bluuebunny/crossref_metadata_2025 huggingface dataset:
A Lanchester‐type aggregated‐force model of conventional ground combat
Authors: Taylor James G.
Published: May 2007

This article develops a Lanchester‐type model of large‐scale conventional ground combat between two opposing forces in a “sector”. It is shown that nonlinear Helmbold‐type equations of warfare with operational losses may be used to represent the loss‐rate curves that have been used in many aggregated‐force models. These nonlinear differential equations are used to model the attrition of combat capability (as quantified by a so‐called firepower index) in conjunction with a rate‐of‐advance equation that relates motion of the contact zone (or FEBA) between the opposing forces to the force ratio and tactical decisions of the combatants. This simplified auxiliary model is then used to develop some important insights into the dynamics of FEBA movement used in large‐scale aggregated‐force models. Different types of behavior for FEBA movement over time are shown to correspond to different ranges of values for the initial force ratio, for example, an attack will “stall out” for a range of initial force ratios above a specific threshold value, but it will “break out” for force ratios above a second specific threshold value. Such FEBA‐movement predictions are essentially based on being able to forecast changes over time in the force ratio.
Approximate Bayesian intervals for the reliability of series systems from mixed subsystem test data
Authors: Lampkin Harold , Winterbottom Alan
Published: May 2007

The determination of exact Bayesian intervals for the reliability of a series system from subsystem test data gives rise to computational difficulties involving severe loss of computing precision as the number of subsystems in the system increases. The end points of Bayesian intervals are percentage points of the posterior distribution and these are shown to be well approximated by Cornish and Fisher expansions when the number of subsystems is small. As the number of subsystems in the system increases even greater accuracy is guaranteed by the asymptotic nature of the expansions. The system posterior distribution function is also shown to be well approximated by an Edgeworth expansion.
Characterizations of the exponential distribution by higher‐order gap
Authors: Ahsanullah M.
Published: May 2007

Suppose X1,X2, ⃛,Xn is a random sample of size n from a continuous distribution function F(x) and let X1,n, ≦ X2,n ≦ ⃛ ≦ Xn,n be the corresponding order statistics. We define the jth‐order gap gi,j as gi,j = Xi+j,n − Xi,n, 1 ≦ i < n, 1 ≦ j ≦ n − i. In this article characterizations of the exponential distribution are given by considering the distributional properties of gk,n‐k, 1 ≦ k ≦ n.
Decomposition algorithms for finding the shortest path between a source node and a sink node of a network
Authors: Tufekci Suleyman
Published: May 2007

Decomposition algorithms for finding a shortest path between a source node and a sink node of an arbitrary distance network are developed. Different decomposition algorithms are proposed for different network topologies. Since Shier's algorithm compares very favorably with other decomposition algorithms in all the network topologies, we compare our algorithms against Shier's algorithm. It is shown that the efficiency of the proposed algorithms compares very favorably with Shier's algorithm. For special types of networks the computational requirements of the proposed algorithm is a polynomial of O(n2).
Another inventory model with a mixture of backorders and lost sales
Authors: Park Kyung S.
Published: May 2007

This article presents another inventory model for situations in which, during the stockout period, a fraction b of the demand is backordered and the remaining fraction 1 − b is lost. By defining a time‐proportional backorder cost and a fixed penalty cost per unit lost, a unimodal objective function representing the average annual cost of operating the inventory system is obtained. The optimal operating policy variables are calculated directly.
Finite‐production‐rate inventory models with first‐and second‐shift setups
Authors: Chand Suresh , Sethi Suresh
Published: May 2007

This article considers the production planning problem of a shop which can produce in either one shift or two shifts. Setup cost is charged whenever there is an increase in the production rate from one period to the next. Efficient planning horizon procedures have been developed for this model. A numerical example has been included to illustrate the planning horizon results.
On preservation of classes of life distributions under reliability operations: Some complementary results
Authors: Bondesson Lennart
Published: May 2007

A counterexample of general character is constructed showing that the NWUE class is not preserved under mixing. Some general classes of life distributions are introduced and their behavior under mixing and convolution is studied. These classes have a theoretical character but coincide in many cases with well‐known classes. It is proved that the DMRL class is not preserved under convolution.
On prediction intervals for normal samples
Authors: Jayachandran Toke
Published: May 2007

It is shown that many of the normal theory prediction intervals for statistics of random samples are still valid when the samples are correlated and have a specified covariance structure.
A closed‐from approach for multi‐item inventory grouping
Authors: Aggarwal Vijay
Published: May 2007

