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1) The difference between linearity and bias

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In linearity, measurement data have bigger difference compared to the reference values while bias has relatively constant and not dependent on reference value and the data measurement is higher.

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Fundamental of MSA: Katelyn
Key Aspects of a MSA: Katelyn
GR&R Study: Katelyn & Qiu Ling
Root Causes for poor GR&R Studies: Qiu Ling
GR&R using Minitab(TEAM ASSIGNMENT): Qiu Ling

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Evaluation on new digital mesuring system that measures fuel injector nozzle diameter

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Evaluation on new digital mesuring system that measures fuel injector nozzle diameter

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-2 operators measure 9 nozzles collected from production floor
- each operator measured the pipes in different order twice
- 36 measurements were obtained
- specification of nozzle diameter  -> 9012+/- 7
tolerance = 14 microns

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Identical characteristic and environment in a short time span

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MSA due to operator(reproducibility) & gauge(repeatability)
- MSA due to  reproducibility -> involved in operator to operator variation & operator part variation

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Gauge: equipment or instrumentation used for measurement

R&R: (Repeatability and Reproducibility) - combination effect on operators

GR&R: determine variation amount in data linked to measurement system and comparing with variation total.

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% Linearity = "Linearity " /"Process Variation "  x 100%

Bias= [slope *Reference Value] + constant

(Y= mX + c)

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Repeatability
- one measurement variation when done by 1 operator

Reproducibility
- conducted by different operators

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Bias = "Bias" / "Tolerance or Process variation" x 100%

If bias is high: possible root causes
- not following measurement protocol
- measurement error in the reference value
- instability

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- lack of maintenance for equipment
- human error
: environment factors
: physical conditions

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- measurement procedures NOT clear
- operator NOT properly trained in using and reading gauge
- operational definition unclear -> NO specific measure as such everyone collects data the same way

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- Used when each part is measured by 1 operator
- Used in destructive testing scenarios (batch is assumed to be homogenous)

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- Used when each part is measured multiple times by each operator
- Used for non-destructive scenarios

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Since all the values generated from GR&R Study (Crossed) suggests that the measurement system is acceptable based on the guidelines from AIAG, the MSA is acceptable

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Precision
- repeatability
- reproducibility
Accuracy
- Stability
- Bias - deviation of average and reference
- Linear

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Since there is no significant difference nozzle measurement done as most points are exactly overlapping each other, it indicates that there is no disagreement between the nozzle measurements done by the QC engineers.

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Comparing nozzle measurements done by QC engineer 1 and 2, measurements done by QC engineer 2 appear slightly lower than QC engineer 1

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Based on graph,  the there is no significant variability in measurements for nozzle, as all the points are close and overlapping the average measurement.
This means that the QC engineers had no difficulty in measuring the nozzle precisely

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Xbar Chart (Compare Part-To-Part variation to repeatability component)

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Xbar Chart (Compare Part-To-Part variation to repeatability component)

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Most of the points that present the mean diameter of nozzle measured in X bar chart are statistically out of control, with only Nozzle 4 being within the control limits set.
This indicates the  variation between the measured nozzles (part-to-part variation) across the QC engineers is greater than expected

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Based on the comparison between the nozzle measurement done by QC engineer 1 and 2, QC engineer 2's measurement showed more variability in comparison as it as more points that touches the LCL, set control limits

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Based on the graphical representation that allow quick comparison between contributions of part - to - part and measurement system variation to total variation.
This graph shows that most of the variations is caused by the part-to-part variation since it has the highest percentage out of all the different components

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Based on the % Study Var that is 8.97%, < 10%, the measurement is acceptable based on the guidelines from AIAG.

Based on % Tolerance & % Process that is 4.63% and 9.38% respectively, < 10% the measurement is acceptable based on the guidelines from AIAG

Based on the Number of Distinct Catergories(NDC) = 15, more than the AIAG recommended value of 5 or more, it denotes an acceptable measurement system

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Based on the Total Gage R&R % contribution that should be as small as possible, since it is at 0.80% < 1%, measurement system is acceptable based on guidelines from AIAG whereby most variation observed for the measurement of nozzle is caused by the nozzles and not the equipment of QC engineers

Based on the subcategories of Total Gage R&R, repeatability contributes towards 0.69 % and reproducibility (operator) contributes towards 0.11% of total % contribution, it indicates that the variation from repeated nozzle measurements by same QC engineer is higher than the variation when nozzle is measured by different QC engineers

Based on the % contribution for Part-To-Part, it indicates that the nozzle measurement captured close to 100% of the part variation, and since % is high, it also indicates that system can distinguish between nozzles

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Based on the p-value, since p-value for nozzle (0.00) < alpha value (0.05) is shows that both contribute to a statistically significant amount of variation to the measured nozzle.
Even though p-value of operator (0.05) = alpha value (0.05), p-value should be higher than 0.05 to be justified as not significant in amount of variation observed.
However, since p-value for nozzle is smaller than operator, it suggests that the characteristics of nozzle may be causing operator to measure particular nozzles differently.

Based on the p-value from interaction between nozzle and operator (0.707) > alpha value (0.05), it indicates that the interaction between nozzle and operator is not statistically significant

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Crossed Design is used since each of the 9 nozzles were measured twice by 2 operators in random orders to generate 36 measurements

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Types of Gage Repeatability & Reproducibility (GR & R) Study

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Types of Gage Repeatability & Reproducibility (GR & R) Study

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Sample usage
Equipment used
Operator
Protocol
Environment

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MSA
- Experimental
- Mathematical

Use to determine: variation and measurement contributing to overall process