Cost analysis of pro rata and free-replacement warranties

This article examines the short run total costs and long run average costs of products under warranty. Formulae for both consumer cost under warranty and producer profit are derived. The results in the case of the pro rata warranty correct a mistake appearing in Blischke and Scheuer [5]. We also show that expected average cost to both the producer and the consumer of a product under warranty depends on both the mean of the product lifetime distribution and on its failure rate.     

A good simple percentile estimator of the weibull shape parameter for use when all three parameters are unknown

In this paper we consider a simple three-order-statistic asymptotically unbiased estimator of the Weibull shape parameter c for the case in which all three parameters are unknown. Optimal quantiles that minimize the asymptotic variance of this estimator, c? are determined and shown to depend only on the true (unknown) shape parameter value c and in a rather insensitive way. Monte Carlo studies further verified that, in practice where the true shape parameter c is unknown, using always c? with the optimal quantities that correspond to c = 2.0 produces estimates, c?, remarkably close to the theoretical optimal. A second stage estimation procedure, namely recalculating c? based on the optimal quantiles corresponding to c?, was not worth the additional effort. Benchmark simulation comparisons were also made with the best percentile estimator of Zanakis [20] and with a new estimator of Wyckoff, Bain and Engelhardt [18], one that appears to be the best of proposed closed-form estimators but uses all sample observations. The proposed estimator, c?, should be of interest to practitioners having limited resources and to researchers as a starting point for more accurate iterative estimation procedures. Its form is independent of all three Weibull parameters and, for not too large sample sizes, it requires the first, last and only one other (early) ordered observation. Practical guidelines are provided for choosing the best anticipated estimator of shape for a three-parameter Weibull distribution under different circumstances.     

Nonlinear integer programming for various forms of constraints

A theoretical and computational investigation is made of the performance of a dynamic-programming-based algorithm for nonlinear integer problems with various types of constraints. We include linear constraints, aggregated linear constraints, separable nonlinear constraints and constraints involving maxima and minima. Separability of the objective function is assumed. The new feature of the algorithm is that two types of fathoming or pruning are used to reduce the size of tables and number of computations: fathoming by bounds and fathoming by infeasibility.     

The logarithmic poisson gamma distribution: A model for leadtime demand

This paper considers an inventory system in which demand occurrences arise according to a stationary Poisson process, demand sizes at each occurrence follow a logarithmic distribution, and leadtimes are random variables with the gamma distribution. Both the exact and approximate distribution for leadtime demand are derived and computations are performed which compare the approximation to the exact distribution. The results have application to both repairable and consumable item inventory systems.     

Sequencing independent jobs with a single resource

This paper examines problems of sequencing n jobs for processing by a single resource to minimize a function of job completion times, when the availability of the resource varies over time. A number of well-known results for single-machine problems which can be applied with little or no modification to the corresponding variable-resource problems are given. However, it is shown that the problem of minimizing the weighted sum of completion times provides an exception.     

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.     

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.     

A new approach for dealing with the startup problem in discrete event simulation

This article proposes a practical, data-based statistical procedure which can be used to reduce or remove bias owing to artificial startup conditions in simulations aimed at estimating steady-state means. We discuss results of experiments designed to choose good parameter values for this procedure, and present results of extensive testing of the procedure on a variety of stochastic models for which partial analytical results are available. The article closes with two illustrations of the application of the procedure to more complex statistical problems which are more representative of the kinds of purposes for which real-world steady-state simulation studies might be undertaken.