The problem of optimally coordinating the replenishments of the many items in stock with one another is dealt with in this article. Specifically, it considers this coordination based on classifying the items into a few groups with common order cycles for all the items in a particular group. Assuming that the cumulative distribution by value of the inventory can be characterized by a Pareto function of the type f(n) = n/(an + b), (a, b > 0), it establishes that the optimal boundaries of the groups can be obtained as closed‐form expressions by solving a system of simultaneous equations. The composition of the successive groups thus obtained is found to equipartition the total cost and to follow geometric sequences in relation to the number of items, the value of items, and the lengths of the order cycles. Graphs have been proposed to aid the implementation of the grouping scheme. Simple iterative schemes are outlined within the framework of the Pareto function to handle other relevant costs.
A note on a prediction interval for a first‐order Gauss Markov process
Authors: Jayachandran Toke
Published: May 2007

Let Xt, t = 1,2, ⃛, be a stationary Gaussian Markov process with E(Xt) = μ and Cov(Xt, Xt+k) = σ2ρk. We derive a prediction interval for X2n+1 based on the preceding 2n observations X1,X2, ⃛,X2n.
Extrapolation of the mean lifetime of a large population from its preliminary survival history
Authors: Keilson J. , Sumita U.
Published: May 2007

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.
On estimating the scale parameter of the exponential distribution with a known linear relation between the location and the scale parameter
Authors: Joshi Suneeta , Sathe Y. S.
Published: May 2007

In this article we study the estimation of the average excess life θ in a two‐parameter exponential distribution with a known linear relationship between α (the minimum life) and θ of the form α = aθ, where a is known and positive. A comparison of the efficiencies of estimators which are linear combinations of the smallest sample value and the sample sum of deviations from the smallest sample value and the maximum likelihood estimators is made for various sample sizes and different values of a. It is shown that these estimators are dominated in the risk by the minimum‐risk scale equivariant estimator based on sufficient statistics. A class of Bayes estimators for inverted gamma priors is constructed and shown to include a minimum‐risk scale equivariant estimator in it. All the members of this class can be computed easily.
IFR results for repairable systems
Authors: Chaganty Narasinga R.
Published: May 2007

Consider a k‐out‐of‐n system with independent repairable components. Assume that the repair and failure distributions are exponential with parameters {μ1, ⃛,μn} and {λ1, ⃛,λn}, respectively. In this article we show that if λi – μi = Δ for all i then the life distribution of the system is increasing failure rate (IFR).
TTT transforms and age replacements with discounted costs
Authors: Bergman Bo , Klefsjö Bengt
Published: May 2007

The ordinary age replacement problem consists of finding an optimal age at which a unit, needed in a continuous production process, should be replaced in order to minimize the average long‐run cost per unit time. Bergman introduced a graphical procedure based on the total‐time‐on‐test (TTT) concept for the analysis of the age replacement problem. In this article, that idea is generalized to the situation of discounted costs. We also study a more general age replacement problem in which we have a form of imperfect repair.
A new approach for dealing with the startup problem in discrete event simulation
Authors: Kelton W. David , Law Averill M.
Published: May 2007

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.
A note on a difficulty inherent in estimating reliability from stress–strength relationships
Authors: Harris Bernard , Soms Andrew P.
Published: May 2007

This note calls attention to a difficulty which arises frequently in the application of stress‐strength methods in reliability theory. This difficulty has led to unanticipated catastrophic failures in a number of applications.
Minimax trees, paths, and cut sets
Authors: Corley H. W. , Golnabi H.
Published: May 2007

The notions of minimax paths, trees, and cut sets are defined for undirected graphs; and relationships between these entities are established. Simple solution procedures based on these relationships are presented.
Mean hazard rate and its application to the normal approximation of the weibull distribution
Authors: Makino Toji
Published: May 2007

It is important for applied statisticians to know if data that can be described by the Weibull distribution can also be described by the normal distribution. Some investigations have been published on this subject. In this article, we review the results in papers related to the above problem. Next, we define the mean hazard rate. We then investigate the properties of the mean hazard rate for the Weibull distribution and the normal distribution, respectively. Finally, we discuss the method of approximating the normal distribution by the Weibull distribution using the mean hazard rate.
Inference on a future reliability parameter with the weibull process model
Authors: Miller Grady
Published: May 2007

