1065.305—Verifications for accuracy, repeatability, and noise.
(a)
This section describes how to determine the accuracy, repeatability, and noise of an instrument. Table 1 of § 1065.205 specifies recommended values for individual instruments.
However, it may be useful to consider these verifications to define a specification for a new instrument, to verify the performance of a new instrument upon delivery, or to troubleshoot an existing instrument.
(c)
In this section we use the letter “y ” to denote a generic measured quantity, the superscript over-bar to denote an arithmetic mean (such as y ), and the subscript “ref ” to denote the reference quantity being measured.
(1)
Prepare an instrument so it operates at its specified temperatures, pressures, and flows. Perform any instrument linearization or calibration procedures prescribed by the instrument manufacturer.
(2)
Zero the instrument as you would before an emission test by introducing a zero signal. Depending on the instrument, this may be a zero-concentration gas, a reference signal, a set of reference thermodynamic conditions, or some combination of these. For gas analyzers, use a zero gas that meets the specifications of § 1065.750.
(3)
Span the instrument as you would before an emission test by introducing a span signal. Depending on the instrument, this may be a span-concentration gas, a reference signal, a set of reference thermodynamic conditions, or some combination of these. For gas analyzers, use a span gas that meets the specifications of § 1065.750.
(4)
Use the instrument to quantify a NIST-traceable reference quantity, y
ref. For gas analyzers the reference gas must meet the specifications of § 1065.750. Select a reference quantity near the mean value expected during testing. For all gas analyzers, use a quantity near the flow-weighted mean concentration expected at the standard or expected during testing, whichever is greater. For noise verification, use the same zero gas from paragraph (d)(2) of this section as the reference quantity. In all cases, allow time for the instrument to stabilize while it measures the reference quantity. Stabilization time may include time to purge an instrument and time to account for its response.
(5)
Sample and record values for 30 seconds (you may select a longer sampling period if the recording update frequency is less than 0.5 Hz), record the arithmetic mean, y
i and record the standard deviation, σi of the recorded values. Refer to § 1065.602 for an example of calculating arithmetic mean and standard deviation.
(6)
Also, if the reference quantity is not absolutely constant, which might be the case with a reference flow, sample and record values of y
refi for 30 seconds and record the arithmetic mean of the values, y
ref. Refer to § 1065.602 for an example of calculating arithmetic mean.
(7)
Subtract the reference value,y
ref (ory
refi ), from the arithmetic mean,y
i. Record this value as the error,ε
i.
(8)
Repeat the steps specified in paragraphs (d)(2) through (7) of this section until you have ten arithmetic means (y1, y2, yi, ...y10 ), ten standard deviations, (σ1, σ2, σi ,...σ10 ), and ten errors (ε1, ε2, εi ,...ε10 ).
(i) Accuracy.
Instrument accuracy is the absolute difference between the reference quantity, y
ref (or y
ref ), and the arithmetic mean of the ten y
i, y values. Refer to the example of an accuracy calculation in § 1065.602. We recommend that instrument accuracy be within the specifications in Table 1 of § 1065.205.
(ii) Repeatability.
Repeatability is two times the standard deviation of the ten errors (that is, repeatability = 2 · σ
ε ). Refer to the example of a standard-deviation calculation in § 1065.602. We recommend that instrument repeatability be within the specifications in Table 1 of § 1065.205.
(iii) Noise.
Noise is two times the root-mean-square of the ten standard deviations (that is, noise = 2·rms
[=E T=7334]σ) when the reference signal is a zero-quantity signal. Refer to the example of a root-mean-square calculation in § 1065.602. We recommend that instrument noise be within the specifications in Table 1 of § 1065.205.
(10)
You may use a measurement instrument that does not meet the accuracy, repeatability, or noise specifications in Table 1 of § 1065.205, as long as you meet the following criteria:
(i)
Your measurement systems meet all the other required calibration, verification, and validation specifications in subparts D, F, and J of this part, as applicable.
(ii)
The measurement deficiency does not adversely affect your ability to demonstrate compliance with the applicable standards.