Uncertainty Cal Lab (Temp)

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Estimation of Measurement Uncertainty

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Important Terms and Definitions

Measurement Process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity.

Accuracy Closeness of agreement between a measured quantity value and a true quantity value of a measurand.

Precision Closeness of agreement between indications or measured quantity values obtained by replicate measurements on the same or similar objects under specified conditions.

Contd..

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Calibration Calibration is a measurement process that assigns values to the property of an artifact or to the response of an instrument relative to reference standards or to a designated measurement process with measurement uncertainties.The purpose of calibration is to eliminate or reduce bias in the user's measurement system relative to the reference base.A calibration may be expressed by a statement, calibration function, calibration diagram, calibration curve, or calibration table.

Contd..

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Error Measured quantity value minus a reference quantity value

Systematic Error Component of measurement error that in replicate measurements remains constant or varies in a predictable manner.

Random Error Component of measurement error that in replicate measurements varies in an unpredictable manner.

Contd..

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Repeatability Measurement precision under such a set of conditions that includes the same measurement procedure, same location, and replicate measurements on the same or similar objects over an extended period of time, but may include other conditions involving changes.

Reproducibilitymeasurement precision under such a set of conditions that includes different locations, operators, measuring systems, and replicate measurements on the same or similar objects.

Contd..


Measurement Traceability Measurement traceability is a chain of references / corrections that have been incorporated in measurement process starting from the primary standard at BIPM and ending at the final measurement that is under consideration.

Broadly speaking measurement traceability has its roots in two different areas of measurements

1. Measurement Accuracy (Error)2. Measurement Uncertainty

Contd..


Measurement Traceability

Error

Uncertainty

Uncertainty

Primary Standard at BIPM

Error

Uncertainty

National Standard at NPSL

Ref. Standard at Cal. Lab

Error

Ref. Standard at any client lab

Error

Uncertainty

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Uncertainty of Measurement Non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used.

Measurement uncertainty includes components arising from systematic effects, such as components associated with corrections and the assigned quantity values of measurement standards, as well as the definitional uncertainty. Sometimes estimated systematic effects are not corrected for but, instead, associated measurement uncertainty components are incorporated.

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Types of Uncertainty

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Type B UncertaintyType B evaluation of standard uncertainty is usually based on scientific judgment using all of the relevant information available, which may include:

• previous measurement data, • experience with, or general knowledge of, the

behaviour and property of relevant materials and instruments,

• manufacturer's specifications, • data provided in calibration and other reports,

and • uncertainties assigned to reference data taken

from handbooks.

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2. Uncertainty Type B Few of Common factors that contribute tothe measurement uncertainty of arediscussed below.

i. Uncertainty due to Resolution of Unit Under Test (UUT) UB1

For digital indicating devices, resolution uncertainty is understood to be half of the least significant digit, with a rectangular distribution. A rectangular distribution is also used for analog timers, since these devices move in discrete steps from one fraction of a second to the next.

ii. Uncertainty due to Combined Uncertainty of Standard UB2

The Expanded Value of the uncertainty is divided by the coverage factor (2) and the resultant combined uncertainty is taken as it is for further calculation of Uncertainty.

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iii. Uncertainty due to Accuracy of UUT UB3

The Accuracy of a Unit Under Test is divided by Square root of 3 (factor for Rectangular Distribution) to obtain the uncertainty contribution factor due to accuracy of unit under test.

iv. Uncertainty due to Drift of Standard UB4

The Expanded Value of the uncertainty is divided by Square root of 3 (factor for Rectangular Distribution) to obtain the uncertainty contribution factor due to drift of standard.

OrDifference of combined uncertainties obtained from current calibration certificate and the previous year’s calibration certificate is taken as uncertainty contribution factor due to Drift of Standard.

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Combined Uncertainty It is taken as the square root of sum of squares of all the Uncertainty contributions obtained from various factors / sources

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Expanded Uncertainty

Expanded uncertainty (UE) or (U)

= Uc * k

(k = 2, representing approximately a 95 % level of confidence)

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Uncertainty Budget (General Example)

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Combined Uncertainty Model Equation:

Where

ci = sensitivity co-efficient

ui = standard uncertainty component

Uncertainty of Measurement

Normal Distribution

Distribution factor = 1

Rectangular Distribution

Distribution factor = √ 3

Triangular Distribution

Distribution factor = √6

Commonly Used Probability Distributions

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Sensitivity Coefficient (ci )

It is denoted as ci and is the factor that is

associated with the each type B uncertainty component. It is the measure of interdependency of each of the type B uncertainty component to all the other type B components involved in the estimated Combined Uncertainty Uc under consideration.

It is determined by the sum of partial derivatives of each of the type B uncertainty component with respect to the component under consideration including its own partial derivative as well.

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Simple & Brief Explanation of Coefficient of Sensitivity

If we have UB1, UB2, UB3, UB4 & UB5 as the five type B uncertainty components then their corresponding Sensitivity Coefficients would be c1, c2, c3, c4, & c5 respectively

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Confidence interval

Procedure: Convert an uncertainty quoted in a handbook, manufacturer's specification, calibration certificate, etc., that defines a "confidence interval" having a stated level of confidence, such as 95 % or 99 %, to a standard uncertainty by treating the quoted uncertainty as if a normal probability distribution had been used to calculate it (unless otherwise indicated) and dividing it by the appropriate factor for such a distribution. These factors are 1.960 and 2.576 for the two levels of confidence given.

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Coverage factor

In general, the value of the coverage factor k is chosen on the basis of the desired level of confidence to be associated with the interval defined by U = kuc. Typically, k is in the range 2 to 3. When the normal distribution applies and uc is a reliable estimate of the standard deviation of y, U = 2 uc (i.e., k = 2) defines an interval having a level of confidence of approximately 95 %, and U = 3 uc (i.e., k = 3) defines an interval having a level of confidence greater than 99 %.

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References• Vocabulary of International Metrology (VIM), 2008, OIML

• Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, 1297, 1994

• Expression of Uncertainty and Confidence in Measurement, M3003, Dec 1997, Ed 1, UKAS

• Expression of the Uncertainty of Measurement in Calibration, EA-4/02, Dec 1999, European Accreditation

• Guide for Estimation of Uncertainty in Testing, G104 – A2LA, Jul 2002, The American Association for Laboratory Accreditation

• Guide for Estimation of Uncertainty of Dimensional Calibration and Testing Results, G103 – A2LA, Dec 2008, The American Association for Laboratory Accreditation

Uncertainty Cal Lab (Temp)

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