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The process of evaluating papers for journal publication is a measurement process, similar to the other measurement processes of qualitative material in the social sciences. A good qualitative measurement technique rarely has a reliability coefficient of more than about 0.50 i.e., a correlation of 0.50 of one measurement with another measurement by the same technique. The square root of the reliability of a measure is the upper limit of its validity. If it is assumed that journal editing as a measurement process is as good as good qualitative measurement can possibly be, given this experience in the social sciences it would estimate the validity of a judgment of article quality to be about 0.70. The two major journals in Sociology accept about 16 per cent of the papers submitted to them. If the quality of papers judged is approximately normal, then one can say that papers judged to be 1 standard deviation or more above the mean of papers submitted will be accepted. Assuming a correlation of 0.70 between the true quality of the paper and the judged quality, one can estimate the proportion of acceptances of papers of different quality.

This paper generalizes, by the use of compound distributions, a result of HAIGHT (1966) on counts that are delayed but not lost. An application of Markov chains indicates a simple method of numerical evaluation of the distributions involved. Finally a continuous time analogue is studied. [ABSTRACT FROM AUTHOR]

In a paper in this Journal, Watson (1961) has discussed the use of group screening methods for detecting effective factors. The methods are analogous to those suggested by Doff man (1943) for the medical problem of detecting a rare defect among members of a large population by using pooled blood samples. One step in Watson's derivation of the probability that an effective factor is declared significant is invalid. The purpose of this note is to derive the correct expression for this probability and show how the correction affects the subsequent theory. None of Watson's qualitative statements about the efficiency of group screening methods nor his numerical example are seriously affected. [ABSTRACT FROM AUTHOR]

This article presents a list of books related to operations research. Some of the books enlisted are--"Progress in Operations Research, Volume III: Relationship Between Operations Research and the Computer," by Julius S. Aronofsky; "Technological Forecasting and Long-Range Planning," by Robert U. Ayres; "Technology: Processes of Assessment and Choice," by Harvey Brooks; "Modern Production Management," 3rd. ed., by Elwood S. Buffa; "Systems Analysis Techniques," by Ralph Deutsch; "An Introduction to Mathematical Probability," by Martin Eisen; and "Operations Management: Selected Read," by Gene K. Groff and John F. Muth.

Many methods have been developed to determine the proper reorder points and order quantities in an inventory system. These methods are based on a wide range of inventory models—from elementary deterministic models to sophisticated probabilistic models with time-varying parameters. This paper deals with two topics related to these calculations which were encountered during the design of an inventory control system for a firm in the heavy goods industry. A mathematical model is developed to describe the average annual variable cost of maintaining the inventory. Based on this model, the paper evaluates the savings obtained by using a simultaneous solution for reorder point and order quantity rather than a simpler separate solution. Then, this model is extended to describe the effect of batch withdrawals as a renewal process. The paper presents an adjustment which can be applied to the original reorder points based on unit withdrawals. Both of these topics are described in the context of a practical application. [ABSTRACT FROM AUTHOR]

Comments on a study by James M. Goodwin and Erich W. Giese that derived an expression for the probability that a given number of spares for each element of a complex system will be sufficient to ensure continued operation without requiring a spare when none is available. Error in their analysis; Consideration of an item obeying Poisson failure statistics with constant failure rate and repair time

Enumerates the practical operating considerations to be associated with the problems in order to achieve a real world applications in the use of probability estimates for management decision making. Emphasis that the probability estimates should be used by management in an independent manner; Case example to illustrate the utilization of the probability estimates by management; Comments on the remark by Healy.

The article discusses the effects of accounting variations on decision making and the paper "An Experimental Design for Study of Effects of Accounting Variations in Decision Making" by R.E. Jensen. The statistical methodology and design used by Jensen in his research of the effects of alternative accounting reporting techniques in the selection of portfolios and their security evaluation is examined as is the data collection. The limitation of whether or not there was adequate control over the research environment and the probability level of the statistical tests is not known in Jensen's paper because he does not mention these issues.

