The impact of war has shown the need for cumulative records by its sudden demands for the training and placement of teen-age persons. Actually, need for such records has been there all the time. During war-times the need for information about large numbers of persons is immediate and the best condition to satisfy such a need is the cumulative record. This is because of the nature of the cumulative record, which by definition and by the best practices is a record of all the facts about pupils...

Topics: DTIC Archive, DEPARTMENT OF EDUCATION WASHINGTON DC, *EDUCATION, *HANDBOOKS, PREDICTIONS, STUDENTS,...

This Memorandum presents tables giving the values of the individual terms of the negative binomial distribution for 130 pairs of parameter values in Part 1. Part 2, giving the cumulated terms of the same distributions, is in a form directly usable for solving problems which require the determination of probabilities of the occurrence of not more than x events. The negative binomial distributions is described and illustrative examples are given which use this distribution as a tool in the study...

Topics: DTIC Archive, RAND CORP SANTA MONICA CA, *LOGISTICS, *TABLES(DATA), *STATISTICAL DISTRIBUTIONS,...

The report describes a method for scheduling preventive maintenance to minimize expected average hourly maintenance cost based on a criterion of periodically observing deterioration in one or more equipment performance characteristics. The mathematical procedure requires expressing the deterioration phenomenon in the form of a simple Markov process. The implication of this method is that a forecast of equipment failure is based only on existing performance level and is independent of any...

Topics: DTIC Archive, ARINC RESEARCH CORP WASHINGTON DC, *MAINTENANCE, *SCHEDULING, *TIRES, MATHEMATICAL...

The discussion concerns the rules for deciding which inventory levels are optimal or preferred at the various stockage points in a system. The focus is dictated by the key role played by stockage decisions in a material system. Stockage policy has a pervasive, if implicit, control over the systems operating costs: It determines the level of investment and the frequency of shortages, of requisitions, of new procurements, and of repair actions. The survey is broken down into three parts: (1) a...

Topics: DTIC Archive, RAND CORP SANTA MONICA CA, *MANAGEMENT ENGINEERING, *SPARE PARTS, REPLACEMENT THEORY,...

Mathematical expressions are derived for the operational availability of a system having a finite number of standby spare components. The availability expressions are then used in a decision criterion for the selection of items to be stocked to support units on extended missions with no resupply capability. Various algorithms for determining how best to allocate constrained resources so as to maximize system operational availability are examined. Comparisons with the current Navy shipboard...

Topics: DTIC Archive, Choi, Boo Woong, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *INVENTORY CONTROL,...

A periodic review inventory system is viewed as a servomechanism in which the input is demand and the output is the inventory level. Under the assumptions that lead time is fixed and demand is random, an order rule is determined which minimized the long run average inventory. The order rule allows for any method of forecasting future demands and completely determines the operating doctrine for each such method. Graphical portrayal is used to illustrate the essential features of the model in a...

Topics: DTIC Archive, DECISION STUDIES GROUP PALO ALTO CA, *INVENTORY CONTROL, *REPLACEMENT THEORY,...

A previous paper described a method for determining a preventive maintenance schedule based upon a part replacement prior to in-service failure. The model used related equipment operating time between maintenance actions under such a schedule to the expected average hourly cost of maintenance. The present monograph focuses attention on the savings to be realized from scheduling preventive maintenance and from improvements in reliability.

Topics: DTIC Archive, Welker, E L, ARINC RESEARCH CORP WASHINGTON DC, *COST EFFECTIVENESS, *RELIABILITY,...

A number of tests and estimates for mean life and other parameters derived under the exponential distribution assumption are studied under the alternative condition that the distribution has an increasing (decreasing) failure rate. The tests and estimates considered are, for the most part, based on censored and truncated samples. It is shown that the usual acceptance sampling procedures based on mean life generally favor the producer (consumer) in the IFR (DFR) case. However, acceptance...

Topics: DTIC Archive, BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA MATHEMATICS RESEARCH LAB, *RELIABILITY,...

