Measurement-based methane inventories, where oil and gas facilities are surveyed and these data are compiled to estimate total methane emissions, are becoming the gold standard for quantifying emissions. There is a current lack of statistical guidance for the design and analysis of such surveys. The only existing method is a Monte Carlo (MC) procedure which is difficult to interpret, computationally intensive, and open-source code for its implementation is not available. We provide an alternative method by showing that a methane survey corresponds to a multi-stage sampling design. We present estimators of the total emissions and its variance which do not require simulation. We show that the variance contribution from each stage of sampling can be estimated and can inform the design of future surveys. We also introduce a modification of the estimator which is more efficient. Finally, we propose combining the multi-stage approach with a simple MC procedure to model measurement error.