MEGR 3171  ·  UNC Charlotte Weekly Course Guides
Dr. Roger Tipton
Mechanical Engineering & Engineering Science
Week 3 of 15 MEGR 3171  ·  Module 1: Precision Measurement & Signal Science

Uncertainty Analysis & Calibration

Quantify how errors propagate through multi-variable engineering models and document a complete sensor calibration — two skills every practicing measurement engineer must master.

Module 1  Precision Measurement & Signal Science Alciatore Ch. 3
Semester Progress
Week 3 / 15

Overview

Week 3 at a Glance

Week 3 is the analytical core of Module 1. You will learn the Kline-McClintock method for propagating uncertainty through any equation that combines multiple measured quantities, and you will perform a complete sensor calibration that connects your hardware measurements to a traceable reference standard.

By the end of this week you can answer the question that defines credible engineering measurement: "Given my instruments and my method, what is the uncertainty in my final result?"

Kline-McClintock methodSingle-sample uncertaintyMulti-sample uncertaintyCalibration proceduresStandards and traceabilityUncertainty reporting
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Why it matters in practice. The Kline-McClintock method is used in every engineering test report, journal article, and product validation document. If you cannot propagate uncertainty, you cannot publish or certify a measurement result.

Objectives

What You Will Be Able to Do

Course objectives (CO) define program-level skills. Module objectives (MO) define specific weekly targets that build toward them.

Course Objectives (CO)

CO1: Quantify and correctly report measurement uncertainty using the Kline-McClintock method for multi-variable models.
CO2: Teach students techniques for designing and conducting laboratory experiments.

Module Objectives (MO) — Week 3

Apply the Kline-McClintock formula to propagate uncertainty through a multi-variable expression.
CO1
Distinguish between single-sample and multi-sample (repeated-measurement) uncertainty estimates.
CO1
Perform a multi-point sensor calibration and compute a calibration curve with associated uncertainty.
CO1
Explain the hierarchy of measurement standards (primary, secondary, working) and the concept of metrological traceability.
CO1
Format and report measurement results in compliance with standard engineering conventions.
CO2
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Review these objectives before you start each assignment. They map directly to what is assessed on the quiz, homework, and exams.

Suggested Learning Path

How to Work Through This Week

Follow this sequence. Each step prepares you for the next. Do not attempt graded work before completing the instructional material it depends on.

1
Read Alciatore Ch. 3
Sections 3.1-3.4 are essential. Work through Example 3.2 (uncertainty in a resistance measurement) by hand before lecture — it is the template for every Kline-McClintock problem in the course.
2
Attend Lecture
Lecture 1 covers the Kline-McClintock derivation and worked examples. Lecture 2 covers calibration procedures and standards. The problem session includes a full uncertainty propagation problem.
3
Complete the Lab Calibration Exercise
This week's lab anchors the Kline-McClintock method to your actual Arduino sensor. You will calibrate a sensor against a reference and report the result with full uncertainty analysis.
4
Begin Module 2 Homework
Module 2 Homework problems build directly on the uncertainty methods introduced this week. Starting now gives you time to ask questions before the due date.

Instructional Material

Required Readings, Videos, and Resources

Complete all required items before moving to graded activities. The Aligns to column maps each resource to the module objectives it directly supports.

ResourceWhat You Will GainAligns toEst. Time
Read
Alciatore Ch. 3 — Measurement System Behavior (Uncertainty) (5th Ed.)		 Kline-McClintock derivation, single-sample vs. multi-sample strategies, and formal uncertainty reporting conventions. MO1-MO5 60-75 min
Lab
Lab Exercise: Arduino Sensor Calibration		 You will calibrate one sensor from your Arduino kit against a reference standard, compute a calibration curve, and report the result with Kline-McClintock uncertainty bounds. MO3, MO5 ~2 hr lab
Explore
JCGM 100:2008 — Guide to the Expression of Uncertainty in Measurement (GUM)		 The international standard for uncertainty analysis. The approach taught in this course is directly aligned with the GUM framework. MO4 Optional

Graded Learning Activities

Assignments and Due Dates

All graded work is submitted through Canvas. Complete the listed prerequisites before attempting each assignment.

AssignmentPrerequisitesWhat Is AssessedAligns toPoints
Module 2 Homework: Uncertainty Analysis
End of Week 4		 Complete Ch. 3 reading and attend both lectures before starting the uncertainty propagation problems. Kline-McClintock calculations on multi-variable engineering expressions, calibration curve fitting, and formal uncertainty reporting. MO1-MO5 50 pts
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Academic integrity. Your calibration data must come from your own hardware run during the scheduled lab period. Reference values must be traceable to the lab equipment provided — do not substitute values from a datasheet or another student's lab session.