The paper presents some of the problems discovered in the use of peacetime and/or wartime costs in limited war cost-effectiveness studies. Two basic costing methods currently in practice and how they relate to the question of peacetime and wartime costs are discussed. An additional costing method for limited war systems analysis is suggested.

Topics: DTIC Archive, Surmeier, John J, RAND CORP SANTA MONICA CA, *COST EFFECTIVENESS, *LIMITED WARFARE,...

The author previously examined the Weibull process with unknown scale parameter as a model for Bayesian decision making. Here the analysis is extended by treating both the shape and scale parameters as unknown. It is not possible to find a family of continuous joint prior distributions on the two parameters that is closed under sampling, hence a family of prior distributions is used that places continuous distributions on the scale parameter and discrete distributions on the shape parameter....

Topics: DTIC Archive, Soland, Richard M, RESEARCH ANALYSIS CORP MCLEAN VA, *RELIABILITY, UNCERTAINTY,...

Countable state, finite action Markovian decision processes are studied under the average cost criterion. The problem is studied by using the known results for the discounted-cost problem. Sufficient conditions are given for the existence of an optimal rule which is of the stationary deterministic type. This rule is shown to be, in some sense, a limit point of the optimal discounted-cost rules. Sufficient conditions are also given for the optimal discounted-cost rules to be epsilon-optimal with...

Topics: DTIC Archive, Ross, Sheldon M, STANFORD UNIV CA DEPT OF STATISTICS, *DECISION THEORY, *PROBABILITY,...

The Weibull distribution is useful in analyzing the probabilistic lifetimes of many electrical components and complex systems. It is attractive for Bayesian decision-making because its right-hand cumulative function is of an exponential form which allows all life-test data to be easily incorporated into the decision-making process. Unfortunately no natural conjugate prior distribution exists if both the shape and scale parameters of the Weibull distribution are assumed to be unknown. If the...

Topics: DTIC Archive, Soland, Richard M, RESEARCH ANALYSIS CORP MCLEAN VA, *DECISION THEORY, *SAMPLING,...

Extreme value distribution laws are obtained for the lifetimes of multi-component systems with replaceable components, under various assumptions on the asymptotic relationship between number of components in the system and number of spare components. Results are given for limiting distribution laws of order statistics from nonhomogeneous samples and samples of random size, and applied to the superposition of renewal processes. An attempt is made to put extreme value theory into a general...

Topics: DTIC Archive, Harris, Robert, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *REPLACEMENT...

The overall evaluation objective was to determine whether adequate management controls existed over the turn-in, transfer and donation of excess and surplus personal property. The specific objective was to assess the safeguards in place to ensure that excess and surplus personal property was appropriately disposed of and received by authorized recipients. We did not evaluate the reutilization and sale of excess and surplus property.

Topics: DTIC Archive, INSPECTOR GENERAL DEPT OF DEFENSE ARLINGTON VA, *MANAGEMENT PLANNING AND CONTROL,...

Research efforts during this period concentrated on the following topics: (a) Deformation of Solids - work on the topic has progressed to the point where the physical mechanisms of creep can be brought in. (b) Excursions of Markov Processes - Two papers by Salminer are completed in this area. (c) Stochastic Differential Geometry - Starting with a Brownian motion on a Riemannian manifold, the exit time from a ball is considered. The distribution of the exit time is used to investigate the...

Topics: DTIC Archive, Cinlar,E, NORTHWESTERN UNIV EVANSTON IL, *Markov processes, Control, Control theory,...

A generalization of Freund's bivariate exponential model is discussed. Probabilistic properties of this model with minimal distribution assumptions are derived including the joint survival function and Laplace-Stieltjes transform. (Author)

Topics: DTIC Archive, Tosch,Thomas J, CLEMSON UNIV S C DEPT OF MATHEMATICAL SCIENCES, *FAILURE, *BIVARIATE...

