Error Propagation Calculation Chain

validated scientific chain v1.0.0 cc-by-sa

Block ID: bfae8bc1-0155-4057-887f-694fb4ded7ec

Community-contributed block. PromptDNA makes no guarantee of output quality or fitness for purpose. User assumes all responsibility for use.

Template

Propagate measurement uncertainty through the calculation described in {measurement_context}. Work stepwise: (1) List each measured quantity with its value, uncertainty, and how that uncertainty was determined — instrument resolution, statistical spread of repeats, or manufacturer specification — because the source dictates whether it's treated as standard uncertainty directly or needs conversion. (2) Classify uncertainties as Type A (statistical, from repeated observations) or Type B (systematic or specified), and state any suspected correlations between inputs, since the standard formulas assume independence. (3) Write the functional relationship between inputs and the result symbolically. (4) Apply propagation: for addition/subtraction combine absolute uncertainties in quadrature; for multiplication/division combine relative uncertainties in quadrature; for general functions use the partial-derivative method, showing each sensitivity coefficient. (5) Compute the combined standard uncertainty and, if required, expand with a stated coverage factor. (6) Report the result with uncertainty to appropriate significant figures — the uncertainty itself to one or two digits, the value rounded to match — and identify which input dominates the total, since that's where improvement effort pays.

Propagate measurement uncertainty through the calculation described in {measurement_context}. Work stepwise: (1) List each measured quantity with its value, uncertainty, and how that uncertainty was determined — instrument resolution, statistical spread of repeats, or manufacturer specification — because the source dictates whether it's treated as standard uncertainty directly or needs conversion. (2) Classify uncertainties as Type A (statistical, from repeated observations) or Type B (systematic or specified), and state any suspected correlations between inputs, since the standard formulas assume independence. (3) Write the functional relationship between inputs and the result symbolically. (4) Apply propagation: for addition/subtraction combine absolute uncertainties in quadrature; for multiplication/division combine relative uncertainties in quadrature; for general functions use the partial-derivative method, showing each sensitivity coefficient. (5) Compute the combined standard uncertainty and, if required, expand with a stated coverage factor. (6) Report the result with uncertainty to appropriate significant figures — the uncertainty itself to one or two digits, the value rounded to match — and identify which input dominates the total, since that's where improvement effort pays.

Variables

Name	Type	Required	Trust level
measurement_context		yes

uncertaintyerror-propagationmeasurementchain-of-thought

Ratings

0.0

Overall (0)

0.0

Accuracy

0.0

Consistency

0.0

Clarity

0.0

Efficiency

Benchmarks

Not yet self-validated against any benchmark. Automated, evaluative only - not a factor in whether this block was published.

Submitted by James P FounderMod via mcp · 2026-07-18