Process Instruments (Measurement Features)

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Table of Contents

An overview of key concepts about process instrumentation: measurement precision(a static feature that identifies the degree of agreement between the indication of the instrument and the characteristics of the measurand in measurement or monitoring), measurement uncertainty, metrological confirmation, and calibration.


By measurement precision we mean:

  • according to ISO-IMV (International Metrology Vocabulary):“…closeness of agreement betweenindicationsormeasured quantity valuesobtained by replicatemeasurementson the same or similar objects under specified conditions”;
  • 根据IEC-IEV(国际电学词汇)的说法:“..quality which characterizes the ability of a measuring instrument to provide an indicated value close to a true value of the measurand” (Note: call in this case, however, not Precision but Accuracy);
  • or we could deduce the following practical definition from the previous ones:“…by testing a measuring instrument under conditions and with specified procedures, the maximum positive and negative deviations from a specified characteristic curve (usually a straight line)”.


instrument accuracy and precision

Furthermore, the concept of repeatability of the measurement is not included (which is instead considered in the case of verification of precision over several measuring cycles.


计量确认验证that the measuring instrument keeps the accuracy and uncertainty characteristics required by the measurement process over time.

Sometimes this concept of imprecision for some common types of instruments (such as gauges, resistance thermometers, thermocouples, etc.) is also called precision or accuracy class, which according to the International Reference Vocabularies ISO-IMV and IEC-IEV :“class ofmeasuring instrumentsor测量系统that meet stated metrological requirements that are intended to keepmeasurement errorsor仪器测量不确定性和in specified limits under specified operating conditions” (ie, the accuracy measured must be less than accuracy rated: See also Figure 1).

Instrument Measurement Accuracy
Instrument Measurement Accuracy

图1 - 测量精度概念的例证



Measurement Uncertainty
Instruments measurement uncertainty

By measurement uncertainty we mean:

  • according to ISO-IMV (Internat. Metrology Vocabulary):“non-negative parameter characterizing the dispersion of thequantity valuesbeing attributed to ameasurand, based on the information used”;
  • according to ISO-GUM (Guide to Uncertainty of the Measurement):“result of the estimation that determines the amplitude of the field within which the true value of a measurand must lie, generally with a given probability, that is, with a determined level of confidence”.

From the above definitions we can deduce two fundamental concepts of measurement uncertainty:

  1. Uncertainty is the result of an estimate, which is evaluated according to the following two types:
  • A类:when the evaluation is done by statistical methods, that is through a series of repeated observations, or measurements.
  • B类:when the evaluation is done using methods other than statistical, that is, data that can be found in manuals, catalogs, specifications, etc.

2. The uncertainty of the estimate must be given with a certain probability, which is normally provided in the three following expressions (see also Table 1):

  • Standard uncertainty (u):at the probability or confidence level of 68% (exactly 68.27%).
  • Combined uncertainty (uc):the standard uncertainty of measurement when the result of the estimate is obtained by means of the values of different quantities and corresponds to the summing in quadrature of the standard uncertainties of the various quantities relating to the measurement process.
  • Expanded uncertainty (U):假设正常或高斯概率分布,在95%的概率或置信度(正好95.45%)或2个标准偏差处的不确定性。

Standard uncertainty u(x)(a)

The uncertainty of the result of measurement expressed as a standard deviation u(x) º s(x)

Type A evaluation (of uncertainty)

Method of evaluation of uncertainty by the statistical analysis of series of observations

Type B evaluation (of uncertainty)


Combined standard uncertainty uc(x)

Standard uncertainty of the result of measurement when that result is obtained from the values of a number of other quantities, equal to the positive square root of a sum of terms, the terms being the variances or covariances of these other quantities weighted according to how the measurement result varies with changes in these quantities

Coverage factor k

为了获得扩展的不确定性,用作合并标准不确定性的乘数的数值因素(通常为95%的概率为2,概率为 @ 99%)

Expanded uncertaintyu(y)= k。你c(y)(b)

Quantity defining an interval about the result of a measurement that may be expected to encompass a large fraction of the distribution of values that could reasonably be attributed to the measurand (normally is obtained by the combined standard uncertainty multiplied by with a coverage factor k = 2, namely with the coverage probability of 95%)

(a) The standard uncertainty u (y), ie the mean square deviation s (x), if not detected experimentally by a normal or Gaussian distribution, can be calculated using the following relationships:

你(x) = a/Ö3, for rectangular distributions, with an amplitude of variation ± a, eg Indication errors

你(x) = a/Ö6, for triangular distributions, with an amplitude of variation ± a, eg Interpolation errors

(b) The expanded measurement uncertainty U (y) unless otherwise specified, is to be understood as provided or calculated from the uncertainty composed with a coverage factor 2, ie with a 95% probability level.

Table 1- Main terms & definitions related to measurement uncertainty according to ISO-GUM


The metrological confirmation is the routine verification and control operation that confirms that the measuring instrument (or equipment) maintains theaccuracyand不确定性特征required for the measurement process over time.