The Principal Investigator and the Co-investigator attended four conferences giving papers at two of them. The Principal Investigator organized a Conference on Stochastic Failure Models, Replacement and Maintenance Policies, Accelerated Life Testing. He continued his research on shock models, wear processes, replacement and maintenance policies; revised the paper Life Distribution Properties of Devices Subject to a Levy Wear Process, wrote the paper Pure Jump Damage Processes. He also wrote...

Topics: DTIC Archive, Abdel-Hameed,M, NORTH CAROLINA UNIV AT CHARLOTTE DEPT OF MATHEMATICS, *Replacement...

This document describes two problem areas concerning systems subject to periodic checkout, which were investigated with the aid of a computer. The first part (Parameter Estimation) summarizes the results of a Monte Carlo analysis to determine the feasibility and accuracy of measuring system failure rates, checkout error probabilities, and repair effectiveness from the numbers of systems passing and failing in three consecutive checkouts. The second part (Availability Analysis) describes, mainly...

Topics: DTIC Archive, Howard, W J, TRW SPACE TECHNOLOGY LABS REDONDO BEACH CA, *MAINTENANCE, *AVAILABILITY,...

A new class of non-decreasing stochastic processes is characterized. These processes satisfy a generalization of the notion of an increasing failure rate. From physical considerations, these processes seem suitable for describing the process of cumulative wear or damage. The main interest with the model is an investigation of the first time until the process exceeds a random barrier. For this class of processes, it is shown that the first passage time random variable across a random barrier has...

Topics: DTIC Archive, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *FAILURE(MECHANICS), *STOCHASTIC...

A model of the real and monetary costs involved in supplying spare parts from current production is presented. The model leads to a cost function for each part individually depending on its production characteristics and its demand probability function, and on certain policy variables. By choosing appropriate values for the policy variables, the cost function for each part can be minimized independently of the others.

Topics: DTIC Archive, RAND CORP SANTA MONICA CA, *INDUSTRIAL PRODUCTION, INVENTORY, MANAGEMENT PLANNING AND...

This paper is concerned with (i) the maximization of net return Summation, j = 1 to j = n, of pi sub j (y sub j, t sub j) and, (ii) the maximization of average net return Summation, j = 1 to j = n, of pi sub j (y sub j, t)/t of a deterministic multicommodity system subject to linear restrictions on the inventory levels y sub j and the review periods t sub j (j = 1, ..., n). The first problem is a symmetric quadratic program. For the second problem, an algorithm is given for finding the optimal...

Topics: DTIC Archive, Hueda, Enrique, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *INVENTORY...

The paper is a study of the effects of using mean absolute deviation (MAD) to estimate variability in setting reorder levels for the inventory of a stock item. The method presently employed by NavSup in setting such reorder levels involves exponentially smoothed estimates of the mean and variance of the demand process. Any error involved in setting reorder levels results in a change in the underlying risk which in turn can be translated into costs. Such errors for the method of estimation...

Topics: DTIC Archive, Zehna, Peter W, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *INVENTORY CONTROL, *NAVAL...

We develop and estimate optimal age replacement policies for devices whose age is measured in multiple time scales. For example, the age of a jet engine can be measured in chronological time, the number of flight hours, and the number of landings. Under a single-scale age replacement policy, a device is replaced at age or upon failure, whichever occurs first. We show that a natural generalization to k 2 scales is to replace non-failed devices when their usage path crosses the boundary of a...

Topics: DTIC Archive, Frickenstein, Scott G, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *POLICIES, *TIME,...

A new class of reliability point-process models for dependent components is introduced. The dependence is expressed through a regression, following a form suggested for survival data analysis involving the current life-length of the components. After formulating the current-life process as a Markov process with stationary transitions and stating some general results on asymptotic behavior, the authors describe the stationary distributions in some bivariate examples. Finally, they discuss...

Topics: DTIC Archive, Slud,Eric, MARYLAND UNIV COLLEGE PARK DEPT OF MATHEMATICS, *MATHEMATICAL MODELS,...

