Evaluating Uncertainties in Interpolations Between Calibration Data for Thermocouples

Two methods for evaluating thermocouple calibration uncertainty over the temperature range of the calibration are presented, when the thermocouple is calibrated at only a few temperatures. The evaluation of the uncertainty at fixed-point temperatures is well established, but it is often not clear how the uncertainty arising from interpolation between fixed points can be determined. We present a conventional method, based on that described in the “Guide to the expression of uncertainty in measurement” (GUM), and a numerically-based Monte Carlo method, for quantifying the calibration uncertainty arising from the use of an interpolating polynomial defined by calibration data. The two methods are compared and found to be in excellent agreement, but the Monte Carlo method is, in general, more flexible, e.g., when measurements are described by non-normal distributions.