An inferential procedure is presented which provides confidence intervals for a future reliability parameter when reliability growth testing is only partially completed. Hypothesis tests based on this method are uniformly most powerful unbiased. These results are applicable if (1) the system failure rate can be modeled as the intensity function of a Weibull process and (2) efforts to improve reliability are assumed to continue at a steady rate throughout the intervening period of testing. The usefulness of this methodology is illustrated by evaluating the risk of not reaching some future reliability milestone. If such risk is unacceptably high, program management may have time to identify problem areas and take corrective action before testing has ended. As a consequence, a more reliable system may be developed without incurring overruns in the scheduling or cost of the development program.
Allocation policies and cost approximations for multilocation inventory systems
Authors: Federgruen Awi , Zipkin Paul
Published: May 2007

Consider a central depot that supplies several locations experiencing random demands. Periodically, the depot may place an order for exogenous supply. Orders arrive after a fixed leadtime, and are then allocated among the several locations. Each allocation reaches its destination after a further delay. We consider the special case where the penalty‐cost/holding‐cost ratio is constant over the locations. Several approaches are given to approximate the dynamic program describing the problem. Each approach provides both a near‐optimal order policy and an approximation of the optimal cost of the original problem. In addition, simple but effective allocation policies are discussed.
Coordinating order cycles under joint replenishments of multi‐item inventories
Authors: Aggarwal Vijay
Published: May 2007

A recent work obtained closed‐form expressions for the problem of optimal partitioning multi‐item inventories into a given number of groups, where each group has a common order cycle for all the items in the group, and a Pareto function characterizes the distributions by value of the inventory. The optimal order points so obtained for the groups may have no synchronization among themselves at all. This note extends the closed‐form analysis to the requirement that the order cycles be coordinated so that each cycle is an integral multiple of the shortest order cycle. The extent of suboptimality which thus follows is investigated. Several alternatives to achieve integrality have been considered and compared through an illustrative example within the framework of the Pareto function.
A load‐sharing model: The linear breakdown rule
Authors: Schechner Zvi
Published: May 2007

An n‐component parallel system is subjected to a known load program. As time passes, components fail in a random manner, which depends on their individual load histories. At any time, the surviving components share the total load according to some rule. The system's life distribution is studied under the linear breakdown rule and it is shown that if the load program is increasing, the system lifetime is IFR. Using the notion of Schur convexity, a stochastic comparison of different systems is obtained. It is also shown that the system failure time is asymptotically normally distributed as the number of components grows large. All these results hold under various load‐sharing rules; in fact, we show that the system lifetime distribution is invariant under different load‐sharing rules.
A generalization of the entropy model for brand purchase behavior
Authors: Kapur J. N. , Bector C. R. , Kumar Uma
Published: May 2007

Hemiter's entropy model for brand purchase behavior has been generalized for Renyi's measure of entropy which is a more general concept than Shannon's measure of entropy used by Herniter and which includes Shannon's measure as a limiting case. The generalized model considered here is more flexible than Herniter's model since it can give different marketing statistics for different products and it can give these statistics even when only some of the brands are considered.
The capital supply curve in capacity expansion models: Some economic and algorithmic aspects
Authors: Sen S. , Saraf S. K. , Soyster A. L. , Murphy F. H.
Published: May 2007

Capacity expansion models typically minimize the discounted cost of acquisition and operation over a given planning horizon. In this article we generalize this idea to one in which a capital supply curve replaces the usual discount rate. A capital supply curve is a means to model financial outlook, investment limits, and risk. We show that when such a curve is included in a capacity expansion model, it will, under certain conditions, provide a less capital intensive solution than one which incorporates a discount rate. In this article, we also provide an algorithm that solves capacity expansion models that incorporate a capital supply curve. The attractive feature of this algorithm is that it provides a means to utilize the “discount rate” models efficiently. Throughout, we give applications in power generation planning and computational experience for this application is also presented.
Limit laws in the best of 2n ‐ 1 bernoulli trials
Authors: Groeneveld Richard A. , Arnold Barry C.
Published: May 2007

A series of independent Bernoulli trials is considered in which either an outcome of type A or type B occurs at each trial. The series terminates when n outcomes of one type have occurred. Two observable random variables of interest are the total number of outcomes in the series and the number of outcomes of the “losing kind.” Two methods of approximation of the expectations of these random variables for large n are obtained and compared. The limiting distribution of the number of outcomes of the “losing kind” is considered when a beta distribution is assigned to p.
An analysis of constrained robust regression estimators
Authors: Askin Ronald G. , Montgomery Douglas C.
Published: May 2007