The objective of this study was to assess the capability of main transmissions, intermediate gearboxes, tail rotor gearboxes, main rotor hubs, and swashplates on the UH-1 and AH-1 to operate with no scheduled overhaul periods. Overhaul and accident records, inspection procedures, and the functional capability of the caution and warning subsystem and its condition- monitoring devices were examined, and failure mode, effects and criticality analyses were performed to determine if any part or...

Topics: DTIC Archive, Knudsen, G E, BELL HELICOPTER TEXTRON INC FORT WORTH TX, *DRIVES, *HELICOPTERS,...

Consider a unit in continuous operation. When this unit fails, it is immediately replaced. In addition, opportunities arise according to a renewal process when we can either replace this unit at a reduced cost or do nothing. The problem is formulated as a Markov decision process. If the unit has increasing failure rate, the replacement policy that minimizes the expected total discounted cost or the average cost of maintenance is characterized by a single parameter i* : If an opportunity exists,...

Topics: DTIC Archive, Sethi, Davinder P., CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *REPLACEMENT...

During this period the principal investigator was partially supported and performed research in the areas of shock models and wear processes, maintenance and replacement policies for devices subject to shocks or wear, and positive dependent of life distributions. The research activities resulted in six publications with the following titles: 'Optimal Replacement Policies for Devices Subject to a Gamma Wear Process,' 'Optimality of the One Step Look-Ahead Stopping Times,' 'When to Stop a War,'...

Topics: DTIC Archive, Abdel-Hameed,M, NORTH CAROLINA UNIV AT CHARLOTTE DEPT OF MATHEMATICS, *MATHEMATICAL...

In a load sharing system, the failure of one or more components increases the load on other nonfailed components, thereby increasing their chances of failure, and the failure of the system. Examples of load sharing systems include many mechanical, thermal and electrical structures. System reliability is measured by the probability that the system is capable of performing its prescribed task or surviving for a prescribed duration. Traditional reliability models often postulate that component...

Topics: DTIC Archive, Taylor,Howard M, CORNELL UNIV ITHACA NY, *MATHEMATICAL MODELS, *COMPOSITE MATERIALS,...

A method for analyzing time between failure data is developed. The method uses total time on test plots for a nonhomogeneous Poisson process failure model. Engine failure data is used to illustrate the method. A graphical method for determining optimum replacement intervals is presented. (Author)

Topics: DTIC Archive, Barlow,Richard E, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *REPLACEMENT...

Regenerative stopping problems are stopping problems which recommence from the initial state upon stopping. An algorithm is presented which solves a semi-Markov regenerative stopping problem with a finite number of continue actions by solving a sequence of stopping problems. New results for the optimal stopping problem are obtained as well as for the regenerative stopping problem. Two models in the literature are used as detailed examples of the algorithm. (Author)

Topics: DTIC Archive, Miller,Bruce L, CALIFORNIA UNIV LOS ANGELES DEPT OF SYSTEM SCIENCE, *CONTROL THEORY,...

This report discuss the problem of dynamic optimal investigation of a two-state (in control, out of control) system. The true state can only be inferred from reported costs and the time since the last correction. It is demonstrated that when the parameters satisfy certain conditions, such problems can be efficiently solved as regenerative stopping problems. Some general results for regenerative stopping problems are also obtained. In the last section the problem is generalized to n two-state...

Topics: DTIC Archive, Buckman ,A Gregory, CALIFORNIA UNIV LOS ANGELES DEPT OF SYSTEM SCIENCE, *CONTROL...

Availability quantifies the propensity of a system to be functionally operative upon demand. It increases if operating times between failures (up times) are long, and decreases if, following failure or anticipatory removal, logistics delays and repair (down times) are protracted. This chapter summarizes the general availability concept and discusses the limitation of operational availability suggesting that mission availability is often more useful and appropriate.

Topics: DTIC Archive, Gaver, Donald P, NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF OPERATIONS RESEARCH,...

