MEASURE FOR MEASURE
The Right Number
How many data points do you need for calibration?
by Dilip Shah
Recently, I was asked the following question: "How many data points should I measure when calibrating a voltmeter with a range of 0 to 100 volts?" The person wanted to know the minimum number of data points necessary to calibrate the voltage range to ensure measurement performance of the instrument was characterized correctly and with confidence.
A voltmeter is a device that measures voltage. To calibrate a voltmeter, you need a traceable source device to generate a voltage the voltmeter can measure. Most measurement devices have a variable range of values they can measure. Examples include digital multimeters, micrometers, dial indicators and weighing balances. The source device may be a fixed or a variable range device. Examples of fixed source devices include gage blocks, weights and fixed-value resisters. In the question posed, a variable voltage source device is required for calibration.
Taking measurements during the calibration process consumes time, and time is money. So, understandably, the calibration supplier does not want to make extra unnecessary measurements. But, the supplier also wants to ensure that an adequate number of measurements were made to ensure confidence in the calibration.
It’s important to remember that measurement equipment may behave in a linear manner across its whole range, or it may behave nonlinearly. You may need to extrapolate our measurement assumptions across the range, so it’s crucial that you know how the measurement device behaves. Find this out by taking the adequate number of data points. Consider the following measurement scenarios as examples.
Figure 1 shows a single-point measurement made at the midpoint—at 50 volts on the 0 to 100 volt range. This provides information about that one single point of reference at which the measurement was made. Other conclusions cannot be derived without prior history or performance data.
Figure 2 shows three measurements made at 30, 60 and 90 volts. As the figure shows, there can be three separate inferences made about the linearity of the measurement (not including the best fit line estimation). If the measurement range was nonlinear, it would complicate interpretation of data further.
Figure 3 shows five measurements made at 20, 40, 60, 80 and 100 volts. Making four or five measurements across a range would be the best scenario to determine the confidence in calibration and to interpolate the other values between the range measurements.
When the measurement range is nonlinear, it is important to consider the extreme points in the range aside from the intermediate points. With the advent of computer spreadsheet software, it is easy to chart data, draw trend lines and even generate the equation defining the trend line to make assumptions about how many measurements should be made across the range. Generating the trend line for a nonlinear characteristic of a measurement is a powerful tool that was not readily available in the days before computers (see Figure 4).
To obtain more confidence in the measurement and to get a better trend line prediction, taking repeated measurements at each point is suggested. Usually, three to five repeated measurements are required. Any more than five repeated measurements would not yield any more significant information.
Many calibration certificates list one data point for the full range of a measurement parameter. But realistically, establishing confidence in equipment performance can’t be done based on one data point. If this is the case with your calibration service supplier, you should seriously review the value and adequacy of this data with your calibration supplier to ensure the calibrated item is fit for use for product acceptance within your organization by the end user.
If this is a repeat calibration from a previous one, the calibration supplier also should calibrate the exact point values measured before. For example, if the previous year’s calibration was performed at 20, 40, 60, 80 and 100 volts, the current calibration also should be performed at the same values of 20, 40, 60, 80 and 100 volts. This helps establish a good calibration history of the measurement instrument by making an apples-to-apples comparison of its previous performance.
Calibration suppliers compare the instrument’s value measured against the specification of the measuring instrument. If the "as left" value is out of specification, they may adjust the instrument to bring it within specification. Therefore, it is also a good idea to specify both "as found" and "as left" values, even if no adjustments were made during calibration. Some instruments require a zero check and adjustment before calibrating at the other data points. If that is the case, that also should be reported on the calibration certificate.
As a consumer of calibration services, the end user should be aware of these best practices and specify requirements in advance to its calibration supplier. This helps ensure there is no misinterpretation on what is required and any questions can be clarified before actually calibrating the instrument.1
- Dilip Shah, "Supplier Demand," Quality Progress, May 2010, pp. 48-50.
Dilip Shah is president of E = mc3 Solutions in Medina, OH. He is the past chair of ASQ’s Measurement Quality Division and past chair of Akron-Canton Section. Shah is also co-author of The Metrology Handbook (ASQ Quality Press, 2012), an ASQ-certified quality engineer, quality auditor, calibration technician and an ASQ fellow.