When evaluating the performance of a municipal waste sorting plant, the key metric is the recovery rate — how much of a specific material (e.g., drink cartons, plastics, metals) is successfully separated into product fractions. However, recovery is not directly measured. It is calculated from the mass balance, and therefore, the quality and representativeness of sampling directly shape the reliability of the reported performance.
This article looks at how sampling mass, timing, and frequency affect both the calculated input composition and the recovery value. The examples are based on measured data for drink cartons (DK) fraction from a large-scale municipal sorting facility.
1️⃣ How small are our samples, really?
The plant processes approximately 800 tonnes per day. If a single composite sample of 50–120 kg is taken once a week from the mixed residue + ONF stream, this represents:
Even in the most comprehensive case, the analysis covers only 0.005 % of the weekly throughput — that is five-thousandths of one percent. This scale alone shows why even small inconsistencies in sampling can produce large apparent variations in recovery.
2️⃣ Mass representativeness — what the data shows (drink cartons)
From laboratory data collected across multiple weeks:
The step from 50 kg → 100–120 kg reduces statistical spread by about 20 %. The shift to separate sampling (ONF + Residue) — about 3× total material — cuts uncertainty by more than half, even though the average DK share decreases slightly (from 0.75 % to 0.61 %), leading to more realistic, stable results.
3️⃣ Temporal representativeness — the “snapshot” problem
Most plants perform one sampling day per week, typically on a fixed weekday, due to laboratory schedules. That single day becomes a snapshot rather than an average of weekly operations.
This introduces systematic timing bias, influenced by:
The plant’s condition (before/after cleaning, before/after downtime),
The degree of sensor contamination (especially optical NIR sensors),
Input composition fluctuations between days or shifts.
Thus, a “weekly sample” may actually represent the state of the plant, not the average of the process.
🎯 A consistent weekly snapshot is not a substitute for process representativeness — it only provides stability, not accuracy.
4️⃣ How does this affect recovery?
Recovery (R) is calculated as:
R = (Product mass of the material) / (Input mass of the material)
or, expressed through the mass balance:
R = m_out,DK / (m_in,total × p_in,DK)
Since the input share p_in,DK is derived from sampling, any uncertainty there directly affects recovery.
Assuming that Residue+ONF together represent 75 % of the total input (α = 0.75) and that the “true” recovery is 50 %, the uncertainty range becomes:
The visual below shows the difference clearly:
In other words:
The 50 kg sampling can make a plant appear anywhere between 28 % and 72 % recovery, purely due to sampling noise.
At 3×100 kg, the uncertainty shrinks dramatically, to about ±11 pp (39–61 %).
The “lower but stable” recovery values observed after the sampling reform are therefore more credible, not worse.
5️⃣ Operational and resource constraints
Each residue-stream analysis (~120 kg) requires about one full working day (8 hours) for manual sorting. Therefore:
Three samples per week = ≈ 3 person-days of work;
or for a two-person team, two full working days just to process ONF + Residue samples.
As a result, increasing sampling quantity or frequency inevitably competes with other laboratory duties (e.g., product analyses). There is thus a practical ceiling: for most facilities, 3×100 kg per week is the upper practical limit where the gain in precision still justifies the cost.
6️⃣ The long-term statistical perspective
Sampling error cannot be eliminated — but it can be averaged out. With consistent weekly measurements, the long-term mean converges toward the true process value as random errors balance each other out.
This principle underpins a rational approach:
New facilities: larger or more frequent samples are essential to capture the initial variability and establish a baseline distribution.
Mature facilities: once the process is stable and data follow a normal distribution, less frequent sampling (e.g., every 2 weeks) can still yield reliable averages.
The key is long-term continuity. Random noise cancels out — systematic bias does not. Therefore, process monitoring must include trend tracking and control of operating conditions during sampling.
7️⃣ Putting it together — accuracy, effort, and realism
Bottom line:
Even the best mass balance depends on representative sampling.
A typical analysis covers only 0.001–0.005 % of the actual material flow.
Doubling sample mass or splitting streams provides measurable statistical benefits.
Yet, economic realism defines the true optimum — precision must serve decision-making, not overwhelm it.
🧭 Conclusion
Accurate mass balances require more than weighing and sorting — they require understanding the statistical nature of sampling. A plant’s reported recovery rate is only as good as the representativeness of its input estimation. By combining larger and better-separated samples, controlled timing, and long-term averaging, we move from numbers that are merely precise toward numbers that are true.
