error

(redirected from Measurement error)
Also found in: Dictionary, Thesaurus, Medical, Legal, Financial.

error,

in law: see appealappeal,
in law, hearing by a superior court to consider correcting or reversing the judgment of an inferior court, because of errors allegedly committed by the inferior court.
..... Click the link for more information.
.

Error

 

in automatic control systems, the difference between the set point and the actual value of the quantity being controlled in a control process. At any given moment, the error can be regarded as the sum of the static error—the error under steady-state conditions—and the dynamic error—the error in a transient response. In the statistical analysis of automatic control systems, the distinction between steady-state and transient errors loses its meaning, and the quality of performance of such a system is evaluated by criteria associated with the probability characteristics of the error. An example of such a criterion is the minimum mean-square error.


Error

 

When a number a is taken as the approximate value of a quantity whose exact value is x, the error of a is the difference xa, which is also called the absolute error. The ratio of xa to a is called the relative error. An error is usually characterized by indicating its maximum possible value. The maximum possible value of the absolute error is the number Δ (a) such that ǀxaǀ ≤ Δ(a). The maximum possible value of the relative error is the number δ(a) such that

The maximum values of relative errors are often expressed as percentages. The numbers Δ(a) and δ(a) are taken as small as possible.

If a is the approximate value of x with a maximum absolute error of Δ(a), this fact can be written x = a ± Δ(a). The analogous expression for the relative error is x = a(1 ± δ(a)).

The maximum values of the absolute and relative errors indicate the maximum possible divergence between x and a. In addition to these values, an error is often characterized by the nature of its origin and by the frequency of occurrence of different values of xa. The methods of probability theory are used in this approach to errors.

The error of the result in the numerical solution of a problem is caused by inaccuracies intrinsic to the formulation of the problem and to the means used to solve it. Errors stemming from the inaccuracy of a mathematical description of an actual process—for example, from an inaccurate statement of the original data—are said to be inherent errors. Errors of method arise because of the inaccuracy of the method used in solving the problem. Computational errors are the result of inaccuracies in computations.

When computations are performed, initial errors pass in succession from operation to operation, accumulating and giving rise to new errors. The appearance and propagation of errors in computational work are studied by numerical analysis.

REFERENCES

Berezin, I. S., and N. P. Zhidkov. Metody vychislenii, 3rd ed., vol. 1. Moscow, 1966.
Bakhvalov, N. S. Chislennye metody. Moscow, 1973.

G. D. KIM

error

[′er·ər]
(computer science)
An incorrect result arising from approximations used in numerical methods, rather than from a human mistake or computer malfunction.
(science and technology)
Any discrepancy between a computed, observed, or measured quantity and the true, specified, or theoretically correct value of that quantity.

Error

Breeches Bible, the
the Geneva Bible, so dubbed because it stated that Adam and Eve made themselves breeches. [Br. Hist.: Brewer Dictionary, 101]
Cortez
alluded to in a poem by Keats, mistaken for Balboa, as discoverer of Pacific Ocean. [Br. Poetry: “On First Looking into Chapman’s Homer”]
Wicked Bible, the
misprinted a commandment as “Thou shalt commit adultery.” [Br. Hist.: Brewer Dictionary, 102]
seacoast of Bohemia
Shakespearean setting in a land with no seacoast. [Br. Drama: Shakespeare The Winter’s Tale, III,iii]

error

(1)
A discrepancy between a computed, observed, or measured value or condition and the true, specified, or theoretically correct value or condition.

error

(programming)
A mental mistake made by a programmer that may result in a program fault.

error

(3)
(verb) What a program does when it stops as result of a programming error.
References in periodicals archive ?
Adjustment for measurement error to account for the differences between personal and ambient exposures led to modest increases in the HRs for BS (0-3.
Two approaches were used to account for tool measurement error in crack detection sizing criteria.
Creating relational plots of the shape and displacement of the [+ or -] measurement error probability spaces will provide a way to visualize and quantify the required measurement performance that will be necessary to establish acceptable resolution of analyte concentration results.
Although the goal is to uncover an ex post change below zero, the rationale is that setting a slightly tougher RT benchmark builds in a safety margin to allow for possible RT measurement error (Buti, Eijffinger, and Franco 2003; European Commission 2002; Sapir 2004).
For the calculation of E for sea scallops in this analysis, shell-height measurement error distributions were assumed to be normally distributed with means and standard deviations from experiment 2.
In practice, these assumptions may not hold; revisions often have a systematic and predictable component, which implies that the measurement error is also systematic.
In the latter, each datum within a time series is assumed to have an amount of measurement error that is inversely correlated with the maturity of the datum.
Given the widespread use of time estimates in costing products and services, decision-makers who use the figures should be aware of the extent of measurement error that affects the accuracy of their costing systems.
The measurement error during stair ascending and descending at 80 to 120 steps per minutes were -1.
Because only one of the four identified studies (Hayward and Hofer 2001) used a statistical method that accounted for measurement error (Table 1), we sought to obtain and reanalyze the original data for the other three studies.
As the measurement error for distance is [+ or -] 2 m, the error for calculated rates of shoreline change over the 10 year period of the study is [+ or -] 0.
We also found that freezing introduced additional measurement error along with a decrease in UAC.

Full browser ?