Recent theoretical and empirical work in portfolio theory has exhibited a natural evolution from the two-moment EV model popularized by Markowitz through the higher moment models to selection on the basis of the entire probability function. This latter approach, referred to as the Stochastic Dominance (SD) approach to portfolio selection, has been shown to be theoretically superior to all of the "moment methods" and has been the focus of an increasing volume of empirical work. In comparison with the EV model, however, the SD approach has one potentially significant deficiency from the standpoint of empirical testing. With a given set of portfolios to evaluate, the computer processor time required for the determination of the EV efficient set is quite short. One can calculate and sort means and variances on several hundred portfolios in a matter of seconds. In contrast, the processor time required for the determination of the SD efficient set for the same number of portfolios can be prohibitive. The purpose of this paper is to examine the factors responsible for the relatively time-consuming nature of empirical tests of SD efficiency and to present the major results of our search for efficient algorithms for conducting SD tests. Section I briefly examines the time-consuming nature of the tests for SD efficiency. Section II presents and evaluates; our most efficient algorithms for obtaining true SD efficiency results. Section lit examines an approach that yields approximate SD efficiency results with further reductions in required processor time. [ABSTRACT FROM AUTHOR]

This paper is the first in a series of articles introducing a new conceptual and methodological framework for the use of experts in decision situations. Presented is the first theory of expert resolution wholly consistent with the Bayesian or subjectivist view of probability. The approach taken rests philosophically on the foundations of decision analysis. The results form practical tools for solving expert resolution problems. The present paper develops a structure in which the expert resolution problem may be logically formulated and conceptually solved. A framework is developed which enables a decision maker to encode his state of reformation concerning an expert. Application of the tools of Bayesian inference provides a mechanism by which a decision maker can incorporate an expert's opinion into his own. The more complicated case in which a decision maker is confronted with the diverse judgments of more than one expert is also addressed in detail. Additionally, the problem of determining the economic worth of one or a panel of experts is presented. [ABSTRACT FROM AUTHOR]

This paper considers a preemptive priority and a nonpreemptive priority queuing model in the steady state. Each model assumes two priority levels, a single-service channel, no queue-length limit, and negative exponential interarrival-time and service-time distributions. The paper develops a set of computationally efficient recursion formulas that allow exact calculation of the state probabilities. In the nonpreemptive-priority case, this is the first time that a complete solution for the equilibrium-state probabilities has been obtained. [ABSTRACT FROM AUTHOR]

Assignment problems arise whenever elements of a finite set have to be paired with elements of another finite set in such a way as to maximize a certain function of the pairing. In this paper three different formulations of such a problem are given. They are analyzed and a method for obtaining a low-cost solution is developed. [ABSTRACT FROM AUTHOR]

This paper deals with a nonstationary discrete-time Markov process whose transition probabilities vary periodically in time. Each transition results in a reward that varies within the same cycle as the transition matrix. For infinite processes a policy-iteration algorithm is developed that effectively determines an optimal policy maximizing the total discounted reward. The paper represents an extension of R. A. HOWARD's policy-iteration technique for stationary Markov processes. A numerical example is given in which the developed iteration algorithm is demonstrated. [ABSTRACT FROM AUTHOR]

Joint ordering strategies are of extreme importance in many inventory control situations. This paper considers a situation involving two items having identical characteristics including unit Poisson demand. The joint ordering rule is to order both items up to a level Q each time the level of either of them drops to zero. Expressions for the probability mass function of the remnant stock, the expected value of the remnant stock, the expected time between orders, and the long-run cost per unit time are shown. The joint ordering strategy is compared with the situation where the two items are treated independently. When the cost of placing an order for two items is equal to that for a single item, it turns out that it is never preferable to use the independent strategy. [ABSTRACT FROM AUTHOR]

In this paper Kendall's technique of the embedded Markov chain[5] is applied to a queuing system `with general independent input and a wide class of service-time distributions The matrix of transition probabilities is found to be formally identical `with that discussed in our earlier study,[9] which will be taken as read in the present paper Using the results of reference 9 we can write down the equilibrium distribution of waiting-times for customers in the more general system in terms of the roots of a transcendental equation An example is considered that arose in Bailey's study of hospital systems[1] [ABSTRACT FROM AUTHOR]

Many manufacturing firms produce component parts both for assembly into new products and to meet orders for spare parts. An inventory model for this situation would involve two types of demands: probabilistic demand as spares and deterministic (or scheduled) withdrawals as components for assembly. Relevant costs would include a setup cost for replenishment orders, inventory carrying costs, and backorder costs. An analytical model approximating these characteristics is formulated. An optimal dynamic program for the periodic review case is briefly discussed; this policy is extremely costly to implement, however. Two feasible operating policies are considered in the paper: a continuous review (Q, r)-type policy and a simple periodic review scheduling heuristic. The paper concludes with sample economic comparisons of the cost of the (Q, r)-type policy and the heuristic policy for a set of numerical examples. [ABSTRACT FROM AUTHOR]

