SYE6047 Chap.10 Measurement Systems and Hypothesis Testing
Measurement Systems and Hypothesis Testing
Observed variation has two sources
An observed measurement combines variation in the item or process with variation introduced by the measurement system. The system includes the standard, workpiece, instrument, appraiser, procedure, environment and assumptions.
Improvement decisions are unreliable when measurement error is large relative to the distinction the team wants to make.
Accuracy through bias, stability and linearity
Bias is the difference between the average observed value and an accepted reference. Stability asks whether that bias remains consistent over time. Linearity asks whether bias changes across the instrument's operating range.
A gauge may be accurate near one reference but biased at another, so one calibration point cannot establish linearity.
Precision through repeatability and reproducibility
Repeatability is the variation when the same appraiser measures the same characteristic repeatedly with the same method and instrument. Reproducibility concerns differences among appraisers or other stated conditions.
Gage R and R studies deliberately cross parts, appraisers and repeat trials so those components can be estimated rather than guessed from one pair of readings.
Hypotheses make the decision rule explicit
A statistical test states a null hypothesis, an alternative, a significance level and a test statistic.
A two-sided alternative places rejection regions in both tails; a directional claim uses one tail only when justified before the data are examined. Rejecting the null means the data are sufficiently inconsistent with it under the method. Failing to reject does not prove equality, and statistical significance does not by itself establish practical importance.
What this chapter covers
- 01
Measurement system components
- 02
Bias
- 03
Stability
- 04
Linearity
- 05
Repeatability
- 06
Reproducibility
- 07
Null and alternative hypotheses
- 08
One-tailed and two-tailed decisions
Worked example · free
Choose the test before reading the result
- 3State hypotheses and decision rule.
- 4Calculate the z statistic.
- 5Reach and qualify the decision.
Key terms
- Measurement Bias
- The difference between the average observed measurement and an accepted reference value.
- Stability
- Consistency of measurement bias or performance over time.
- Linearity
- The change in measurement bias across the instrument's operating range.
- Repeatability
- Variation under repeated measurement by the same appraiser and method.
- Reproducibility
- Variation associated with different appraisers or stated measurement conditions.
- Null Hypothesis
- The reference statistical claim tested against a specified alternative.
Measurement Systems and Hypothesis Testing FAQ
Can calibration at one reference prove linearity?
No. It can estimate bias near that reference. Linearity requires reference values across the intended operating range and analysis of whether bias changes with magnitude. Stability also needs repeated checks over time, while reproducibility needs measurements across appraisers or other stated conditions.
Select references that span the actual decision range, not merely values that are convenient to measure, and preserve the same documented method across the comparison.
Is repeatability the same as reproducibility?
No. Repeatability holds appraiser and method constant across repeated readings. Reproducibility concerns differences across appraisers or other specified conditions. Together they contribute to measurement-system precision.
Does failing to reject the null prove there is no difference?
No. It means the evidence did not cross the chosen rejection threshold under the test. The study may have low power or a wide uncertainty interval, so report the estimate and practical context.
Exam move
Create a diagnostic table with rows for bias, stability, linearity, repeatability and reproducibility, and columns for what changes, what is held constant and what data are required. For tests, use the same six-line template: parameter, hypotheses, alpha, statistic, decision and qualified interpretation. Add a final column for what the study cannot establish.
One reference repeated in one period can assess local bias and repeatability, but not drift, range-dependent bias or between-appraiser variation. Multiple references across the range address linearity; repeated checks over time address stability; crossed parts, appraisers and trials separate precision components.
For hypothesis questions, state the parameter and alternative before viewing the statistic, choose one or two tails from that alternative, and preserve units through the effect estimate. Practise both outcomes: reject with evidence against the null, and fail to reject without claiming equality. Compare statistical evidence with the engineering tolerance so significance is not mistaken for importance.
End by naming the next measurement property required before process data can be trusted for adjustment or acceptance decisions.