The authors formulate the optimum replacement problem as a concave integer programming problem, and develop an algorithm to solve the formulated problem.

Topics: DTIC Archive, Babayev, D A, ARMY FOREIGN SCIENCE AND TECHNOLOGY CENTER CHARLOTTESVILLE VA, *LINEAR...

The paper describes a method for determining optimal repair and replacement policies for aircraft, with specific reference to the F-4. The objective of the analysis is to choose the set of policies from all possible alternatives over a finite planning horizon which minimizes the cost of operations. A dynamic program is presented which seeks an optimal path through a series of decision periods, when each period begins with the choice of keeping an aircraft, reworking it before further operation,...

Topics: DTIC Archive, Schwartz, Arnold Neil, CENTER FOR NAVAL ANALYSES ALEXANDRIA VA, *JET FIGHTERS,...

Topics: DTIC Archive, Blischke,Wallace R, UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF DECISION...

This paper addresses inventory system with non-unit order sizes and variable lead times under a continuous review (S-s) policy. Under the assumption of at most one order outstanding, some quite general results are obtained. An example with a specific form of demand and lead time distribution is then analyzed and computation formulas developed. Finally, a heuristic approach is proposed for case when there is likelihood of more than one order outstanding.

Topics: DTIC Archive, Urbach,Richard, DRC INVENTORY RESEARCH OFFICE PHILADELPHIA PA, *INVENTORY ANALYSIS,...

Under an age replacement policy we replace at failure or at the end of a specified time interval, whichever occurs first. This makes sense if a failure replacement costs more than a planned replacement and the failure rate is strictly increasing. We assume that the failure distribution is a Weibull distribution with known shape parameter (greater than one) and unknown scale parameter. Moreover, we assume that a natural conjugate prior distribution with specified parameters is at hand which we...

Topics: DTIC Archive, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *AGING(MATERIALS), *REPLACEMENT...

A Monte-Carlo computer model for evaluating different replacement- parts policies in a project context is developed. The input to the model consists of a description of the schedule of operations in PERT network form, a list of parts, and a list of 'possible demands'. Each part is characterized by the quantity stocked and the time required to repair a defective part, (this time can alternatively be interpreted as a reorder time for the part.) Each possible demand is characterized by where in...

Topics: DTIC Archive, RAND CORP SANTA MONICA CA, *MANAGEMENT ENGINEERING, *REPLACEMENT THEORY, COMPUTERS,...

The following model is considered: A machine is inspected at the beginning of discrete time periods and its operating state (condition) is determined. After each inspection a decision upon whether or not to replace the machine at the end of the period must be made. It is shown that under certain conditions on the costs and the transition probabilities the optimal policy has a simple form. A generalization to the case where one is allowed to stock reserve machines is also given.

Topics: DTIC Archive, Ross, Sheldon M, STANFORD UNIV CA DEPT OF STATISTICS, *MANAGEMENT PLANNING AND...

A two-component failure system in which failure of the secondary component affects the residual life of the primary component is discussed. From two classes of policies and two criteria, optimal policies for replacing the secondary component are derived. (Author)

Topics: DTIC Archive, Tosch, Thomas J, CLEMSON UNIV SC DEPT OF MATHEMATICAL SCIENCES, *FAILURE, *BIVARIATE...

In this note two characterizations of the exponential distribution are discussed, based on a generalization of the lack of memory property. These results were motivated by the notion of 'relevation of distributions' introduced by Krakowski (1973). (Author)

Topics: DTIC Archive, Grosswald,E, NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS, *EXPONENTIAL...

Let Z sub i (t) = (Z sub i1 (t), Z sub i2 (t),...,Z sub im(t)) where Z sub ij (t) = number of cells of type j at t starting at t = 0 with one new cell of type i, with 1 < or = i, j < or = m. Assuming this to be an m-type critical age-dependent branching process, for k = (k sub 1,...,k sub m) an m- vector of non-negative integers, not all of which are zero, it is shown that as t approaches infinity, P(Z sub i (t) = k) approx. = c/t squared for some c > 0. Similarly, let N...