Multicollinearity and nonnormal errors are problems often encountered in the application of linear regression. Estimators are proposed for dealing with the simultaneous occurrence of both multicollinearity and nonnormality. These estimators are developed by combining biased estimation techniques with certain robust criteria. An iteratively reweighted least‐squares procedure is used to compute the estimates. The performance of the combined estimators is studied empirically through Monte Carlo experiments structured according to factorial designs. With respect to a mean‐squared‐error criterion, the combined estimators are superior to ordinary least‐squares, pure biased estimators, and pure robust estimators when multicollinearity and nonnormality are present. The loss in efficiency for the combined estimators relative to least squares is small when these problems do not occur. Some guidelines for the use of these combined estimators are given.
Reliability interpretations of some concepts from economics
Authors: Klefsjö Bengt
Published: May 2007

In a recent article, Chandra and Singpurwalla have pointed out the close relationship between the Lorenz curve, which is frequently used when illustrating income distributions in economics, and the total‐time‐on‐test transform (TTT transform), which has proved to be a very useful tool in reliability. They also presented some characterizations of aging properties by using the Lorenz curve. The purpose of this article is to point out some further results in the same area and to give reliability interpretations of some common measures of income inequality.
The two‐on‐one stochastic duel
Authors: Gafarian A. V. , Ancker C. J.
Published: May 2007

The one‐on‐one stochastic duel is extended to the general two‐on‐one duel for the first time. The state equations, win probabilities, mean value, and variance functions are derived. The case where one side has Erlang (2) firing times and the other is negative exponential is compared with the corresponding “Stochastic Lanchester” and Lanchester models to demonstrate their nonequivalence.
Minimizing the sum of absolute lateness in single‐machine and multimachine scheduling
Authors: Sundararaghavan P. S. , Ahmed Mesbah U.
Published: May 2007

Kanet addressed the problem of scheduling n jobs on one machine so as to minimize the sum of absolute lateness under a restrictive assumption on their common due date. This article extends the results to the problem of scheduling n jobs on m parallel identical processors in order to minimize the sum of absolute lateness. Also, a heuristic algorithm for a more general version with no restriction on the common due date, for the problem of n‐job single‐machine scheduling is presented and its performance is reported.
A note on a model for evasive vehicle movement along a fixed path
Authors: Turner Danny W. , Holmes Paul T.
Published: May 2007

A model for a vehicle moving evasively along a fixed path is defined in terms of a two‐ state semi‐Markov process. An important feature of this model is the continuous movement of the vehicle as a function of time. One potential application of this model is the development of a strategy for the deployment of long‐range missiles on long underground tracks.
Multiechelon repairable‐item provisioning in a time‐varying environment using the randomization technique
Authors: Gross Donald , Miller Douglas R.
Published: May 2007

Multiechelon repairable‐item provisioning systems are considered under a time‐varying environment. Such conditions could arise, for example, in a military context where a shift from peacetime operation to wartime operation takes place; or, in a civilian setting where a public transit system decides to increase its hours of operation or frequency of service. Exact Markovian models, incorporating a finite population of repairable components and limited repair capacity (nonample service), are treated, with transient solutions obtained using the randomization technique. The exact models are compared with the approximate Dyna‐METRIC model which assumes an infinite population of components and ample repair capacity.
Optimal arrangement of systems
Authors: Boland Philip J. , Proschan Frank
Published: May 2007

To location Li we are to allocate a “generator” and ni “machines” for i = 1, …,k, where n1 … n1 ≧ … ≧ nk. Although the generators and machines function independently of one another, a machine is operable only if it and the generator at its location are functioning. The problem we consider is that of finding the arrangement or allocation optimizing the number of operable machines. We show that if the objective is to maximize the expected number of operable machines at some future time, then it is best to allocate the best generator and the n1 best machines to location L1, the second‐best generator and the n2‐next‐best machines to location L2, etc. However, this arrangement is not always stochastically optimal. For the case of two generators we give a necessary and sufficient condition that this arrangement is stochastically best, and illustrate the result with several examples.
A simple Markov model for the analysis of multiple air combat
Authors: Feigin P. D. , Pinkas O. , Shinar J.
Published: May 2007

It is proposed to describe multiple air‐to‐air combat having a moderate number of participants with the aid of a stochastic process based on end‐game duels. A simple model describing the dominant features of air combat leads to a continuous time discrete‐state Markov process. Solution of the forward Kolmogorov equations enables one to investigate the influence of initial force levels and performance parameters on the outcome probabilities of the multiple engagement. As is illustrated, such results may be useful in the decision‐making process for aircraft and weapon system development planning. Some comparisons are made with Lanchester models as well as with a semi‐Markov model.
Scheduling spares with exponential lifetimes in a two‐component parallel system
Authors: Weiss Gideon
Published: May 2007

