# Z94.1 - Analytical Techniques & Operations Research Terminology

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RANDOM. This word may be taken as representing an undefined idea, or, if defined, must be expressed in terms of the concept of probability. A process of selection applied to a set of objects is said to be random if it gives to each one an equal chance of being chosen. Generally, the use of the word “random” implies that the process under consideration is in some sense probabilistic. [22:237, 13:29]

RANDOM FAILURE. (See FAILURE, RANDOM.) 

RANDOM VARIABLE. A real-valued function that maps outcomes, which are elements  of the sample space of a random experiment to the set of Real numbers. Distribution functions associated with random variables provide a probability associated with values of random variables.

RANDOM WALK. The path traversed by a particle which moves in steps, each step being determined by chance either in regard to direction or in regard to magnitude or both. Cases most frequently considered are those in which the particle moves on a lattice of points in one or more dimensions, and at each step is equally likely to move to any of the nearest neighboring points. The theory of random walks has many applications, e.g., to the migration of insects, sequential sampling and, in the limit, to diffusion processes. [22:239, 13:311, 25:393]

RANGE. The difference between the largest observed value and the smallest observed value. 

RANK OF A MATRIX. The maximum number of linearly independent rows of the matrix. Equivalently, the maximum number of linearly independent columns, or the size of the largest square submatrix with an inverse. 

RATING. The value of an item parameter which can be attained under specified conditions. 

READY RATE, OPERATIONAL (COMBAT). Percent of assigned items capable of  performing the mission or function for which they were designed, at a random point in time. 

RECTILINEAR. A distance metric where movement is only allowed in two directions which are perpendicular to each other.

REDUNDANCY. In a system, the existence of more than one means for performing a given function.

REDUNDANCY, ACTIVE. That redundancy wherein all redundant items are operating simultaneously rather than being switched on when needed. 

REDUNDANCY, STANDBY. That redundancy wherein the alternative means of performing the function is inoperative until needed, and is switched on upon failure of the primary means of performing the function. 

REDUNDANT EQUATIONS. A set of equations, one of which may be expressed as a linear combination of the others. Such an equation can be omitted from the system without affecting the solution. 

RELIABILITY (OF AN ITEM, EXPRESSED NUMERICALLY). The probability that an item will perform a required function under stated conditions for a stated period of time.   Note: This definition is used when defining the characteristic intended by such modified terms as assessed reliability and predicted reliability. 

RELIABILITY (GENERAL DEFINITION). Ability of an item to perform a required function under stated conditions for a stated period of time. 

RELIABILITY, HUMAN PERFORMANCE. The probability that man will accomplish all required human functions under specified conditions. 

RELIABILITY, INHERENT. The potential reliability of an item present in its design. 

REPAIR. (See MAINTENANCE, CORRECTIVE.) 

REPAIRABLE UNIT. (See UNIT, REPAIRABLE.) 

REPEATABILITY (MEASUREMENT). (See PRECISION.)

RESPONSE. The reaction of an individual unit to some form of stimulus. It may be reaction to a drug, as in big- assay, or the reaction to a request for information, as in sample surveys of human beings. 

RESTRICTION. An equation or inequality limiting the feasible range of variation of one or more variables. Also used for constraint. 

REVISED SIMPLEX METHOD (COMPUTING FORM). A variant of the simplex method, especially suitable for problems in which the number of variables is much larger than the number of equations. The method employs (1) an implicit inverse, “product form of the inverse,” or (2) an explicit inverse of the current basis to compute an updated row or column of the tableau as required. The simplex multipliers comprise the profit row of the inverse; they are used to test for optimality and to select a new entering variable. 

RIGHT-HAND SIDE. The mathematical expression on the right of the equality or inequality sign in an equation or inequality. In linear programming, by convention, the right-hand side of each constraint is merely the constant term, with the complete linear function as the left-hand side. 

RIGHT-HAND SIDE ELEMENT. An element of the column vector comprising the right-hand sides of the constraints. 

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