Sampling Meters Across 40 Rooftop Units
A retail chain retrofitted controls and economizers on 40 rooftop units (RTUs) across one store. RTUs range from 5 to 25 tons; 8 units serve the sales floor, 32 serve back-of-house and stockrooms with intermittent occupancy. The M&V plan proposes Option B with a sample of RTUs metered for runtime and fan/compressor kW using logging current transducers and a temperature logger at each unit. Budget supports 10 metered units. The owner asks whether 10 is enough and whether they can just meter the 8 sales-floor units because those are the biggest.
1. Evaluate the proposed sample. Is metering only the 8 large sales-floor units acceptable, and how would you design the sample?
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Metering only the 8 sales-floor units is not acceptable: it is a judgment sample biased toward the largest, highest-runtime units, and the 32 back-of-house units have a different duty cycle. Extrapolating the sales-floor savings per unit to all 40 would overstate savings - precisely the error sampling is meant to prevent.
Design a stratified random sample with strata by size/runtime (e.g., sales-floor vs. back-of-house, or tonnage bands), then randomly select within each stratum. If 10 meters are available, allocate roughly in proportion to stratum energy and variability - e.g., 4 sales-floor and 6 back-of-house - and ensure every stratum has at least 2 units so you can estimate within-stratum variance. Random selection, not convenience, is what makes the extrapolation defensible. Document the stratification, the random draw method, and the substitution rule if a meter fails.
2. What statistical statement must accompany the extrapolated savings, and what if the resulting precision is unacceptable?
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You must report savings with a confidence level and precision - e.g., 'savings = 210,000 kWh ± 38,000 kWh at 90% confidence' - using the sample standard deviation and the finite-population correction for sampling without replacement from 40 units. Do not report a bare point estimate.
If precision is unacceptable (say the half-width exceeds ~20–30% of the savings), options in order of preference: (1) increase the sample size or reallocate meters to the highest-variance stratum; (2) meter continuously for a shorter, well-chosen period and use the sample to calibrate an engineering model for the unsampled units; (3) reduce the boundary to the metered units and report savings only for those, explicitly excluding the rest; (4) fall back to Option A with stipulated savings for the unsampled units, clearly labeled as stipulated. Never quietly widen the confidence interval in the text and call it a point estimate.