## Bias Linearity and Stability Study in Measurement

→ This study is very important in measurement system analysis and calibration. It is a combination and interaction of part, operator, and instrument. By using this analysis we can make our system more robust.

### Bias:

→ Bias is the difference between the observed average of measurement and the reference value.
→ The reference value, also known as the accepted reference, true or master value, it serves as an agreed-upon reference for the measurement. It can be determined by averaging several measurements with a higher level of measuring equipment.
→ In other words, the difference between the measured and the standard value for different ranges.
→ It is very important to check the instrument, operator, and part combination as a part of a Measurement System Analysis.

#### Bias Study:

→ Obtain accepted reference value for the part
→ Use layout inspection equipment
→ Measure the same part a minimum of 10 times using the gauge under evaluation
→ Calculate the average of readings
→ Bias = Observed Average - Reference value

#### Possible Causes:

→ Sensor/Instrument is not properly calibrated
→ Improper use of an instrument
→ Unclear Procedures
→ Human Limitations

### Linearity:

→ Linearity is the difference in the bias values through the expected operating range of the gauge.
→ For example, if we have a vernier caliper of 300mm range then at the time of calibration we have to cover the entire range of the vernier so we can compare and decide whether this instrument has variation or not?

#### Linearity Study:

→ Select 5 – 8 parts that can be measured at different operating ranges of the measurement system
→ Determine reference value for each part using layout inspection
→ Use one appraiser to measure parts
→ Take 10 – 12 repeated readings on each part
→ Calculate part’s Bias and plot it against the references
→ Linearity is represented by the slope of the best-fit line of these points

### Stability Study:

→ Stability (or drift) is the total variation in the measurements obtained with a measurement system on the same master or part when measuring a single characteristic over an extended time period.
→ In other words, at different times, the same person uses the same instrument to perform multiple measurements on the same properties of the same object and then calculates the average measured value for each time period.
→ If for each time period, the average measured readings are similar, the measurement system has good stability.
→ If the average readings have a difference then we can say that this system has not good stability.