/ TECHNICAL NOTE

Understanding Measurement Performance and Specifications

The quality of a measurement device is often evaluated by a simple question: How REPEATABILITY accurate is the measurement? While this question seems NON-LINEARITY & simple enough, the answer HYSTERESIS PRECISION may not always be. ACCURACY LONG-TERM STABILITY Choosing the most suitable measurement instrument CALIBRATION REFERENCE requires an understanding UNCERTAINTY of the factors that contribute to the uncertainty of a measurement. This in turn provides an understanding

of what is stated in the Specified accuracy usually includes Repeatability specifications – and what repeatability, which is the capability is not. of the instrument to provide a similar result when the measurement is repeated under constant conditions. The performance of a measurement (Figure 1) However, it may or may not is defined by its dynamics include the hysteresis, temperature

(measurement range, response time), dependency, non-linearity, and long- Measured accuracy (repeatability, precision, term stability. Repeatability alone is and sensitivity), and stability often a minor source of measurement (tolerance for aging and harsh uncertainty, and if the accuracy environments). Of these, accuracy specification does not include other Actual is often considered to be the most uncertainties it may give the wrong important quality; it is also one of the impression of the actual performance Figure 1: Repeatability most difficult to specify. of the measurement. The relationship between the Ideal transfer function Sensitivity and Accuracy measurement values and a known The relationship between the change reference is often referred as the in measurement output and the transfer function. (Figure 2) When

change in reference value is called a measurement is adjusted, this ∆y sensitivity. Ideally this relationship relationship is fine-tuned against ∆x is perfectly linear, but in practice a known calibration reference. Measured all measurements involve some Ideally, the transfer function is Constant imperfections or uncertainty. perfectly linear across the whole sensitivity over full range The agreement of the measured measurement range, but in practice value with the reference value is most measurements involve some Actual often simply called “accuracy”, but change in sensitivity, depending on this is a somewhat vague term. the magnitude of the measurand. Figure 2: Transfer Function This type of imperfection is referred Non-linearity humidity measurement performed as non-linearity. (Figure 3) This in an atmosphere containing certain effect is often emphasized at the chemicals may be affected so that the extremes of the measurement range. measurement is actually influenced It is therefore useful to check if the by the chemicals. This effect may accuracy specification includes be reversible or irreversible. The the non-linearity, and whether or response to some chemicals may be not the accuracy is specified for Measured exceedingly slow, and this cross- the full measurement range. If it is sensitivity to the chemical can easily not, this gives reason to doubt the be confused with drift. An instrument measurement accuracy near the with good selectivity is not affected extremes. Actual by changes in any factors other than Hysteresis is the change in Figure 3: Non-linearity the actual measurand. measurement sensitivity that depends on the direction of the Calibration and change in the measured variable. Uncertainty (Figure 4) This may be a significant Hysteresis If measurement readings deviate cause of measurement uncertainty from the reference, the sensitivity in the case of some humidity of the instrument can be corrected. sensors, which are manufactured This is referred to as adjustment. from material that bonds strongly Adjustment performed at one point to water molecules. If the specified is referred to as offset correction; accuracy does not indicate whether two-point adjustment is a linear Measured hysteresis is included, this source correction for both offset and gain of measurement uncertainty will be (sensitivity). If the measurement left unspecified. In addition, if the has to be adjusted at several points, calibration sequence is made in only this might indicate poor linearity one direction the effect of hysteresis Actual in the measurement, which has to will not be visible during calibration, Figure 4: Hysteresis be compensated for with non-linear and if hysteresis is omitted from the multi-point corrections. In addition, specification, it is also impossible if the adjustment points are the to know the level of hysteresis in same as the calibration points, the measurement. Vaisala thin-film Stability and Selectivity the quality of the measurement polymer sensors have negligible The sensitivity of a measurement between adjustment points remains hysteresis, and this is always device may change over time unverified. included in the specified accuracy. due to aging. In some cases this Once the instrument has been Ambient conditions such as effect may be accelerated by adjusted, it is calibrated to verify temperature and pressure also affect interference from chemicals or other its accuracy. Calibration, which is the accuracy of a measurement. environmental factors. If the long- sometimes confused with adjustment, If the temperature dependency is term stability is not specified, or if means comparing the measured not specified and the operating the manufacturer is unable to provide value with a known reference, called temperature changes significantly, recommendations for the typical a working standard. The working repeatability may be compromised. calibration interval, the specification standard is the first element in the The specification may be given only actually indicates the accuracy traceability chain, which means the for full operating temperature, or at the time of calibration. A slow series of calibrations and references for a specific, limited, or “typical” change in sensitivity (sometimes up to the primary standard. Whereas operating range. Specifications referred to as drift or creep) is a number of instruments calibrated expressed in this way leave other harmful because it may be difficult against a certain reference may be temperature ranges unspecified. to observe and might cause latent accurate in relation to each other problems in control systems. (high precision), the absolute Selectivity is defined as the accuracy with regards to the primary instrument’s insensitivity to standard cannot be verified if changes in factors other than the the calibration uncertainty is not actual measurand. For instance, specified. Traceability of calibration means long-term stability (precision) are the calibration uncertainty was ±1.6 that the chain of measurements, important, but absolute accuracy %RH, the total uncertainty with references, and related uncertainties against a traceable reference is less regards to the primary calibration up to the primary standard is known significant. This is especially the standard would exceed the and professionally documented. This case in a dynamic process, where specification, and the performed allows calculation of the uncertainty the variations in temperature and analyses – which are heavily of the calibration reference and humidity are large and the stability dependent on ambient humidity determination of the instrument’s of the measurement, rather than inside the testing facility – would not accuracy. absolute accuracy, is crucial. be comparable and it would not be On the other hand, if for example possible to confirm that the analyses What Is “Accurate the measurement is used to verify were performed under standard enough”? that the testing conditions inside a conditions. When choosing a measurement laboratory are comparable with other Accuracy specification alone, without instrument, it is necessary to laboratories, the absolute accuracy information about the calibration consider the level of accuracy and traceability of calibration is of reference uncertainty, leaves the required. For instance, in standard utmost importance. An example of absolute accuracy of the instrument ventilation control applications such an accuracy requirement is undefined. where relative humidity is adjusted in the standard TAPPI/ANSI T402 Vaisala takes pride in providing for human comfort, ±5 %RH might – Standard conditioning and testing professional and comprehensive be acceptable. However, in an atmospheres for paper, board, pulp specifications that are based on application such as cooling tower handsheets, and related products, international standards, scientific control, more accurate control and which defines the testing condition testing methods, and empirical smaller margins are required to in a paper testing laboratory data. For customers this means increase operating efficiency. as 23 ±1,0 °C and 50 ±2 %RH. If comprehensive and reliable the specified accuracy of the When the measurement is used as information that supports them in measurement was e.g. ±1.5%RH but a control signal, repeatability and making the correct product choices.