Topics: DTIC Archive, Weiner, Howard J., STANFORD UNIV CA DEPT OF STATISTICS, *REPLACEMENT THEORY,...

This paper is concerned with the following question. A system has one vital component for which there are n spares. Whenever the vital component fails, the system fails. The authors like to schedule the replacement of the vital component with the spares so as to prolong the life of the system as much as possible. This problem can be generalized to where there are several components in the system and the scheduling of replacements refers to each of the components. They deal mainly with the first...

Topics: DTIC Archive, Derman,Cyrus, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *Replacement...

A summary of the Weibull distribution and three representative sampling procedures to determine point and confidence interval estimates of the parameters that occur in the functional form of the Weibull distribution are presented. Following this, a model, assuming the Weibull distribution, is proposed which could have possible applications in analyzing Polaris Missile Systems Trouble Failure Reports to determine point estimates of the reliability of the Polaris Missile components.

Topics: DTIC Archive, Hager, Charles F, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *DISTRIBUTION FUNCTIONS,...

Aerospace engine management is an exceedingly complicated problem with important consequences. Analytical management techniques may have potential application in a future, integrated engine management system. Fundamental to any such system is information about engine lives and the number of engine replacements required to meet flying hour program requirements. In this report, the engine management problem is described in the context of a production system producing flying hours. This...

Topics: DTIC Archive, George, Laurence L, TECHNOLOGY INC DAYTON OH, *JET AIRCRAFT, *JET ENGINES,...

A life distribution F (a distribution function (d.f.) such that F(x) = 0 for x 0), with survival function the superior limit of F is approximately 1-F is new better than used (NBU). The dual notion of a new worse than used (NWU) life d.f. is defined by reversing the inequality. The boundary members of the NBU and NWU classes, obtained by insisting an equality, are the exponential d.f.'s. The NBU class of life distributions has proved to be very useful in performing analyses of lifelengths....

Topics: DTIC Archive, Chen,Yuan-Yan, FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS, *DISTRIBUTION...

A system must operate for t units of time. A certain component is essential for its operation and must be replaced, when it fails, with a new component. The class of spare components is grouped into n categories with components of the ith category costing a positive amount (C sub i) and functioning for an exponential length of time with rate (lambda sub i). The main problem of interest is, for a given t, to assign the initial component and subsequent replacements from among the n categories of...

Topics: DTIC Archive, Derman, C, Lieberman, G J, Ross, S M, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH...

At the beginning of each period a system is in a certain state. Depending on the state, choice of an action determines the income for that period and the transition probabilities for moving to the next state. The problem is to choose the action at the beginning of each period which will maximize future total discounted income. A modified dynamic programming method for this problem is described. The method gives improved error control by showing how to compute upper and lower bonds on the...

Topics: DTIC Archive, CALIFORNIA UNIV LOS ANGELES WESTERN MANAGEMENT SCIENCE INST, *INVENTORY CONTROL,...

This study evaluates data from the Total Army Personnel Database (TAP-DB) which feeds the Enlisted Master File (EMF), with a three-fold purpose: (1) To determine the current state of the enlisted personnel management system. (2) To review any on-going initiatives to improve the overall reliability of the system. (3) To recommend future directions for improvements of the overall system.

Topics: DTIC Archive, Kwinn, Michael J., Jr., MILITARY ACADEMY WEST POINT NY, *PERSONNEL MANAGEMENT,...

In this paper, five different two-species nonlinear evolution equations are described that represent, (a) mixed attrition Lanchester combat with resupply and (b) four different models of information war. Their dynamical properties are analyzed and it is shown that four of the five are environmentally unstable. The meaning of this is interpreted for C3I, counter-C3, and intelligence operations. For the environmentally unstable systems it is shown that the relationships between the parameters in...

Topics: DTIC Archive, Moose,P H, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *Combat information centers,...