A set of n spare components whose life lengths are exponentially distributed with rates μ1, …,μnare available to keep a two‐component parallel system in operation. We derive the optimal order of replacement of failed components in order to maximize the system life length.
An efficient heuristic for the multi‐item newsboy problem with a single constraint
Authors: Nahmias Steven , Schmidt Charles P.
Published: May 2007

This article treats the problem of determining optimal and approximately optimal order quantities for a multiple‐item inventory system subject to a single constraint on space or budget. Although this problem can be solved by the usual method of Lagrange multipliers, we wish to consider a more efficient scheme that requires fewer computations. We provide calculations that compare and contrast four approximation techniques. In particular, we have discovered a method that yields a direct algebraic expression of the problem parameters for allocation and achieves an expected profit within 90% of the optimal in about 90% of the cases tested.
An acceptance life test for high‐reliability products
Authors: Angus John E. , Schafer Ray E. , Rutemiller Herbert C.
Published: May 2007

This article introduces a replacement life‐test procedure for the exponential failure rate: Failure‐free operation of a unit for at least tk consecutive time units is designated a “success”; the acceptance test is passed if and only if the first success is encountered before k unit failures have been recorded. Test plans are presented and the test is compared with the usual time‐truncated test and to the truncated sequential probability ratio test. It is shown that this new test has smaller expected test time than the time truncated test when the true failure rate is small relative to the null hypothesized failure rate. Consistency and unbiasedness are proved and methods for making inferences on failure rate are described.
A method for estimating the parameters of reliability models
Authors: Naik D. N.
Published: May 2007

The maximum likelihood estimates (MLE) of transition rates in a finite‐state continuous‐time Markov process with an absorbing state are obtained, when there are a number of independent realizations of the process. This process is explained as a model for deteriorating systems of reliability theory through example. The asymptotic properties of MLES as the observed number of realizations tend to infinity are studied. Extension of these results to semi‐Markov processes is discussed.
Approximations for departure processes and queues in series
Authors: Whitt Ward
Published: May 2007

Methods are developed for approximately characterizing the departure process from a single‐server queue and calculating approximate congestion measures for several single‐server queues in series. These methods are modifications of the previously described asymptotic method and stationary‐interval method for approximating a stochastic point process. The approximations are evaluated by comparing approximate congestion measures for queues in series with previous simulation results.
Cost analysis of warranty policies
Authors: Nguyen D. G. , Murthy D. N. P.
Published: May 2007

This article analyzes two general warranty policies involving an initial free replacement period, followed by a pro rata period. We examine the short‐run total costs and longrun average costs under these policies. Formulas for both consumer costs and manufacturer profits under warranty are derived. We also study the expected number of purchases over the product life cycle under both policies. Bounds for the expected total costs and expected number of purchases are obtained for the case where the failure distribution of the item is new better than used.
Stochastically minimizing the makespan in flow shops
Authors: Foley R. D. , Suresh S.
Published: May 2007

In this article, we are concerned with scheduling stochastic jobs in a flowshop with m machines and zero intermediate storage. We assume that there are n ‐ 2 identically distributed and 2 fast stochastic jobs. Roughly, the main result states that the makespan is stochastically minimized by placing one of the fast jobs first and the other last.
Estimation for a weibull accelerated life testing model
Authors: Glaser Ronald E.
Published: May 2007

It is sometimes reasonable to assume that the lifetime distribution of an item belongs to a certain parametric family, and that actual parameter values depend upon the testing environment of the item. In the two‐parameter Weibull family setting, suppose both the shape and scale parameters are expressible as functions of the testing environment. For various models of functional dependency on environment, maximum likelihood methods are used to estimate characteristics of interest at specified environmental levels. The methodology presented handles exact, censored, and grouped data. A detailed accelerated life testing analysis of stress‐rupture data for Kevlar/epoxy composites is given.
Finite Markov chain models skip‐free in one direction
Authors: Latouche G. , Jacobs P. A. , Gaver D. P.
Published: May 2007

Finite Markov processes are considered, with bidimensional state space, such that transitions from state (n, i) to state (m, j) are possible only if m ≤ n + 1. The analysis leads to efficient computational algorithms, to determine the stationary probability distribution, and moments of first passage times.
Sample sizes for β‐expectation tolerance limits which control both tails of the normal distribution
Authors: Chou Youn‐Min
Published: May 2007

