# Title 43

## SECTION 3175.135

### 3175.135 Uncertainty determination.

§ 3175.135 Uncertainty determination.(a) Reference uncertainty calculations for each transducer of a given make, model, URL, and turndown must be determined as follows (the result for each transducer is denoted by the subscript i):

(1) *Maximum error* (*E*i). The maximum error for each
transducer is the maximum difference between any input value from
the test device and the corresponding output from the transducer
under test for any required test point, and must be expressed in
percent of transducer span.

(2) *Hysteresis* (*H*i). The testing required in §
3175.132 requires at least three pairs of tests using both
ascending test points (low to high) and descending test points
(high to low) of the same value. Hysteresis is the maximum
difference between the ascending value and the descending value for
any single input test value of a test pair. Hysteresis must be
expressed in percent of span.

(3) *Repeatability* (*R*i). The testing required under
§ 3175.132 requires at least three pairs of tests using both
ascending test points (low to high) and descending test points
(high to low) of the same value. Repeatability is the maximum
difference between the value of any of the three ascending test
points for a given input value or of the three descending test
points for a given value. Repeatability must be expressed in
percent of span.

(b) *Reference uncertainty of a transducer.* The reference
uncertainty of each transducer of a given make, model, URL, and
turndown (Ur,i) must be determined as follows:

(c) Reference uncertainty for the make, model, URL, and turndown of a transducer (Ur) must be determined as follows:

*U*r = s ×

*t*dist Where: s = the standard deviation of the reference uncertainties determined for each transducer (Ur,i) tdist = the “t-distribution” constant as a function of degrees of freedom (n-1) and at a 95 percent confidence level, where n = the number of transducers of a specific make, model, URL, and turndown tested (minimum of 5)

(d) *Influence effects.* The uncertainty from each
influence effect required to be tested under § 3175.133 must be
determined as follows:

(1) *Zero-based errors of each transducer.* Zero-based
errors from each influence test must be determined as follows:

*e.g.,*1,000 psi for static-pressure effects, 50 °F for ambient temperature effects) And: D

*Z*n,i =

*Z*n,i−

*Z*ref ,i Where: Zn,i = the average output from transducer i with zero input from the test device, during the testing of influence effect n Zref,i = the average output from transducer i with zero input from the test device, during reference testing.

(2) *Span-based errors of each transducer.* Span-based
errors from each influence effect must be determined as
follows:

(3) Zero- and span-based errors due to influence effects for a make, model, URL, and turndown of a transducer must be determined as follows:

*E*z,n = sz,n × tdist

*E*s,n = ss,n ×

*t*dist Where: Ez,n = the zero-based error for a make, model, URL, and turndown of transducer, for influence effect n, in percent of span per unit of magnitude for the influence effect Es,n = the span-based error for a make, model, URL, and turndown of transducer, for influence effect n, in percent of reading per unit of magnitude for the influence effect sz,n = the standard deviation of the zero-based differences from the influence effect tests under § 3175.133 and the reference uncertainty tests, in percent ss,n = the standard deviation of the span-based differences from the influence effect tests under § 3175.133 and the reference uncertainty tests, in percent tdist = the “t-distribution” constant as a function of degrees of freedom (n-1) and at a 95 percent confidence level, where n = the number of transducers of a specific make, model, URL, and turndown tested (minimum of 5).