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Sensor Accuracy Budget

Calculate total sensor system accuracy using RSS and worst-case methods from offset, gain, nonlinearity, resolution, and temperature drift errors.

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Formula

e_RSS = √(e₁² + e₂² + ... + eₙ²)

e_WC— Worst-case: sum of all errors (% FS)
e_RSS— RSS: root-sum-square (% FS)

How It Works

A sensor accuracy budget is a systematic analysis of all error sources in a measurement chain and their combined effect on total system accuracy. Individual error terms include: offset error (zero shift from ideal), gain/sensitivity error (slope deviation), nonlinearity (deviation from a straight line), resolution (quantisation or noise floor), and temperature drift (change in any parameter with temperature). Two combination methods are used: worst-case (sum of all absolute errors) assumes all errors are simultaneously at their maximum and in the same direction — it gives a guaranteed bound but is overly conservative. RSS (root-sum-square) treats each error as statistically independent and combines them in quadrature: e_total = √(e₁² + e₂² + ... + eₙ²). RSS gives a realistic estimate for systems where errors are truly independent and uncorrelated; it is commonly used in instrumentation and calibration standards. For safety-critical applications, use worst-case; for system design trade-offs, use RSS as a working estimate.

Worked Example

Problem
A temperature sensor system has: offset = 0.2% FS, gain error = 0.3% FS, nonlinearity = 0.1% FS, resolution = 0.05% FS, temperature drift = 0.01% FS/°C over 25 °C range. Calculate total accuracy.
Solution
1. Temperature error: e_temp = 0.01 × 25 = 0.25% FS 2. RSS total: e_RSS = √(0.2² + 0.3² + 0.1² + 0.05² + 0.25²) = √(0.04 + 0.09 + 0.01 + 0.0025 + 0.0625) = √0.205 = 0.453% FS 3. Worst-case total: e_WC = 0.2 + 0.3 + 0.1 + 0.05 + 0.25 = 0.90% FS Result: RSS accuracy ±0.45% FS; worst-case ±0.90% FS. For a 100 °C span, RSS error is ±0.45 °C, worst-case ±0.90 °C.

Practical Tips

  • ✓Identify the dominant error term first — reducing it provides the most system improvement. If temperature drift dominates, adding temperature compensation is more effective than improving ADC resolution.
  • ✓System calibration can eliminate offset and gain errors entirely, leaving only residual nonlinearity and temperature drift in the budget. Always specify post-calibration accuracy.
  • ✓For sensor datasheet comparisons, confirm whether accuracy specs are before or after calibration — some manufacturers specify total error band (TEB) including temperature drift, others specify each term separately.

Common Mistakes

  • ✗Using worst-case for every budget analysis — the worst case for a 10-error system may be 5× higher than RSS, leading to unnecessarily over-specified and expensive components.
  • ✗Forgetting temperature drift as a separate error term — if the operating temperature range is 50 °C and drift is 0.01% FS/°C, the drift contribution (0.5% FS) may dominate all other terms.
  • ✗Treating correlated errors as independent in RSS — if offset and gain both increase with temperature from the same mechanism, they are correlated and must be added directly, not in RSS.

Frequently Asked Questions

Use worst-case for safety-critical applications (medical devices, safety instrumentation), type-approval testing where guaranteed bounds are required, or when errors are correlated. Use RSS for design trade-off studies, component selection, and when estimating the typical accuracy a production system will achieve across its population.
TEB is a single specification used by some sensor manufacturers that encompasses all error sources (offset, gain, nonlinearity, temperature effects) over a specified operating temperature range. It is the maximum deviation from the ideal output at any temperature and pressure combination. TEB = worst-case total error and is the most conservative and useful specification for system design.
% FS (percent of full scale) is the same absolute error regardless of the measured value. It is the standard for sensor specifications. % of reading means the error scales with the measured value (common in multimeters). Convert: absolute error = (% FS / 100) × full-scale range. For a 0–100 kPa sensor, 0.5% FS = 0.5 kPa error at any point in the range.

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