Sample sizes for tolerance limits are given on a normal distribution. β‐Expectation tolerance intervals are defined and constructed to control the proportion in each tail of the normal distribution. We also require with a high probability that the proportion in each tail is close to its corresponding expected coverage. Under these conditions. we dctcrniine a minimum sample size and its accompanying tolerance limits. Graphs of minimum sample sizes for the tolerance limits are provided. The computation for minimum samplc sizes is based on the bivariate noncentral t distribution. Examples are given to illustrate the use of the graphs.
Testing goodness of fit to the increasing failure rate family with censored data
Authors: Santner Thomas , Tenga Robert
Published: May 2007

One important thrust in the reliability literature is the development of statistical procedures under various “restricted family” model assumptions such as the increasing failure rate (IFR) and decreasing failure rate (DFR) distributions. However, relatively little work has been done on the problem of testing fit to such families as a null hypothesis. Barlow and Campo proposed graphical methods for assessing goodness of fit to the IFR model in single‐sample problems. For the same problem with complete data, Tenga and Santner studied several analytic tests of the null hypothesis that the common underlying distribution is IFR versus the alternative that it is not IFR for complete data. This article considers the same problem for the case of four types of censored data: (i) Type I (time) censoring, (ii) Type I1 (order statistic) censoring, (iii) a hybrid of Type I and Type I1 censoring, and (iv) random censorship. The least favorable distributions of several intuitive test statistics are derived for each of the four types of censoring so that valid small‐sample‐size α tests can be constructed from them. Properties of these tests are investigated.
New ANSI versions of MIL‐STD‐414 and MIL‐STD‐105D
Authors: Schilling E. G.
Published: May 2007

When acceptance sampling plans are applied to measurement characteristics, a choice between application of a variables or an attributes sampling plan must be made. With the recent revision by the American Society for Quality Control for the American National Standards Institute of the ANSI/ASQC Z1.9 variables system and the ANSI/ASQC Z1.4 attributes system, the standards have now been matched so that it is possible to move between them. This article will discuss exploitation of the resulting synergistic relationship to achieve more rational and more effective acceptance sampling.
Some experiences using MIL‐STD‐105 in the united states air force
Authors: Cocca O. A.
Published: May 2007

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).
The effect of nonnormality on variables sampling plans
Authors: Montgomery Douglas C.
Published: May 2007

Acceptance sampling plans based on variables have been in use for many years. Recently, there has been a renewal of interest in these plans, because of the relative efficiencies that they offer with respect to attributes sampling regarding sample size. Furthermore, in situations where acceptable quality levels are very small, and a high level of protection is desired, variables sampling is often much more efficient than attributes sampling. An important disadvantage of variables sampling is that the distribution of the parameter being inspected must be known. Most standard variables sampling plans assume that the distribution of this parameter is normal. This article examines the effect of the normality assumption in variables sampling. Methods to detect departures from normality are reviewed.
Some recent findings in bayesian attribute single and double sampling
Authors: Case Kenneth E. , Chen Shao‐Shing
Published: May 2007

This article deals with several items, including theoretical and applied results. Specific topics include (1) a discrete, economically based, attributes acceptance sampling model and its adaptations, (2) relevant costs, (3) relevant prior distributions, (4) comparison of single‐ and double‐sampling results, and (5) reasons for marginal implementation success following excellent implementation efforts. The basic model used is one developed by Guthrie and Johns; adaptations include provisions for fixed costs as well as modifications to permit double sampling. Optimization is exact, rather than approximate. Costs incorporated into the model are for sampling inspection, lot acceptance, and lot rejection. For each of these three categories a fixed cost is included as well as two variable costs, one for each item and the other for each defective item. Discrete prior distributions for the number of defectives in a lot are used exclusively. These include the mixed binomial and Polya distributions. Single‐ and double‐sampling results are compared. Double sampling regularly performs at only slightly lower cost per lot than single sampling. Also, some cost and prior distribution sensitivity results are presented. Comments are provided regarding actual implementation experiences in industry. Practical deficiencies with the Bayesian approach are described, and a recommendation for future research is offered.
Risk preference, multiple attributes, and multiple criteria in bayesian acceptance sampling plans
Authors: Moskowitz Herbert
Published: May 2007

Although there has been considerable research directed toward developing Bayesian acceptance sampling plans, little consideration has been given to incorporating a decision‐maker's risk attitude or treating such problems in terms of multiple‐type defects and multiple criteria. We review our own work which is focused on the above issues. A model incorporating risk preference is shown to yield substantial differences in the characteristics of an optimal sampling plan relative to a typical Bayesian linear cost (risk neutral) model. Bayesian models and optimization schemes for a variety of multiple‐type defect plans are reviewed. A bicriterion acceptance model, employing average outgoing quality and average inspection cost is also formulated. Traditional versus interactive optimization procedures are compared empirically in terms of ease of use, satisfaction with solutions, and insight gained into the problem.
A minmax search for the critical level of a system: The asymmetric case
Authors: Abigadol Noomi , Ben‐Tal Aharon
Published: May 2007

