Linearity is a critical concept in the Measure Phase of Lean Six Sigma that evaluates the consistency and accuracy of a measurement system across its entire operating range. It assesses whether a measuring instrument or gauge provides equally accurate readings at low, middle, and high values within…Linearity is a critical concept in the Measure Phase of Lean Six Sigma that evaluates the consistency and accuracy of a measurement system across its entire operating range. It assesses whether a measuring instrument or gauge provides equally accurate readings at low, middle, and high values within its measurement spectrum.
When examining linearity, practitioners analyze the bias or systematic error of a measurement device at multiple reference points throughout its range. A measurement system with good linearity demonstrates consistent accuracy regardless of where in the range the measurement falls. Poor linearity indicates that the measurement bias changes as the measured values increase or decrease.
To evaluate linearity, you select several reference standards spanning the full measurement range, typically five or more points. Each standard is measured multiple times, and the results are compared against the known true values. The difference between measured values and reference values represents the bias at each point.
The analysis involves plotting these bias values against the reference values and fitting a regression line through the data points. The slope of this line indicates the degree of linearity. A slope close to zero suggests good linearity, meaning bias remains relatively constant across the range. A significant slope indicates that bias changes systematically as measured values change.
Linearity problems can arise from worn equipment, improper calibration, environmental factors, or inherent design limitations of the measurement device. These issues can lead to inaccurate data collection, which undermines process analysis and decision-making.
Addressing linearity concerns may involve recalibrating instruments, replacing worn components, implementing environmental controls, or selecting more appropriate measurement tools. Understanding and correcting linearity issues ensures that measurement data accurately represents process performance across all operating conditions, enabling reliable statistical analysis and informed improvement decisions throughout the DMAIC methodology.
Linearity in Six Sigma: A Complete Guide for Green Belt Certification
What is Linearity?
Linearity is a measurement system analysis (MSA) concept that evaluates whether a measurement device maintains consistent accuracy across its entire operating range. In simple terms, it assesses whether your measuring instrument performs equally well when measuring small values as it does when measuring large values.
Linearity is the difference in bias values throughout the expected operating range of the measurement system. A measurement system with good linearity will have consistent bias (or no bias) whether measuring at the low end, middle, or high end of its range.
Why is Linearity Important?
Understanding linearity is critical for several reasons:
• Data Integrity: If your measurement system has poor linearity, the data you collect may be unreliable at certain ranges, leading to incorrect conclusions about your process.
• Process Control: Poor linearity can cause you to make wrong decisions about process adjustments, potentially introducing variation rather than reducing it.
• Quality Assurance: Products measured at different points in the measurement range may be incorrectly classified as conforming or non-conforming.
• Root Cause Analysis: Linearity issues can mask true process problems or create phantom problems that waste resources to investigate.
How Linearity Works
Linearity is typically assessed through a study that involves:
Step 1: Select reference parts or standards that cover the full operating range of the measurement system (typically 5 or more parts spanning low, mid, and high values).
Step 2: Measure each reference part multiple times (usually 10-12 times per part) in a randomized order.
Step 3: Calculate the bias at each reference point. Bias = Average measured value - Reference value.
Step 4: Plot the bias values against the reference values and perform regression analysis.
Step 5: Analyze the slope of the regression line. A slope of zero (horizontal line) indicates perfect linearity. A non-zero slope indicates linearity error.
Interpreting Linearity Results
• Good Linearity: The regression line is relatively flat (slope near zero), and bias is consistent across the measurement range.
• Poor Linearity: The regression line has a significant slope, indicating that bias changes as the measured value changes.
• Statistical Significance: The p-value for the slope should be greater than 0.05 to conclude that linearity is acceptable (slope is not significantly different from zero).
Linearity vs. Other MSA Components
• Bias: A single measure of systematic error at one point; linearity examines how bias changes across the range.
• Stability: Examines bias over time; linearity examines bias over the measurement range.
• Repeatability: Variation when the same operator measures the same part; linearity focuses on accuracy, not precision.
Exam Tips: Answering Questions on Linearity
Tip 1: Know the Definition Remember that linearity specifically addresses how measurement accuracy (bias) changes across the operating range. Questions may try to confuse you with repeatability or reproducibility concepts.
Tip 2: Understand the Graph On exams, you may be shown a linearity plot. A flat line indicates good linearity. A line with a steep slope (positive or negative) indicates poor linearity.
Tip 3: Remember the Regression Analysis Linearity is assessed using linear regression. The slope of the best-fit line is the key indicator. A slope statistically equal to zero means acceptable linearity.
Tip 4: Connect to Practical Applications Questions may ask when to perform a linearity study. The answer typically involves situations where the measurement system is used across a wide range of values.
Tip 5: Distinguish from Calibration While related, linearity is not the same as calibration. Calibration adjusts a measurement system to reduce bias; linearity assesses whether bias is consistent across the range.
Tip 6: Know Acceptance Criteria Linearity is typically considered acceptable when the slope is not statistically significant (p-value > 0.05) and when the %Linearity is less than 10% of the tolerance or process variation.
Tip 7: Watch for Keywords Exam questions about linearity often include phrases like across the range, operating range, different reference values, or bias at different levels.