This paper explores several important notions relevant to modern utility theory. Restricting the discussion to the consideration of bivariate utility functions, the paper defines and examines the interrelationships between (1) independence in the utility sense, (2) trade-off or indifference curves, and (3) transformation curves (as defined herein). Following the form in which a set of basic axioms of utility are stated, independence is defined in terms of indifference between 50-50 gambles, and it is shown that, if the condition of the definition holds, then φ (x, y), the bivariate utility function, can be written as a function of x plus a function of y. The concepts of trade-off curve (indifference curve) and transformation curve are also defined on the basis of the indifference relation but are not concerned with gambles. After exploring relationships among the three notions it is shown how the utility curves for the two variables under independence can be constructed on the basis of two trade-off curves. [ABSTRACT FROM AUTHOR]

A new conceptual and analytical vehicle for problems of temporal planning under uncertainty, involving determination of optimal (sequential) stochastic decision rules is defined and illustrated by means of a typical industrial example. The paper presents a method of attack which splits the problem into two non-linear (or linear) programming parts, (i) determining optimal probability distributions, (ii) approximating the optimal distributions as closely as possible by decision rules of prescribed form. [ABSTRACT FROM AUTHOR]

Considers several salvo-firing situations in military operations where the cumulative damage contribution is unimportant. Characteristics of a salvo kill probability under a two-dimensional situation; Features of the target properties considered under the study.

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This paper deals with systems (such as electronic devices and corporations) that are designed to accomplish multiple goals and whose internal structures are characterized by networks of interacting component parts. Each component of such a system is typically associated with a probability of failure, while each system goal is associated with a reward value. Failure of any network component may ultimately result in the inability to achieve one or more goals and force the forfeiture of the associated rewards. A basic problem in component-system design is to determine how the expectation of total reward may be maximized through the cost-limited acquisition of redundant (backup) components. This paper provides a formal statement of this redundancy-optimization problem and argues that the problem may not be solved easily by standard linear or integer programming techniques. It introduces an algorithm to solve this problem, proves its convergence, and presents computational results taken from a battery of test problems and an algorithm-efficiency study based on these tests. [ABSTRACT FROM AUTHOR]

This note gives a rigorous proof of the queuing formula L=λW, using as hypotheses only that the limiting averages, λ and W, exist and are finite. The proof is related to one given in a previous paper by the author that used a discounted analogue and Tauberian theorems. The proof in the present paper, however, is direct and avoids the use of transforms. Some comments are offered on the relation between the proof and the heuristic arguments for L= λW commonly encountered in the literature. [ABSTRACT FROM AUTHOR]

This paper discusses optimal stopping rules for fixed-sample acceptance tests where the observations with time delays are obtained sequentially. It studies two cases, one with a known prior distribution and the other one without a prior distribution, discusses Bayes-optimal and minimax stopping rules, and considers a stopping rule using the maximum likelihood estimate of θ, the probability of a single success. An example is given assuming that the prior distribution is a beta distribution. It is shown that the Bayes-optimal stopping rule thus obtained approaches the stopping rule using the maximum likelihood estimate when the beta parameters, α and β, approach zero. [ABSTRACT FROM AUTHOR]

This paper presents methods for computing point and interval estimates of descriptors of simulated queuing systems. The methods, which rely on the renewal process representation of certain processes, extend the results of CRANE and IGLEHART, and the author. In particular, the paper shows that computation of three sample quantities suffices to generate point and interval estimates for twelve system descriptors. [ABSTRACT FROM AUTHOR]

This paper presents sufficient conditions for a multiattribute utility function to be either multiplicative or additive. The number of requisite assumptions to imply the main result is equal to the number of attributes. Because the assumptions involve only trade-offs between two attributes at a time or lotteries over one attribute, it is reasonable to expect that decision makers can ascertain whether these assumptions are appropriate for their specific problems. Procedures are given for verifying the assumptions and assessing the resulting utility functions. The paper concludes with a sketch of a recent application of the results to a six-attribute problem relating to the development of Mexico City's airport facilities. [ABSTRACT FROM AUTHOR]

The article comment on the criticisms by researchers J. Cohen C. M. Dayton and Donald L. Meyer on a survey paper by the author on the power of statistical tests. The major point of all the criticisms was on the supposed "after-the-fact" or post hoc usage of power. Two other issues dealing with the conditional nature of power and the reporting schemes are also mentioned. The author finds it difficult to be upset with the major points proposed by Meyer outside of misinterpretations. The author has no objections to the viewpoint presented in the paper. To some people the classical approach makes equally good sense, but the author chooses not to be pigeonholed as a "classicist" or a "Bayesian." The author believes a reasonable researcher can and should entertain all philosophical viewpoints, and select that one or several with which he is most comfortable. Once the Bayesian viewpoint is adopted, then the power issue is trivial. However, the Bayesian viewpoint has not been adopted and utilized for published research very often in the behavioral sciences.

