect test reliability are considered. In the first case, the probability that the test will detect an existing defect is constant over all values of elapsed time since the incidence of the defect. In the second case, the test will detect the defect if, and only if, the lapsed time since incidence exceeds a critical threshold T which characterizes the test. The cost of delayed detection is an arbitrary increasing function (the “disutility function”) of the duration of the delay. Expressions for the long-run expected disutility per unit time are derived for the above two cases along with results concerning the best choice of type of test (where the decision rules make reference to characteristics of the disutility function).     

The dynamic transportation problem: A survey

The dynamic transportation problem is a transportation problem over time. That is, a problem of selecting at each instant of time t, the optimal flow of commodities from various sources to various sinks in a given network so as to minimize the total cost of transportation subject to some supply and demand constraints. While the earliest formulation of the problem dates back to 1958 as a problem of finding the maximal flow through a dynamic network in a given time, the problem has received wider attention only in the last ten years. During these years, the problem has been tackled by network techniques, linear programming, dynamic programming, combinational methods, nonlinear programming and finally, the optimal control theory. This paper is an up-to-date survey of the various analyses of the problem along with a critical discussion, comparison, and extensions of various formulations and techniques used. The survey concludes with a number of important suggestions for future work.     

Computing equilibria via nonconvex programming

The problem of determining a vector that places a system in a state of equilibrium is studied with the aid of mathematical programming. The approach derives from the logical equivalence between the general equilibrium problem and the complementarity problem, the latter being explicitly concerned with finding a point in the set S = {x: < x, g(x)> = 0, g(x) ≦ 0, x ≧ 0}. An associated nonconvex program, min{? < x, g(x) > : g(x) ≦ 0, x ≧ 0}, is proposed whose solution set coincides with S. When the excess demand function g(x) meets certain separability conditions, equilibrium solutions are obtained by using an established branch and bound algorithm. Because the best upper bound is known at the outset, an independent check for convergence can be made at each iteration of the algorithm, thereby greatly increasing its efficiency. A number of examples drawn from economic and network theory are presented in order to demonstrate the computational aspects of the approach. The results appear promising for a wide range of problem sizes and types, with solutions occurring in a relatively small number of iterations.     

The United States Coast Guard Computer-Assisted Search Planning system (CASP)

This paper provides an overview of the Computer-Assisted Search Planning (CASP) system developed for the United States Coast Guard. The CASP information processing methodology is based upon Monte Carlo simulation to obtain an initial probability distribution for target location and to update this distribution to account for drift due to currents and winds. A multiple scenario approach is employed to generate the initial probability distribution. Bayesian updating is used to reflect negative information obtained from unsuccessful search. The principal output of the CASP system is a sequence of probability “maps” which display the current target location probability distributions throughout the time period of interest. CASP also provides guidance for allocating search effort based upon optimal search theory.     

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.     

A heuristic procedure for allocating tasks in fault-tolerant distributed computer systems

One way of achieving the increased levels of system reliability and availability demanded by critical computer-based control systems is through the use of fault-tolerant distributed computer systems. This article addresses the problem of allocating a set of m tasks among a set of n processors in a manner that will satisfy various task assignment, system capacity, and task scheduling constraints while balancing the workload across processors. We discuss problem background, problem formulation, and a known heuristic procedure for the problem. A new solution-improving heuristic procedure is introduced, and computational experience with the heuristics is presented. With only a modest increase in the amount of computational effort, the new procedure is demonstrated to improve dramatically solution quality as well as obtain near-optimal solutions to the test problems.     

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.     

An optimum group maintenance policy

In this article we present an optimum maintenance policy for a group of machines subject to stochastic failures where the repair cost and production loss due to the breakdown of machines are minimized. A nomograph was developed for machines with exponential failure time distributions. The optimal schedule time for repair as well as the total repair cost per cycle can be obtained easily from the nomograph. Conditions for the existence of a unique solution for the optimum schedule and the bounds for the schedule are discussed.