By metrological confirmation we mean according to ISO 10012 (Measurement Mgt System):“set of interrelated or interacting elements necessary to achieve metrological confirmation and continual control of measurement processes”,and generally includes:

  • 仪器校准and verification;
  • any necessary adjustment and the consequent new calibration;
  • the comparison with the metrological requirements for the intended use of the equipment;
  • 成功的积极的计量的标签confirmation.
Metrological confirmation
Metrological confirmation for process instrumentation


0. Equipment scheduling
1. Identification need for calibration
2. Equipment calibration
3. Drafting of calibration document
5. There are metrological requir.???
6. Compliance with metrological req. 6a. Adjustment or repair 6b. Adjustment Impossible
7.起草文件确认 7a. Review intervals confirm 7b. Negative verification
8. Confirmation status identification 8a. Recalibration phase (2 to 8) 8b. State of identification
9.满意的需求 9a。满足的需求 9b。不需要满足

Table 1 – Main phases of the metrological confirmation (ISO 10012)
Table 1 highlights three possible paths of metrological confirmation:

  1. the left path that normally achieves the satisfaction of the positive outcome of the metrological confirmation without any adjustment of the instrument in confirmation to phase 6;
  2. the first left path and then the middle one from phase 6a to 9a, in case of positive adjustment or repair of the instrument in confirmation and whose recalibration satisfies the confirmation: therefore, in this case, it will be necessary to reduce only the confirmation interval;
  3. the first path on the left and then the right from phase 6b to 9b, in case of negative adjustment or repair of the instrument in confirmation, which does not satisfy the result of the confirmation: therefore the instrument must be downgraded or alienated.

Metrological confirmation can usually be accomplished and fulfilled in two ways:
Comparing the Maximum Relieved Error (MRE) with the Maximum Tolerated Error (MTE), ie:
mre <= mte
Comparing the Max. Relieved Uncertainty (MRU) with Tolerated Uncertainty (MTU, ie:
mru <= mtu
With reference to the previous articles, and taking into consideration the one on the Calibration, related to the evaluation of the calibration results in terms of Error and Uncertainty of a manometer, respectively equal to:

  • MRE: ±05 bar
  • MRU: 066 bar

如果最大误差和耐受性不确定性均为0.05 bar,则如果按MRE进行评估,则计量表是合规的,而如果根据MRU进行评估,则不合规,因此应遵循表1的路径2或PATH 3;如果不属于它,则将降级。


Instrumentation calibration is the operation to obtain under specified conditions, the relationship between the values of a measurand and the corresponding output indications of the instrument in calibration.


  • according to ISO-IMV (International Metrology Vocabulary):“在指定条件下,第一步的操作建立了quantity valuesmeasurement uncertaintiesprovided by测量标准and correspondingindications和associated measurement uncertainties and, in a second step, uses this information to establish a relation for obtaining ameasurement result从指示”;
  • or we could deduce the following practical example from the previous one:“operation performed to establish a relationship between the measured quantity and the corresponding output values of an instrument under specified conditions”.
Instrument calibration

Calibration should not be confused with the adjustment, which means: “set of operations carried out on ameasuring systemso that it provides prescribedindicationscorresponding to givenvaluesof aquantityto be measured (ISO-IMV).

Hence, the adjustment is typically the preliminary operation before the calibration, or the next operation when a de_calibration of the measuring instrument is found.

Calibration should be performed on 3 or 5 equidistant measuring points for increasing (and decreasing) values in the case of instruments with hysteresis phenomena: eg manometers):

Figure 1 presents the calibration setup, while Table 1 presents the calibration results.


图1 - Manom​​ete的校准设置




Relieved Errors





0 0.05 0.05 0.05
2 1.95 2.05 - 0.05 0.05
4 3.95 4.05 - 0.05 0.05
6 5.95 6.00 - 0.05 0.00
8 7.95 8.00 - 0.05 0.00
10 10.00 0.00
Table 1 – Calibration Results

From the calibration results shown in Table 1, the metrological characteristics of the manometer (or pressure gauge) can be obtained in terms of:

  • Measurement Accuracy:that is, maximum positive and negative error: ± 0.05 bar
  • Measurement Uncertainty:or instrumental uncertainty that takes into account the various factors related to the calibration, namely:

IrefUncertainty of the reference standard 0.01 bar (supposed)
E最大限度测量的最大误差可缓解0.05 bar
EresError of resolution of the manometer 0.05 bar
从中构成不确定性uccan be derived from the following relation:
Instrument calibration formula
and then the extended uncertainty (U), at 95% confidence level (ie at 2 standard deviations):

Calibration formula instruments
Obviously, the measurement uncertainty of the manometer (usually called instrumental uncertainty) is always higher than the measurement accuracy (because it also takes into account the error of resolution of the instrument in calibration and the uncertainty of the reference standard used in the calibration process).

The article describes the standardized analog pneumatic signals (20 to 100 kPa) and electrical signals (4 to 20 mA), as well as the innovative analog and digital hybrid signals HART (Highway Addressable Remote Transducer) and the state of the art of current digital communication protocols commonly called BUS.


