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How Do I Calculate Absolute Accuracy or System Accuracy?

Hardware: Multifunction DAQ (MIO)

Problem:
I am aware of the online accuracy calculator, but how does it calculate my system accuracy based on the inputs I give it? Also, what if for some reason I cannot use the online accuracy calculator such as for cascaded SCXI modules? How do I calculate the absolute accuracy of my components and the system accuracy of my entire measurement?

Solution:
There are three steps when calculating the system accuracy of a measurement:
  1. Determine our accuracy and environment parameters.
  2. Calculate Absolute Accuracy for each system component
  3. Use the absolute accuracy values to calculate the System Accuracy and System Accuracy Relative to Input (RTI) 
You can refer to the Online Accuracy Calculator for more information regarding computing absolute accuracy.

Step 1: Identify variables affecting the calculated accuracy

First, determine how each component is connected to the system and identify all pertinent variables that will affect the calculated accuracy. For this example, we'll assume an SCXI-1125 isolation module is cascaded using the SCXI-1352 cable to an SCXI-1141 filter module. This filter module is then connected to an NI 6052E DAQ device.

SCXI 1125  ->  SCXI 1141  ->  NI 6052E

Assume the following:

  • Single Point Reading (no averaging)
  • Ambient Temperature = 25°C
  • SCXI-1125 Filter = 10 KHz
  • SCXI-1125 Input Range = +/- 10 V
  • SCXI-1141 Input Range = +/- 5 V
  • NI 6052E Input Range = +/- 5 V
  • "Typical" vs. "Max" % Reading? = "Typical"
  • Time Since Last Calibration = Less Than 1 Year

Step 2: Calculate the Absolute Accuracy for each Component

Next, calculate the Absolute Accuracy for each component. For any individual device with gain (either an amplifier or attenuator), for a specified nominal range, National Instruments provides an absolute accuracy specification in millivolts. Depending upon the presentation of different errors, there are two different equations to use to calculate the accuracy. Both set of equations are listed below:

Equation 1:
Absolute Accuracy
= ±(VoltageReading*GainError + VoltageRange*OffsetError + NoiseUncertainity)

GainError = ResidualAIGainError + GainTempco*TempChangeFromLastInternalCal + ReferenceTempco*TempChangeFromLastExternalCal

OffsetError = ResidualAIOffsetError + OffsetTempco*TempChangeFromLastInternalCal + INL_Error

NoiseUncertainity = (RandomNoise*3)/(100).5

You can obtain the parameter values in the above equation by looking at the specifications found in each component's catalog or user manual. In our example code, there is a sample VI called Absolute Accuracy Calculator.

Equation 2:
Absolute Accuracy = ±((Input Voltage * % of reading) + (Range*% Offset of the Range) + System Noise + Temperature Drift)

You can obtain the parameter values in the above equation by looking at the specifications found in each component's catalog or user manual.
  • Input Voltage  — the voltage range the device is configured for. For example, for +- 10V, Input Voltage = 10.
  • % of reading — a raw % accuracy based on the input gain. This accounts for gain error.
  • Offset — the maximum offset error. Many times, this offset can be in ppm instead of % so in order to change this into %, use this conversion: 1% = 1000 ppm.
  • System Noise — error introduced to the measurement by the device itself. This will often depend on filter settings or whether a single sample is taken as opposed to multiple samples being averaged.
  • Temperature Drift — This accounts for errors introduced by ambient temperature variation.

Temperature Drift = ±(Input Voltage * % of Reading/° C + Offset/° C) * Temperature Difference

Temperature effects are already accounted for in the specification values unless your ambient temperature is outside of the 15 to 35° C range. For instance, if the ambient temperature of your measurement system is at 45° C, you must account for 10° C of temperature difference. In this case, since the temperature is assumed to be 25° C, we don't have to add in anything for Temperature Drift.

Please note that terminal blocks or connector blocks are not considered gain stages unless they have attenuation circuitry. Modules or DAQ devices that do not have amplifiers are also not considered gain stages.

Step 3: Calculate the system accuracy and system accuracy RTI

Finally, we will use the Absolute Accuracy from each component to calculate the System Accuracy and System Accuracy RTI. Like the Pythagorean Theorem, the System Accuracy is equal to the square root of the sum of the squares of each component's Absolute Accuracy.

System Accuracy = ( (Absolute Accuracy 1)^2 + (Absolute Accuracy 2)^2 + (Absolute Accuracy 3)^2 + ...) )^(1/2)

The System Accuracy Relative To Input (RTI) is calculated as follows:

System Accuracy RTI = System Accuracy / Input Voltage

System Accuracy Example Calculations for the above setup:

Here are the absolute accuracy calculations for each component of our system:

Absolute Accuracy - SCXI-1125

Absolute Accuracy = ±((Input Voltage * % of reading) + Offset + System Noise + Temperature Drift)
Absolute Accuracy = ±((10 V * 0.002478) + 0.01 V + 0.0191 V + N/A)
Absolute Accuracy = ±54.88 mV

Absolute Accuracy - SCXI-1141

Absolute Accuracy = ±((Input Voltage * % of reading) + Offset + System Noise + Temperature Drift)
Absolute Accuracy = ±((5 V * 0.0002) + 0.0006 V + 0.001420 V + N/A)
Absolute Accuracy = ±3.02 mV

Absolute Accuracy - PCI-6052E

Absolute Accuracy = ±((Input Voltage * % of reading) + Offset + System Noise + Temperature Drift)
Absolute Accuracy = ±((5 V * .000071) + 0.000476 V + 0.000491 V + N/A)
Absolute Accuracy = ±1.322 mV

System Accuracy

System Accuracy = ( (Absolute Accuracy 1)^2 + (Absolute Accuracy 2)^2 + (Absolute Accuracy 3)^2 + ...) )^(1/2)
System Accuracy = ( (54.88 mV)^2 + (3.02 mV)^2 + (1.322 mV)^2 ) )^(1/2)
System Accuracy = ± 65.90 mV

System Accuracy RTI

System Accuracy RTI = System Accuracy / Input Voltage
System Accuracy RTI = ± 0.06590 V / 10 V
System Accuracy RTI = 0.659 %

For more information, see the Using Calibration to Improve Measurement Accuracy presentation linked below.


Related Links:
Support Utilities: Accuracy Calculator
Developer Zone Example: Absolute Accuracy Calculator
NI Developer's Zone: Using Calibration to Improve Measurement Accuracy
NI Developer's Zone: Accuracy and Uncertainty
KnowledgeBase 2W3ISON1. Finding the Accuracy of Measurements in the Units of a Sensor
KnowledgeBase 3IHCT5LE: Absolute Accuracy of Dynamic Signal Acquisition Devices

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Report Date: 05/05/2003
Last Updated: 03/11/2010
Document ID: 2X4HGEBG

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