Rational approaches for combining redundant, independent measurements to minimize combined experimental uncertainty

General methods for combining multiple, independent measurements for minimized uncertainty are presented. Although the methods are general, the presentation is motivated by the reduction of heat exchanger performance data. It is demonstrated that the prevalent practice of using the arithmetic mean of two measured heat transfer rates for the evaluation of heat exchanger performance, which is widely adopted in the literature and used in engineering standards, does not always lead to reduced experimental uncertainty and very rarely—if ever—leads to a minimized experimental uncertainty. For the case of averaging two redundant measurements, simple criteria are developed to determine whether using the arithmetic mean or a single measurement yields a smaller absolute or relative uncertainty. Then, more general methods are proposed in the form of weighted-linear averages, in which the weight factors are determined to minimize the combined uncertainty. The methods are generally applicable to averaging any number of redundant measurements with varying uncertainties.