On estimating survival for reliability models based on age-related stochastic comparisons

A new class of nonparametric reliability models is introduced and studied. A distribution is said to be better at age s than at age t (sBt) if the residual lifetime at age s is stochastically greater than or equal to the residual lifetime at age t. Applications to various forms of replacement policies, including the cannibalization of failed systems, are noted. For fixed s < t, the problem of estimating a survival curve assumed to belong to the sBt class is addressed using recursive methods. An sBt estimator is derived in closed form, and its uniform strong consistency at an optimal rate of convergence is demonstrated. A simulation study strongly supports the claim that the sBt estimator tends to outperform the empirical survivor function in small- and moderate-size samples. © 1993 John Wiley & Sons, Inc.     

Location of facilities with rectangular distances among point and area destinations

This article is concerned with the optimal location of any number (n) of facilities in relation to any number (m) of destinations on the Euclidean plane. The criterion to be satisfied is the minimization of total weighted distances where the distances are rectangular. The destinations may be either single points, lines or rectangular areas. A gradient reduction solution procedure is described which has the property that the direction of descent is determined by the geometrical properties of the problem.     

Models for multi-item continuous review inventory policies subject to constraints

Models are formulated for determining continuous review (Q, r) policies for a multiitem inventory subject to constraints. The objective function is the minimization of total time-weighted shortages. The constraints apply to inventory investment and reorder workload. The formulations are thus independent of the normal ordering, holding, and shortage costs. Two models are presented, each representing a convex programming problem. Lagrangian techniques are employed with the first, simplified model in which only the reorder points are optimized. In the second model both the reorder points and the reorder quantities are optimized utilizing penalty function methods. An example problem is solved for each model. The final section deals with the implementation of these models in very large inventory systems.     

An optimum t-test for the scale parameter of an extreme-value distribution

A Student's t-test proposed by Ogawa is considered for the hypothesis Ho: σ=σo against the alternative hypothesis H₁: σ ≠ σo, where σ is the scale parameter of the Extremevalue distribution of smallest values with known location parameter μ. The test is based on a few sample quantiles chosen from a large sample so as to give asymptotically maximum power to the test when the number of sample quantiles is fixed. A table which facilitates the computation of the test statistic is given. Several schemes for determining the ranks of the sample quantiles by the optimal spacings are compared and the effect of the bias of the estimate of σ on the test is investigated through a Monte Carlo study.     

An experimental comparison of solution algorithms for the single-machine tardiness problem

A basic problem in scheduling involves the sequencing of a set of independent tasks at a single facility with the objective of minimizing mean tardiness. Although the problem is relatively simple, the determination of an optimal sequence remains a challenging combinatorial problem. A number of algorithms have been developed for finding solutions, and this paper reports a comparative evaluation of these procedures. Computer programs for five separate algorithms were written and all were run on a data base designed to highlight computational differences. Optimizing algorithms developed by Emmons and by Srinivasan appeared to be particularly efficient in the comparative study.     

Computerized scheduling of seagoing tankers

Computerized Scheduling of Seagoing Tankers The tanker scheduling problem considered in this paper is that of the Defense Fuel Supply Center (DFSC) and the Military Sealift Command (MSC) in the worldwide distribution of bulk petroleum products. Routes and cargoes which meet delivery schedule dates for a multiplicity of product requirements at minimum cost are to be determined for a fleet of tankers. A general mathematical programming model is presented, and then a mixed integer model is developed which attempts to reflect the true scheduling task of DFSC and MSC as closely as possible. The problem is kept to within a workable size by the systematic construction of a set of tanker routes which does not contain many possible routes that can be judged unacceptable from practical considerations alone.     

Pseudo-monotonic interval programming

A pseudo-monotonic interval program is a problem of maximizing f(x) subject to x ε X = {x ε Rⁿ | a < Ax < b, a, b ε R^m} where f is a pseudomonotonic function on X, the set defined by the linear interval constraints. In this paper, an algorithm to solve the above program is proposed. The algorithm is based on solving a finite number of linear interval programs whose solutions techniques are well known. These optimal solutions then yield an optimal solution of the proposed pseudo-monotonic interval program.     

Refined prediction for linear regression models

Adequate prediction of a response variable using a multiple linear regression model is shown in this article to be related to the presence of multicollinearities among the predictor variables. If strong multicollinearities are present in the data, this information can be used to determine when prediction is likely to be accurate. A region of prediction, R, is proposed as a guide for prediction purposes. This region is related to a prediction interval when the matrix of predictor variables is of full column rank, but it can also be used when the sample is undersized. The Gorman-Toman ten-variable data is used to illustrate the effectiveness of the region R.     

M/M/1 queues with interdependent arrival and service processes

We study via simulation an M/M/1 queueing system with the assumption that a customer's service time and the interarrival interval separating his arrival from that of his predecessor are correlated random variables having a bivariate exponential distribution. We show that positive correlation reduces the mean and variance of the total waiting time and that negative correlation has the opposite effect. By using spectral analysis and a nonparametric test applied to the sample power spectra associated with certain simulated waiting times we show the effect to be statistically significant.