Independent Order Error Compounding Calculator

Method, formula and assumptions

With independent equally accurate lines, all-correct probability = per-line probability^lines. At-least-one-error probability is its complement; multiply by orders and entered error cost for expectations.

Input definitions and supported units

• Per-line correctness probability (%): Measured or assumed numerical value, from 0 to 100; zero is supported where the stated method permits it.
• Lines per order: Whole-number count, from 1 to 10000; must be positive.
• Orders in wave: Whole-number count, from 0 to 1000000; zero is supported where the stated method permits it.
• Entered cost per erroneous order: Measured or assumed numerical value, from 0 to 1000000; zero is supported where the stated method permits it.

Worked example with answer

99% correctness per line across ten lines gives 90.4382% all-correct orders and 9.5618% with an error. In 1,000 orders, expected erroneous orders are 95.6179 and expected handling cost is 956.1792 at 10 each.

How to use the results

The result distinguishes line accuracy from complete-order accuracy. Expected erroneous orders are fractional across repeated comparable waves.

Results retain full precision internally and display up to four decimal places. Very small nonzero results use scientific notation rather than appearing as zero. Check the labels before comparing values across units.

Limitations and references

Independence often fails when errors share SKU, picker or system causes. This is a stated probability model, not a measured quality forecast or staffing target.

The method is a self-contained arithmetic, geometric or explicitly stated mathematical model. There are no imported tariffs, empirical presets or equipment specifications; measured values and allowances must come from your own process.

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• Order Unit and Line Fill Rate Calculator
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