DAY 19 — Sensitivity Coefficients

What is the main topic of Day 19?

Sensitivity Coefficients

What is a sensitivity coefficient?

A sensitivity coefficient describes how much the output changes when an input changes

What is the sensitivity coefficient formula?

c_i = ∂f/∂X_i

What does the measurement model show in relation to sensitivity coefficients?

It shows how the input quantities are mathematically related to the output

What measurement model is shown?

Y = f(X₁ X₂ ... Xₙ)

Why do sensitivity coefficients matter?

Not every input affects the result equally

What does a sensitivity coefficient show about an input?

It shows how strongly that input influences the measurement result

What question can help interpret a sensitivity coefficient?

How strongly does this input affect my measurement result?

What should come first according to the Day 19 workflow?

The measurement model

What should come after the measurement model?

Sensitivity coefficients

What is the basic sensitivity coefficient formula repeated in Day 19?

c_i = ∂f/∂X_i

Where is the partial derivative evaluated?

At the relevant input estimates

Which GUM reference is given for the basic sensitivity coefficient?

GUM 5.1.3

How can a sensitivity coefficient be understood as a slope?

For a small input change Δy_i = c_iΔx_i

What does a larger magnitude of c_i mean?

The output is more sensitive to that input at the evaluation point

What simple example is given?

Y = 2X + C

What is c_X in the simple example?

c_X = 2

What is c_C in the simple example?

c_C = 1

What does the simple example demonstrate?

The output changes twice as much for a change in X compared with C

What does c_X = 2 mean when X changes by 0.01 °C?

ΔY = 2 × 0.01 °C = 0.02 °C

What does a small change in X produce when c_X = 2?

About twice that change in Y

Is a sensitivity coefficient the same as uncertainty?

No

Is a sensitivity coefficient accuracy?

No

Is a sensitivity coefficient tolerance?

No

Is a sensitivity coefficient error?

No

What does a sensitivity coefficient describe?

The relationship between an input and the output

Is a sensitivity coefficient automatically dimensionless?

No

What determines the units of a sensitivity coefficient?

The output unit divided by the input unit

What unit example is shown for a sensitivity coefficient?

°C/°C = 1

Can other measurement models have different sensitivity-coefficient units?

Yes

How does a sensitivity coefficient transfer input uncertainty to the output?

u_i(y) = c_i u(x_i)

What does the sensitivity coefficient tell us in uncertainty evaluation?

It tells us how the input uncertainty is transferred to the output

Which GUM reference is given for the uncertainty contribution relationship?

GUM 5.1.3

Can a sensitivity coefficient be measured experimentally?

Yes

What experimental approach is described?

Change one input hold other inputs constant and observe the output change

What can the experimental approach provide?

An empirical sensitivity coefficient

Which GUM section is cited for the experimental approach?

GUM 5.1.4

What do sensitivity coefficients describe around the evaluation point?

The behavior of the measurement function

What warning is given about nonlinearity?

If nonlinearity is significant a simple first-order approximation may not be sufficient

What should be checked when nonlinearity is significant?

Whether the model is appropriate for the measurement

What references are listed for Day 19?

GUM JCGM 100:2008 Sections 5.1–5.1.5 and JCGM 100:2008/Amd.1:2026 on nonlinearity in measurement models

What mindset question is recommended besides What is the uncertainty?

How strongly does each input affect my result?

What warning is given about a small uncertainty?

A small uncertainty can still matter if its sensitivity is high

What technical challenge is given on Day 19?

For Y = 3X + C what is the sensitivity coefficient for X?

What witty challenge is given on Day 19?

If c_X = 100 should your uncertainty budget panic?

What should the witty challenge make you consider?

Why the magnitude of a sensitivity coefficient matters when considering how an input affects the result