Analog Control Signals

The traditional most commonly used transmission signal of the type:

  • Direct current signals (Table 1): for connection between instruments on long distances (i.e. in the field area)
  • 直接电压信号(表2):用于短距离的仪器之间的连接(即在控制室中)
(1) Preferential signal

Table 1- Standardized signals in direct current (IEC 60381-1)

– 10
+ 10

(1) Voltage signals that can be derived directly from normalized current signals

(2) Voltage signals that can represent physical quantities of a bipolar nature

Table 2- Standardized signals in direct voltage (IEC 60381-2)

Moreover, given their characteristics, the current signals are used in the field instrumentation, while the voltage signals are used in the technical and control room instrumentation.

Finally, the current signal with respect to the voltage signal has the advantage of not being affected by the length and hence the impedance of the connection line at least up to certain resistance values, as it is illustrated in Figure 1.

Limit supply region analog signals
Limit supply region analog signals

Figure 1 – Example of the limit of the operating region for the field instrumentation in terms of its connection resistanceOmegato the supply voltage V


  • Vdc = Actual supply voltage in volt
  • Vmax= Maximum supply voltage, 30 V in this example
  • Vmin= Minimum supply voltage, 10 V in this example
  • rl =最大。实际电源电压处的欧姆负载阻力:
  • RL <= (Vdc – 10) / 0,02 (in the Example reported in Figure 1)

Hybrid Control Signals

analogical-digital的混合信号,这是protocol type, were standardized “de facto” by a Consortium of Manufacturers as:

HART(高速公路可寻址远程传感器),该数字信号(4×20 mA)精确地叠加到模拟归一化信号(4×20 mA),该数字信号根据标准铃202的频率调制,幅度为+/- 0.5 ma,并且在表3中发现了频率,鉴于叠加信号的高频率,添加的能量实际上为零,因此该调制不会对模拟信号引起任何干扰。


HART protocol
Table 3 – HART protocol with signals standardized BELL 202

Digital Control Signals

Digital signals were normalized towards the end of the 1990s by the International Standard IEC 61158 on Fieldbus Protocol, but still not much applied since it standardizes as many as 8 communication protocols, and as each digital protocol is essentially characterized by following features (see Table 4):

  • Transmission encoding: Preamble, frame start, transmission of the frame, end of the frame, transmission parity, etc.
  • Access to the network: Probabilistic, deterministic, etc.
  • 网络管理:主从,Producer-Consumer, etc.
Standard IEC
Fieldbus Foundation
(1) Protocol initially designed as unique standard protocol IEC

Table 4 – Standardized protocols provided for by the International Standard IEC 61158


Instrumentation measuring chain
Figure 2 – the Typical path of a measurement chain from the field to the control room


  • For pneumatic instrumentation: 140 ± 10 kPa (1.4 ± 0.1 bar) for the pneumatic instrumentation (sometimes the normalized pneumatic power supply in English units is still used: 20 psi, corresponding to ≈ 1.4 bar)
  • For electrical instrumentation: Continuous voltage: 24 V dc for field instrumentation, Alternating voltage: 220 V ac for control and technical room instrumentation

The connection and transmission signals between the various instruments in the measuring and regulating chains are standardized by the IEC (International Electrotechnical Commission):

  • Pneumatic signals (IEC 60382): 20 to 100 kPa (0.2 to 1.0 bar) (sometimes the standardized signal is still in English units: 3 to 15 psi, ≈ 0.21 to 1.03 bar)
  • Electrical signals (IEC 60382):

About the Author

Alessandro Brunelli

Author: Dott. Prof.Alessandro Brunelli– Professor of Instrumentation, Automation, and Safety of Industrial Plants

Cavaliere dell’ Ordine al Merito della Repubblica Italiana (OMRI N. 9826 Serie VI)

Author of “Instrumentation Manual” (available in IT):

  • Part 1: illustrates the general concepts on industrial instrumentation, the symbology, the terminology and calibration of the measurement instrumentation, the functional and applicative conditions of the instrumentation in normal applications and with the danger of explosion, as well as the main directives (ATEX , EMC, LVD, MID, and PED);
  • Part 2: this part of the book deals with the instrumentation for measuring physical quantities: pressure, level, flow rate, temperature, humidity, viscosity, mass density, force and vibration, and chemical quantities: pH, redox, conductivity, turbidity, explosiveness, gas chromatography, and spectrography, treating the measurement principles, the reference standard, the practical executions, and the application advantages and disadvantages for each size;
  • Part 3:illustrates the control, regulation, and safety valves and then and simple regulation techniques in feedback and coordinates in feedforward, ratio, cascade, override, split range, gap control, variable decoupling, and then the Systems of Distributed Control (DCS) for continuous processes, Programmable Logic Controllers (PLC) for discontinuous processes and Communication Protocols (BUS), and finally the aspects relating to System Safety Systems, from Operational Alarms to Fire & Gas Systems, to systems of ESD stop and finally to the Instrumented Safety Systems (SIS) with graphic and analytical determinations of the Safety Integrity Levels (SIL) with some practical examples.

Download the PDF – Traceability & Calibration Handbook

You can download an excerpt of the “Instrumentation Manual” (Brunelli, 2018-2019) by clicking on the following link:

pdf icon可追溯性和校准手册(工艺仪器)


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