# Process variables and the art of calibrating instruments

## Designing and validating procedures for device calibration.

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Let’s start with the basics of calibration: the output of an instrument is measured under one or more known conditions (for example, the current output of a pressure transducer may be measured at 0 and 100 psig), and then a function of the sensor output (typically a linear function, so just a slope and an intercept) is generated to calculate the measured value of the sensor anywhere in that measurement range by knowing the output of the sensor.

Theoretically, in the example of a pressure transducer, this means that you can throw a digital multimeter (DMM) on a transducer and measure it sitting in the open, connect it to a shop air line, measure it with the DMM again, and be done after the calculation of the slope and intercept of the line that you draw through the points on a pressure vs. output current plot. However, there are critical points for not only performing a good calibration, but also making sure that it remains good:

• The stimulus (input—pressure, temperature, flow) is very accurately known.

• The calibration procedure yields repeatable and reproducible results.

• The stimuli/conditions are stable.

• The conditions represent the entire test range (if you expect to measure 0-100 psig on your test system, then you should calibrate at or near 0 and 100 psig) and test the sensor linearity.

• The calibration is performed under the same conditions as the measurement is made using the test system.

• The analysis is performed correctly, with passing and failing criteria.

Let’s step through each of these and discuss how they are relevant to a cleaning skid, so that we can build an effective and efficient calibration procedure. I’ll spend the most time on the first two topics, as they are arguably the most important, as well as a good chunk of time on the last topic, as I feel that it’s often overlooked. I’ll be using flow meters, pressure transducers, and thermocouples as examples.

Before diving into the details, first determine what your measurement accuracy must be, as calibration accuracy has a huge influence on measurement accuracy.

### The stimulus (input) is very accurately known

Accurately knowing what you’re measuring is possibly the single most important point when it comes to calibration because the instrument being calibrated will carry whatever this error is (difference between what you think you’re measuring during calibration and what you’re really measuring) into the test system. Simply stated, if you think you’re measuring 100 psig in calibration, but the pressure is really 98 psig, you’ll report 98 psig whenever the pressure in your system is actually 100 psig, even if you’ve done everything else perfect.

I will also mention here that, in your analysis, you should always use the exact measured stimulus and sensor output values in your calibration calculations and analysis. The way I see this not implemented is when the procedure calls for nominal data points every so many psig, sccm or degrees at some sensor output current. It’s only important that you hit these points very approximately, but if you’re going through the trouble of measuring exact quantities, use the exacted measured quantities, not some nominal value a procedure calls for.

Putting the calibration into the software is probably the single best thing you can do for repeatability and reproducibility.

This typically stipulates that a known, accurate reference instrument (often informally called a “golden unit”) must be used in the calibration setup to be measured alongside the sensor you’re calibrating, or the device under calibration (DUC), or at least be used somewhere in your overall calibration process. Some sensors can be calibrated at some values without one—for example, static torque can be applied using a fixture arm and a weight and then measured by a torque cell, and there are some “stakes in the ground,” such as the density of water—however, in many industries, these gems are few and far between. These are also how primary standards are generated.

Golden units are typically only used for calibration in order to minimize usage and therefore decrease the probability of breaking them, and furthermore are stored in a safe place when not in use. As you can probably imagine, a faulty golden unit can cause quite a stir, as it serves as your “sanity check,” and for this reason many labs calibrate reference sensors (think of them as clones of your golden unit) off of a single golden unit. Typically, these references are used when either running a test that requires a reference instrument or to calibrate test systems, and the golden unit is only used to calibrate the references monthly, or less frequently.

You may hear the terms “primary,” “secondary” and “working” standard. A primary standard is a sensor that is calibrated against some known stimulus, boiling down to manipulating quantities like mass, time and length, if possible, instead of another sensor—so instead of minimizing calibration error due to the stimulus being unknown, this error is removed entirely. Secondary and working standards are sometimes, but rarely, used interchangeably in the context of calibration standards, but the secondary standard usually implies a much closer approximation or much more similarity to some primary standard, as more care is taken to keep them in consistently the same working condition, often implying far less usage than a working standard.

Having a single golden unit is common because it’s usually either costly, time-consuming or both to maintain a sensor’s golden status. “Golden” may also imply that it’s a primary standard, but not always. A typical process may be to send it to the manufacturer or other third-party calibration lab annually (the costs are typically paid by you if they do this, and it’s often not cheap), with the device being gone for about six weeks. Whenever the golden unit is recalibrated, the references should be recalibrated against it. The best way to do this, to avoid tolerance stacking, is to calibrate all references against the golden unit in the same calibration run, compared to calibrating Reference A against the golden unit, then calibrating Reference B against Reference A, then Reference C against Reference B, D against C, and so on. In the latter case, the error accumulates run to run.

A golden sensor doesn’t necessarily have to be a more accurate or precise model compared to the sensors it is used to calibrate, but you need to be assured, somehow, that its reading is accurate (so, at the same time, more accurate and precise doesn’t hurt). If the sensors you are calibrating are known to be not so great when it comes to accuracy or precision, then you probably need a nicer-model sensor for the golden unit. It may be worth it, for example, if your pressure-measurement accuracy requirement is tight and your boss’ or customer’s pockets are deep enough, to shell out for a few very nice pressure gauges or transducers.

I swear by Ashcroft for gauges and Druck for transducers, if you’re able to find them, as they’re not commercially available in the United States anymore.

So, armed with a golden reference sensor, how do you induce some meaningful condition for calibration?

Establishing some stimuli, such as pressure, is relatively easy—simply measure the DUC on a vessel with a vent or other outlet open, or with the transducer off of the vessel at ambient pressure, then attach the DUC and golden transducer, pressurize the vessel, wait for stabilization and measure. To get your in-between points, use a pressure regulator or pump attached to the vessel.

Establishing some stimuli, such as a stable, accurately known flow, can be difficult. However, establishing a known volume or mass and a known period of time is significantly easier. By definition, flow is how much mass or volume is passed in how much time, so most flow meters are calibrated by passing a known volume of fluid through the meter over a known period of time, and then sensitivity is calculated, assuming volume, as:

Think simple, like pouring water from a beaker or bucket into a funnel and through a flow meter, or into a system with a flow meter. If your fluid is a gas, you can use a similar approach with a known volume or mass over time, but the implementation isn’t as simple, of course. Using this method, maintain a steady flow over the course of the measurement period, and use a high sampling rate, if possible. Both will minimize the effect of transients—spikes and dips in the real flow—not being measured.

With flow meters, it’s important to use the same or similar fluid that will be measured in the test system, as viscosity, density and temperature will all affect a flow measurement. This may be a matter of starting the data acquisition at, say, 20 Hz, and then pouring exactly 1 gal of water into a funnel and through the meter and then terminating the acquisition. When you’re using a 4-20 mA output sensor, this implies that there’s some non-zero nominal offset at zero flow, so you should also perform a null measurement, in which you measure the output of the flow meter with zero flow for some period of time and then take the average, which is the term in the equation above.

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