We consider a system composed ofkcomponents, each of which is subject to failure if temperature is above a critical level. The failure of one component causes the failure of the system as a whole (a serially connected system). Ifziis the critical temperature of theith component thenz*= min{zi: i= 1,2,…,k} is thecritical level of the system. The components may be tested individually at different temperature levels, if the temperature is below the critical level the cost is $1, otherwise the test is destructive and the cost ism> 1 dollars. The purpose of this article is to construct, under a budgetary constraint, an efficient (in a minmax sense) testing procedure which will locate the critical level of the system with maximal accuracy.
Probability bounds on downtimes
Authors: Brockett Patrick L. , Hinich Melvin
Published: May 2007

In this article we consider obtaining probability distributions for total downtime incurred for n units when we have only partial moment information about the downtime distribution per individual failure. Extremal distributions based upon the Markov‐Krein Theorem for Chebychev systems of functions and maximum entropy of distributions are presented.
Tests of independence of continuous random variables which guard against special alternatives
Authors: Weiss Lionel
Published: May 2007

For the problem of testing the independence of a set of continuous random variables, where the test is to be based on n independent and identically distributed observations, tests are constructed that guard against all alternatives but are particularly effective against special alternatives of interest. The tests are based on the numbers of observations falling in the cells of a grid constructed using order statistics.
Easily computed approximations for (s,S) inventory system operating characteristics
Authors: Ehrhardt Richard
Published: May 2007

The operating characteristics of (s,S) inventory systems are often difficult to compute, making systems design and sensitivity analysis tedious and expensive undertakings. This article presents a methodology for simplified sensitivity analysis, and derives approximate expressions for operating characteristics of a simple (s,S) inventory system. The operating characteristics under consideration are the expected values of total cost per period, holding cost per period, replenishment cost per period, backlog cost per period, and backlog frequency. The approximations are obtained by using least‐squares regression to fit simple functions to the operating characteristics of a large number of inventory items with diverse parameter settings. Accuracy to within a few percent of actual values is typical for most approximations. Potential uses of the approximations are illustrated for several idealized design problems, including consolidating demand from several locations, and tradeoffs for increasing service or reducing replenishment delivery lead time.
Penalty calculations and branching rules in a LAV best subset procedure
Authors: Armstrong Ronald D. , Beck P. O.
Published: May 2007

Least absolute value (LAV) regression has become a widely accepted alternative to least squares regression. This has come about as the result of advancements in statistical theory and computational procedures to obtain LAV estimates. Computer codes are currently available to solve a wide range of LAV problems including the best subset regression. The purpose of this article is to study the use of penalty calculations and other branching rules in developing the solution tree for the best subset LAV regression.
Weapon acquisition with target uncertainty
Authors: Nickel Ronald H. , Mangel Marc
Published: May 2007

This article is concerned with choosing a mix of weapons, subject to constraints, when the targets to be attacked are known imprecisely. It is shown that the correct method for optimizing the mix of weapons involves a pair of nested optimization problems (two‐stage optimization). Two methods for optimizing the expected utility of a mix are discussed. The first involves a simultaneous attack model, in which it is implicitly assumed that all weapons are used at once. The second involves a sequential attack model, in which targets appear in random order and are attacked one at a time. Particular attention is given to the question of the appropriate mix of general‐purpose and special‐purpose weapons.
Asymptotic distribution of some multivariate “success run” renewal processes, applied to a 2‐i.i.d. unit repairable system
Authors: Wiens Doug
Published: May 2007

If the probability of “failure” in a multivariate renewal process of the “success run” type is very small, then if certain conditions are imposed on the components of the renewals, the joint distribution of their total durations is approximately exponential with all mass along one line. This result is applied to a 2‐i.i.d. unit repairable system of the “1 out of 2:G, Cold Standby” type.
A (Q,R) inventory model with lost sales and erlang‐distributed lead times
Authors: Buchanan David J. , Love Robert F.
Published: May 2007

The exact expression is derived for the average stationary cost of a (Q,R) inventory system with lost sales, unit Poisson demands, Erlang‐distributed lead times, fixed order cost, fixed cost per unit lost sale, linear holding cost per unit time, and a maximum of one order outstanding. Explicit expressions for the state probabilities and a fast method of calculating them are obtained for the case of Q greater than R. Exponential lead times are analyzed as a special case. A simple cyclic coordinate search procedure is used to locate the minimum cost policy. Examples of the effect of lead time variability on costs are given.
Economic design of X¯ control charts for two manufacturing process models
Authors: Panagos Margaret R. , Heikes Russell G. , Montgomery Douglas C.
Published: May 2007