The incentive-type fee function (which has supplanted the Cost-PlusFixed-Fee arrangements of a decade ago) provides an excellent medium for achieving "fee flexibility" or, more exactly, for increasing the fee outcome on government contracts. The originators of incentive contracting stumbled unwittingly on a method for negotiating acceptable fee arrangements under conditions of uncertainty, and the primary purpose of this paper is to establish apodictically that incentive contracts (whether single or multiple) can and do provide the contractor with a method for securing a fee arrangement preferable to that obtainable through a CPFF or a FP (Fixed-Price) contract. Furthermore, this characteristic of incentive contracts can be demonstrated through the use of elementary decision theory. The incentive fee structure provides the contractor with a long-needed procedure for optimizing the expected utility of the fee outcome, and an appreciation of this property should be of value to both contractors and procurement officials with the authority for designing new contract fee arrangements. The paper does not investigate procedures for the optimal negotiation of contracts; rather, it identifies a feature of the incentive contract which appears to be the primary basis for its use and popularity. Our thesis is applicable to both single and multiple incentive contracts. For reasons of simplicity, however, the analysis has been largely confined to the former type of fee arrangement. [ABSTRACT FROM AUTHOR]

This paper deals with the availability and the reliability of a two-unit system with a warm standby and subject to a single repair facility. It assumes the failure times of the units to be exponentially distributed with parameters λ and λ1, respectively, initially, a unit is switched on and the other one is kept as a warm standby. The system breaks down if a unit fails while the other is still under repair. This paper characterizes the system by the probabilities of its being in the up or the down state, sets up integral equations for these probabilities by identifying suitable regenerative stochastic processes, and employs the Laplace-transform technique to solve these equations. It obtains the mean down-time of the system during (0, t) and the mean time to system failure explicitly. [ABSTRACT FROM AUTHOR]

This paper develops a Bayesian analysis of the scale and shape parameters in the Weibull distribution and the corresponding reliability function with respect to the usual life-testing procedures. For the scale parameter θ, Bayesian estimates of θ and reliability are obtained for the uniform, exponential, and inverted gamma prior probability densities. BHATTACHARYA'S results [J. Am. Stat. Assn. 62, 48–62(1967)] for the one-parameter exponential life-testing distribution are reduced to a special case of these rewards. The paper develops a fully Bayesian analysis of both the scale .and shape parameters θ and ξ by independent prior distributions; since in the latter case, analytical tractability is not possible, Bayesian estimates are obtained through a conjunction of a Monte Carlo simulation and numerical-integration techniques. In both cases, the paper carries out a computer simulation and makes a comparison between the Bayesian and the corresponding minimum-variance unbiased, or maximum likelihood, estimates. As expected, the Bayesian estimates are superior. [ABSTRACT FROM AUTHOR]

This paper presents a solution procedure for discrete stochastic programs with recourse (linear programs under uncertainty). It views the m stochastic elements of the requirements vector as an m-dimensional space in which each combination of the discrete values is a lattice point. For a given second-stage basis, certain of the lattice points are feasible. A procedure is presented to delete infeasible points from the space. Thus, the aggregate probability associated with points feasible for this basis can be enumerated, and used to weight the vector of dual variables defined by the basis. Finally, the paper presents a systematic procedure for changing optimal bases so that a feasible and optimal basis is found for every lattice point. [ABSTRACT FROM AUTHOR]

This paper considers the duel between two contestants with unlimited ammunition supplies, each one firing at the other. It assumes that the damage resulting from a round of fire is measurable and has a probability distribution. The cumulative damage function depends both on time and on number of rounds fired. For given rates of fire, damage functions, and other parameters, the paper calculates the probabilities that a given side will win. [ABSTRACT FROM AUTHOR]

This paper derives an expression for the expected completion time of a repair project, such as the servicing of end products, when the servicing is composed of a sequence of repair activities on parts of the end product. These parts are subject to repair with a specified probability and, at first, it is assumed that the completion time of each activity is constant. Subsequently, this assumption is relaxed so that an arbitrary probability distribution can be specified for the activity completion times. The concluding parts of the paper show how to compute the expected end-product service time for a particular class of activity-time probability distributions. [ABSTRACT FROM AUTHOR]