Product Vaisala HMT330 Brand A Brand B

Accuracy at room temperature ±1.0 %RH (0 … 90 %RH) ±0.8 %RH, at 23 °C ±1.3 %RH, at 23 °C ±1.7 %RH (90 … 100 %RH) at +15 … +25 °C (+59 … +77 °F)

Full temperature range accuracy ±(1.5 + 0.015 x reading) %RH Unknown Unknown

Repeatability Included in above figure Unknown Unknown

Hysteresis Included in above figure Unknown Unknown

Non-linearity Included in above figure Unknown Unknown

Calibration uncertainty ±0.6 %RH @ 0 … 40 %RH Unknown Unknown ±1.0 %RH @ 40 … 97 %RH temperature ± 0.10 °C (±0.18 F°)

Figure 5: Comparison of accuracy information in specifications of three different brands of high-accuracy humidity transmitter. Questions to Ask when Choosing an Instrument

• Does the specified accuracy • Is the manufacturer able to provide • Is the recommendation for the include all possible uncertainties: a proper calibration certificate? calibration interval given, or is the repeatability, non-linearity, Does the certificate include long-term stability included in the hysteresis, and long-term stability? information on the calibration accuracy specification? What level • Does the specified accuracy cover method, the references used, and of selectivity is required in the the full measurement range, professionally calculated reference intended operating environment? or is the range for accuracy uncertainty? Does the certificate Is the manufacturer able to provide specification limited? Is the include more than one or two information on, or references for, temperature dependency given calibration points, and is the whole the instrument’s suitability for in the specification, or is the measurement range covered? the intended environment and temperature range defined in the application? accuracy specification?

Glossary Measurement accuracy: Closeness of agreement between a measured quantity value and a true quantity value of a measurand.

Measurement precision: Closeness of agreement between indications or measured quantity values obtained by replicate measurements. Sometimes erroneously used to mean measurement accuracy. Hysteresis: A variation in measurement induced by a direction change.

Non-linearity: A change in measurement sensitivity with regards to the magnitude of the measurand.

Calibration: The comparison of a measurement value against a reference or calibration standard.

Calibration uncertainty: The cumulative sum of measurement uncertainty for the calibration reference along the traceability path from the used calibration reference (working standard) up to the top-level reference (primary standard). Adjustment: The adjustment of the transfer function against a calibration standard. Adjustment at more than two points along the dynamic range indicates poor linearity of the measurement device. Metrological traceability: Property of a measurement result whereby the result can be related to a reference through a documented, unbroken chain of calibrations, each contributing to the measurement uncertainty. Sensitivity: A relation between the indication of an instrument and the corresponding change in a value of a quantity being measured. Selectivity: Independence of a measurement system for changes in other factors than the measurand (environmental variables, chemicals etc). Resolution: The smallest change in measured quantity that causes perceptible change in measurement indication. In electronic instruments, the resolution may be affected by analog output stage resolution and scaling. Stability: Property of a measuring instrument, whereby its metrological properties remain constant over time.

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