Control charts are widely used for process surveillance. The design of a control chart refers to the choice of sample size, the width of the control limits, and the interval between samples. Economic designs have been widely investigated and shown to be an effective method of determining control chart parameters. This article describes two different manufacturing process models to which the X¯ control chart is applied: The first model assumes that the process continues in operation while searches for the assignable cause are made, and the second assumes that the process must be shut down during the search. Economic models of the control chart for these two manufacturing process models are developed, and the sensitivity of the control chart parameters to the choice of model is explored. It is shown that the choice of the proper manufacturing process model is critical because selection of an inappropriate process model may result in significant economic penalties.
The performance of cannibalization policies in a maintenance system with spares, repair, and resource constraints
Authors: Fisher Warren W. , Brennan J. J.
Published: May 2007

This article presents the results of comparing the performance of several cannibalization policies using a simulation model of a maintenance system with spares, repair, and resource constraints. Although the presence of cannibalization has been incorporated into a number of maintenance system models reported in the literature, the questions of whether cannibalization should be done and what factors affect canibalization have received little attention. Policies tested include both no cannibalization and unlimited cannibalization as well as other based on the number of maintenance personnel available, the short‐term machine failure rate at the time of cannibalization, and the relationship between the mean cannibalization and repair rates. The best policies found are those that allow cannibalization only when it can be done quickly relative to repair or when it can be done without delaying part repair actions. The policy of complete cannibalization (always cannibalize when it is possible) is found to perform poorly except when either average maintenance personnel utilization is very low or when mean cannibalization times are very short relative to mean repair times. The latter result casts doubts on the appropriateness of the assumption of complete cannibalization in many models in the literature.
Estimating normal tail probabilities
Authors: Rukhin Andrew L.
Published: May 2007

The estimation problem of normal tail probabilities is considered. The form of generalized Bayes estimators is derived and the asymptotic behavior of the mean square errors is studied. This study shows that the best unbiased estimator, a formula for which is given, is superior to the maximum likelihoood estimator or to a class of generalized Bayes procedures for large parametric values, but can be significantly improved for moderate values of the parameter.
A Lanchester‐type model of combat with stochastic rates
Authors: Karmeshu  , Jaiswal N. K.
Published: May 2007

The effects of environmental stochasticity in a Lanchester‐type model of combat are investigated. The methodology is based on a study of stochastic differential equations with random parameters characterized by dichotomous Markov processes. Exact expressions for the Laplace transforms of the time evolution of the first‐ and second‐order moments of the system are obtained. A special case when the fluctuations in the parameters occur with great rapidity in comparison with the natural time scale of the system is also analyzed. The stochastic stability in the mean‐square sense is discussed by using the Routh–Hurwitz criterion and it is found that the stochastic perturbations tend to destabilize the system.
Minimal forecast horizon procedures for dynamic lot size models
Authors: Chand Suresh , Morton Thomas E.
Published: May 2007

This article presents new results which should be useful in finding production decisions while solving the dynamic lot sizing problem of Wagner–Whitin on a rolling horizon basis. In a rolling horizon environment, managers obtain decisions for the first period (or the first few periods) by looking at the forecasts for several periods. This article develops procedures to find optimal decisions for any specified number of initial periods (called planning horizon in the article) by using the forecast data for the minimum possible number of future periods. Computational results comparing these procedures with the other procedures reported in the literature are very encouraging.
Tabular aids for fitting weibull moment estimates
Authors: Blischke W. R. , Scheuer E. M.
Published: May 2007

Moment estimators for the parameters of the Weibull distribution are considered in the context of analysis of field data. The data available are aggregated, with individual failure times not recorded. In this case, the complexity of the likelihood function argues against the use of maximum‐likelihood estimation, particularly for relatively large sets of data, and moment estimators are a reasonable alternative. In this article, we derive the asymptotic covariance matrix of the moment estimators, and provide listings for BASIC computer programs which generate tables useful for calculation of the estimates as well as for estimating the asymptotic covariance matrix using aggregated data.
Decentralized stockage policies in a multiechelon environment
Authors: Frazza Sally , Kaplan Alan J.
Published: May 2007

Characteristics of supply performance at the top echelon of an optimally managed multiechelon supply system are investigated; insights are developed which are useful in devising coordinated single‐echelon policies which can approximate the benefits derived from multiechelon management.