Follow these 7 steps to make sure your measurements are reliable.

The test accuracy ratio (TAR) has long been included in the study and practice of metrology, but as we saw previously, TAR works for sticky electronics problems, too. As a practicer and professor of electronics engineering, I’ve revealed this to colleagues and students alike.

One day, having finished teaching my engineering courses, I reported to Sundstrand Aerospace to work on my latest engineering assignment. I was filling out a progress report at my desk when I looked up to see my former cubemate Joe with two other fellows. Joe flashed a toothy smile, but his companions looked grim—the same expression you see on the faces of patients waiting in the dentist’s office on “root canal day.” Quite a tooth contrast.

Joe started the conversation with, “Hello professor!”

“Good morning,” I countered. “What’s up?”

Joe said, “This is Rick and Dave. They are responsible for the DMM in our measurement system. I explained the TAR analysis for the current shunt to them, but they have more questions.”

*See: Making Sense of Shunt Sensors: All Your Questions Answered*

Dave started, “Before you go farther, what is the point of all of this extra work to do a TAR analysis?”

I replied, “An excellent question!”

### The TAR Process

In general, a TAR analysis demonstrates due diligence in the design effort and promotes a systematic method to uncover anything that might threaten the design solution integrity. Should a catastrophic event ever occur because of a hardware failure, we do not want it to be because we provided a questionable measurement.

The TAR process consists of seven steps (illustrated in the image below):

- First, we must understand the unit under test (UUT) specifications.
- We must take steps to minimize the effects of noise and loading. This might mean using a twisted, shielded pair, including an instrumentation amplifier, and possibly an active filter.
- Steps must be taken to make sure we understand the manufacturers instrument specifications. This might require a conversation with an application engineer.
- We need to determine the appropriate probability distribution and compute the standard error. The common possibilities include the uniform distribution, the triangular distribution and the normal distribution.
- We must use the root sum of squares to combine the random variables.
- When combined, the uncertainties form a normal (Gaussian) probability distribution. The coverage factor is the number of standard deviations about the mean.
- The last step is to use the ratio of the specification to measurement system accuracy to find the TAR. To be acceptable, the TAR must be four or greater.

With a look of worry, Dave declared, “Wow, this is a lot to absorb!”

I told Dave I had several copies of the sketch for him to use as a roadmap. Dave muttered softly, but audibly, “Looks like the roadmap to hell.” I appreciated his not-so-silent comment and smiled.

### The DMM Acuracy Versus Time

Dave would be using a Keithley Model 2000 6.5-digit DMM. A partial datasheet is shown below:

We use the one-year accuracy specification on the DMM assuming a triangular probability distribution. According to the National Institute of Standards and Technology (NIST), the triangular distribution is a reasonable default model in the absence of any other information.

The nominal DMM input voltage across the shunt is 40mV when 60A flows through it. This means the 100mV scale of the DMM should be used. This is the one-year accuracy assuming the DMM temperature is 23^{o}C ± 5^{o}C. We determine the uncertainty according to the datasheet.

We shall designate a_{DMM_time} as the maximum variation due to time.

The standard error is found assuming we have a triangular probability distribution.

The DMM drift over one year contributes very little to the overall measurement uncertainty.

### The DMM Acuracy Versus Temperature

Another portion of the Keithley 2000 datasheet is shown below:

Ambient temperature is taken to be 23^{o}C. The data sheet indicates no temperature correction is required if the DMM temperature is 23^{o}C ± 5^{o}C. To be conservative, we apply the 28^{o}C to an 80^{o}C temperature coefficient. We’ll designate the amplitude of the deviation produced by temperature a_{DNN_temperature}.

Temperature effects have a rectangular probability distribution. So, next we find the standard error *u _{j(DMMtemperature)}*.

### The Combined Uncertainty

The combined uncertainty is the root sum of squares of the individual uncertainties from the sensor to the readout. The sensor uncertainties are *u _{j(tolerance)}* = ± 0.0231mV and

*u*

_{j(temperature}_{)}= ±0.0156mV. The DMM

*u*is 0.00225mV and

_{jDMMtime}*u*is 0.000293mV. The root sum of squares is used to find the combined uncertainty

_{jDMMtemperature}*u*.

_{j(combined)}### Applying the Coverage Factor

The sixth step in the TAR process defines the coverage factor *K*. The coverage factor refers to the number of standard deviations (standard errors) about the mean (nominal value). If we can use *K* = 3, we will have a 99.73 percent confidence interval. If we cannot achieve that, NIST permits us to use a coverage factor of 1.96, which results in a 95 percent confidence interval. Let’s use *K* = 3.

*Ku _{j(combined)}* = (3)(0.027966 mV) = 0.0839 mV

### Finding TAR

The final step in the process is to calculate the TAR:

The rather expensive (oops, the important investment) Keithley DMM contributes little to the overall measurement uncertainty.

Dave interrupted: “I am not sure why 2mV is used as the specification limit.”

“I got this, professor,” Joe chimed in. “We are supposed to verify a current of 60A ± 3A, and with a 150A, 100mV shunt we have (3A)(0.1V/150A) = 2mV.”

“Joe, did you check your email this morning?” Dave asked, and explained the converter/regulator design group needed to change the specification to 60A ± 1.5A. Joe’s face paled.

“Before we panic, let’s run the numbers,” I suggested. “The new specification limit is 1mV and our measurement system accuracy is the same. Our TAR will be one-half its previous value or 11.9, which is still greater than 4. We’re good!”

All three were now grinning. As they began to walk away, Dave looked over his shoulder and said, “You know, maybe this TAR stuff is not as bad as I thought. Thanks, professor!”