A Closed-Form Solution for Quadratic Distribution Uncetainty from Containment Limits and Probability

Metrologists may obtain Type B uncertainties from such engineering estimates as “The error falls within 2 units 50% of the time.” The procedure requires selecting an appropriate distribution and determining its standard deviation in terms of the containment limits and probability. The latest revision of NCSLI Recommended Practice RP-12, “Determining and Reporting Measurement Uncertainty”, provides such equations for the normal, student’s t, quadratic, cosine, triangular, trapezoidal, u-shaped, and utility distributions. This paper summarizes the Type B estimation procedure, presents the previously unknown quadratic distribution solution discovered during RP-12 development for symmetric, asymmetric, and single-sided containment limits, and gives example uses.