SLVSM33 September 2026 TPS7H6200-SEP
ADVANCE INFORMATION
When combining multiple independent error sources, you can either add them directly (linear/arithmetic sum) or combine them using the root sum square (RSS) method, and the two give very different results. In practice, engineers use linear (worst-case) summation when a specified upper bound on total error is needed in safety-critical or high-reliability applications. While the RSS method is used when a statistically realistic estimate of combined error is more useful, such as when characterizing overall system accuracy under typical operating conditions.
Arithmetic Sum Error
Direct addition simply sums the magnitudes of each error term, which implicitly assumes that all errors are correlated and all occur simultaneously and in the same direction (worst case scenario, see Equation 5). Error sources (like offset, and gain) are typically uncorrelated and random, so the occurrence that all error terms occur at the same time and in the same direction is statistically unlikely.
Applying Equation 5 results in a combined error of 20.5%:
RSS Error
The RSS method, by contrast, calculates the square root of the sum of the squares of each individual error term (see Equation 7), which is the statistically correct way to combine independent, uncorrelated random errors because variances (not standard deviations) add linearly. RSS of the total expected error under normal operating conditions, and the result is always smaller than or equal to the simple linear sum.
Applying Equation 7 results in a combined error of 14.5%