This paper introduces a generalization of the frequently discussed problem of finding the optimum redundancy that maximizes the reliability of a network of components. Past work has restricted consideration to arrangements of redundant components called series-parallel networks. This paper allows a much broader class of arrangements called series-parallelseries networks. It is important to consider such arrangements for realistic situations in which components have more than one failure mode, or the combination of parallel paths introduces a failure probability. A dynamic programming algorithm is used to solve the more general problem for the case in which there are no constraints on the optimum solution. The algorithm is extended to handle multiple constraints using dominance and a variety of elimination methods to reduce the storage required in a compurer implementation of the algorithm. Problems with as many as 15 serial components and three constraints have been solved with reasonable digital computer computation times. [ABSTRACT FROM AUTHOR]

This paper finds sufficient conditions for the ergodicity and recurrence of irreducible and aperiodic Markov chains. They extend some of the ones commonly used. The paper also indicates their use in discussing a certain class of queuing problem with state dependent service times. [ABSTRACT FROM AUTHOR]

Consider an inventory item for which the procurement (or production setup) lead time is nonzero. One of the commonly used methods of determining the reorder point of such an item is to specify the probability of a stockout or a desired service level (fraction of demand that is to be instantaneously satisfied) and then select the reorder level that will provide such service. However, such an approach has assumed that the probability distribution of demand during the lead time is exactly known. In many inventory situations this assumption is not justified, particularly in the case of a slow moving item with limited available sales history. For such a situation this paper explores the use of a Bayesian approach to selecting a reorder point. [ABSTRACT FROM AUTHOR]

In this paper an expression is derived for the probability that a given number of spares for each element of a complex system will be sufficient to ensure continued operation without requiring a spare (for replacement of a failed part) when none is available. Each part of the system being considered is subject to failure according to Poisson statistics, and may be subject to repair in some fixed time. The probability (that the number of spares will be sufficient) for nonreparable parts is obtained as a special case of the result for reparable parts. The probabilities are obtained for a single part by the construction of an artificial model, which differs from the case being considered, allowing the deviation to shrink to zero. Samples of the results obtained are included for several values of the various parameters. The results are generalized to include a variety of parts, both identical and different, and to include the effects of passive redundancy. [ABSTRACT FROM AUTHOR]

This paper discusses the application of personaliastic decision theory in a typical setting of decision making under uncertainty. The criterion for choice of strategy is maximization of expected utility. In this setting it is often difficult to obtain very precise measurements of the decision maker's probabilities on the states of nature. We therefore pay particular attention to several `imprecise' measures of probability, including sets of inequalities and hounds, and see how this information may be used in trying to determine an ordering or partial ordering of the expected utilities of the alternative strategies. At the end of the paper we note how, in practice, one may try to obtain the measures of probability presented herein. [ABSTRACT FROM AUTHOR]

This paper presents derivations of formulas for the probability of killing a point target and for the expected coverage of a population of targets when the bias of the weapon system is randomly distributed in accordance with a prescribed density function The paper considers six cases in which the bias distributions are the gamma (2,3), beta (2,3), Maxwell-Boltzman (2) and Rayleigh (3), where the numbers in parentheses indicate the dimensionality of the associated kill and coverage problem The concept of a random bias is important in situations where a unimodal distribution is perturbed by forced scattering (random or deterministic) into a density whose mode lies along a locus of points (2 dimensional) or on a surface (3 dimensional) The notion is also important when a sampling (or an a priori analysis) of the weapon system indicates that the bias is randomly distributed rather than fixed or when the concept of target evacuation is involved, in determining weapon effectiveness The analysis in this paper is one which employs integration and special functions in the course of denying kill and coverage formulas Conceptually, the discussion is based upon extremely rudimentary principles of probability theory and makes no contributions to this latter field. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of a simple but interesting random collision process The problem revolves the effectiveness of pellets against target objects Appropriate probability density functions are derived from the physical conditions and are used to discuss various properties of the random collision process and the effectiveness of the pellets No new statistical techmques are provided in the paper and it is perhaps noteworthy that such simple, well-known methods can be employed to investigate so many aspects of an interesting problem. [ABSTRACT FROM AUTHOR]

The Program Evaluation and Review Technique (PERT) has been developed and implemented as a technique for planning and evaluating the progress of research and development programs Probability theory is used in PERT to calculate a measure of the uncertainty in meeting scheduled dates These computed probabilities can then be used by managers to aid then judgment in evaluating the validity of schedules for accomplishing program objectives This paper investigates the effect of subdividing activities in PERT flow diagrams on computed probabilities for meeting scheduled dates It is shown that the mechanics of activity subdivision can increase or decrease the computed probabilities, depending upon whether the scheduled date for an event is later or earlier in time than the expected date Management personnel who are using PERT probabilities to aid their judgment in evaluating schedules should be aware of the potential biases inherent in the computation of probabilities. [ABSTRACT FROM AUTHOR]