You've probably seen the ‘k value’ in accuracy specifications. But what does it mean? And what's an expanded uncertainty? In this article, we'll explain how expanded uncertainties are calculated and how they relate to expanded accuracy. We'll also show you how to use this information when choosing between different measurement techniques and equipment.
In real-world calibration scenarios, uncertainty is often reported as expanded uncertainty.
Standard uncertainties are calculated based on a mathematical method called the root-sum-of-squares (RSS). This method is used to calculate the uncertainty of measurements made by repeated trials under ideal conditions. The standard uncertainty is multiplied by the coverage factor to determine the expanded uncertainty. The coverage factor is referred to as the ‘K value’.
So, how is this K value determined?
Let us assume we have a statistically valid data set, for which when plotting a normal distribution, we achieve a bell-shaped curve, which has a mean of zero and a standard distribution of values below 1. This infers that 68% of data points (or 68% of all possible measurements) lie within one standard deviation above or below the mean.
The coverage factor, or ‘k’ value, determines the confidence in the data points within a certain standard deviation value. For k=1, there is a confidence that 68% of data points lie within one standard deviation, while k=2 means a confidence that 95% of the data points would lie within two standard deviations. Similarly, k=3 means a high confidence value that 99.7% of readings would lie within three standard deviations of the mean.
The optimum value of k is chosen as 2 in real-life industry calculations for accuracy specifications because it states that all the specifications will have to be met in at least 95% of the cases, leaving room for only 5% missed specifications.
Uncertainty is the expected deviation from that target value. Understanding these specifications and calculations can help you make better decisions about measurement needs and choosing the right equipment for your application.