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Bibliography

MAINTAINABILITY. A characteristic of design and installation which is expressed as the probability that an item will be retained in or restored to a specified condition within a given period of time, when the maintenance is performed in accordance with prescribed procedures and resources. [28]

MAINTENANCE. All actions necessary for retaining an item in or restoring it to a specified condition. [28]

MAINTENANCE, CORRECTIVE. The actions performed, as a result of failure, to restore an item to specified condition. [28]

MAINTENANCE, PREVENTIVE. The actions performed in an attempt to retain an item in a specified condition by providing systematic inspection, detection and prevention of incipient failure. [29]

MAN-FUNCTION. The function allocated to the human component of a system. [28]

MASTER PROGRAM. The part of a decomposed problem which expresses the extreme point solution of the subproblems as convex combinations and which also satisfy the constraints in the class C0 (the class of constraints which C0 can include all the variables). (See DECOMPOSTION PRINCIPLE.) [19]

MATHEMATICAL PROGRAMMING. The general problem of optimizing a function of several variables subject to a number of constraints. If the function and constraints are linear in the variables and a subset of the constraints restrict the variables to be nonnegative, we have a linear programming problem. [19]

MATRIX ELEMENT. One of the mn numbers of a matrix. [19]

MATRIX GAME. A zero-sum two-person game. The payoff (positive, negative or zero) of player one to player two when player one plays his ith strategy and player two his jth strategy is denoted by aij. The set of payoffs aij can be arranged into an m x n matrix. [19]

MAX-FLOW MIN-CUT THEOREM. A theorem which applies to a maximal flow network problem which states that the maximal flow from the source to the sink is equal to the minimal cut capacity of all cuts separating the source and sink nodes. [14]

MAXIMAL NETWORK FLOW PROBLEM. A problem involving a connected linear network in which goods must flow from an origin (source) to a final destination (sink) over the arcs of the network in such a fashion as to maximize the total flow that the network can support. The arcs are connected at intermediate nodes and each branch has a given flow capacity that cannot be exceeded. The flow into an intermediate node must equal the flow out of that node. [15]

MEAN. The expected value of a random variable.

MEAN LIFE. The arithmetic mean (q.v.) of the times-to-failure of the units of a given item. [20]

MEAN-MAINTENANCE-TIME. The total preventive and corrective maintenance time divided by the total number of preventive and corrective maintenance actions during a specified period of time. [28]

MEAN SERVICE RATE. The conditional expectation of the number of services completed in one time unit, given that service is going throughout the entire time unit.

MEAN TIME BETWEEN FAILURES(MTBF). For a particular interval, the total functioning life of a population of an item divided by the total number of failures within the population during the measurement interval. [28]

MEAN TIME TO FAILURE. This expression applies to components of a system and not to systems. The expected length of time that a component is in use in a system in operation from the moment the component is put into the system to the moment it fails. It is the expected length of life of the components. The meantime-to-failure is sometimes confused with the meantime-between-failures (MTBF) which applies to systems which experience subsystem or component failures which can be replaced or repaired, putting the system into operation again. The confusion occurs in part because for the Poisson failure distributions the two quantities have the same distribution.

MEAN TIME TO REPAIR (MTTR). The total corrective maintenance time divided by the total number of corrective maintenance actions during a given period of time. [28]

MEDIAN. A measure of central tendency with the number of data points above and below it equal; the 50th percentile value. [28]

MINIMAL COST FLOW PROBLEM. A network flow problem in which costs cij are the cost of shipping one unit of a homogeneous commodity from node i to node j. A given quantity F of the commodity must be shipped from the origin node to the destination at minimum cost. [19]

MINIMAX PRINCIPLE. A principle introduced into decision-function theory by Wald (1939). It supposes that decisions are taken subject to the condition that the maximum risk in taking a wrong decision is minimized. The principle has been critized on the grounds that decisions in real life are scarcely ever made by such a rule, which enjoins “that one should never walk under a tree for fear of being killed by its falling. “ In the theory of games it is not open to the same objection, a prudent player being entitled to assume that his adversary will do his worst. [22]

MISSION. The objective or task, together with the purpose, which clearly indicates the action to be taken. [28]

MIXED-INTEGER PROGRAMMING. Integer programs in which some, but not all, of the variables are restricted to integral values. [19]

MODE. The value(s) of a random variable such that the probability mass (discrete random variable) or the probability density (continuous random variable) has a local maximum for this value (or these values). Note: If there is one mode, the probability distribution of the random variable is said to be “unimodal”; if there is more than one mode the probability distribution is said to be “multimodal” (bimodal if there are two modes).

MODEL. A mathematical or physical representation of a system (q.v.) often used to explore the many variables (q.v.) influencing the system.

MONOTONE. A monotonic (or monotone) non-decreasing quantity is a quantity which never decreases (the quantity may be a function, sequence, etc., which either increases or remains the same, but never decreases). A sequence of sets El,E2,... is monotonic increasing if En is contained in En + I for each n. A monotonic (or monotone) non- increasing quantity is a quantity which never increases (the quantity may be a function, sequence, etc,. which either decreases or remains the same, but never increases). A sequence of sets, El,E2,... is monotonic decreasing if En contains En+ I for each n. A monotonic (or monotone) system of sets is a system of sets such that, for any two sets of the system one of the sets is contained in the other. A mapping of a topological space A onto a topological space b is said to be monotone if the inverse image of each point of B is a continuum. A mapping of an ordered set A onto an ordered set B is monotone provided x* precedes (or equals) y* whenever x* and y* are the images in B of points x and y of A for which x precedes y. [21]

MONOTONIC INCREASING FUNCTION. A function f is monotonic increasing on an interval (a, b) if f (y) > f (x) for any two numbers x and y (of this interval) for which x < y. [21]

MONTE CARLO METHOD. A simulation technique by which approximate evaluations are obtained in the solution of mathematical expressions so as to determine the range or optimum value. The technique consists of simulating an experiment to determine some probabilistic property of a system or population of objects or events by the use of random sampling applied to the components of the system, objects, or events.

MOVING AVERAGE. An unweighted average of the latest n observations where the current observations has replaced the oldest of the previous n observations.

MTBF. (See MEAN TIME BETWEEN FAILURES.) [20]

MULTICOMMODITY NETWORK PROBLEM. A network problem in which more than one commodity can flow through the network at the same time. The capacity constraints on the arcs apply to the sum of the flows of the commodities. [19]

MULTICRITERIA OPTIMIZATION. A model and associated algorithm which attempts to find strategies which optimize several criterion measures instead of one. For example, there may be objectives and criterion measurements on economic, social, end environmental issues. The criterion measurements would be in different units.

MULTIPERSON GAME. A game where a number of players are each competitively striving towards a specific objective which any one player only partially controls.

MUTLTIPLE REGRESSION. A statistical procedure to determine a relationship between the mean of a dependent random variable and the given value of one or more independent variables.