The Gage Repeatability and Reproducibility (Gage R&R) study is a structured methodology used in Measurement System Analysis (MSA). Its primary purpose is to quantify the total variation within a measurement system, separating variation caused by the measuring equipment from that introduced by human operators. Without a validated measurement system, collected data cannot be trusted, making subsequent quality control efforts ineffective. Performing a Gage R&R study provides the necessary data to determine if a measurement system is capable of producing reliable, accurate results for process control.
Planning the Gage R&R Study
The success of any Gage R&R analysis depends on thorough planning and preparation before data collection. The scope must be clearly defined, including the specific measurement device, the characteristic being measured, and the operating environment. A standard protocol involves a minimum of three operators measuring ten distinct parts, with each part measured three times (the 3x3x10 setup).
The selected parts must accurately represent the full range of variation (Part Variation or PV) typically encountered in the manufacturing process. If the parts are too similar, the study cannot capture the system’s ability to differentiate between products. Personnel selection requires involving operators who regularly perform the measurement task, ensuring the results reflect real-world conditions.
A standardized measurement procedure must be documented and communicated to all participants. This procedure defines how the part is fixtured, where the measurement is taken, and the steps for reading the device. Documenting the procedure eliminates ambiguity and provides a baseline for assessing operator technique.
Executing the Data Collection
Data collection requires adherence to randomization and blinding protocols to eliminate systematic bias. Randomization ensures the order in which parts are measured is scrambled, preventing influences like learning effects or operator fatigue. A study coordinator manages the measurement flow and ensures the sequence is followed.
Blinding is essential; operators must not know which specific part they are measuring or have access to previous results. This prevents the operator from consciously adjusting their technique to achieve an expected result. The coordinator tracks the parts and measurements using a standardized data sheet, ensuring accurate association of each measurement to the operator, part number, and trial number.
Each operator measures all ten parts three times, or the entire set of ninety measurements (3 operators x 10 parts x 3 trials) is randomized. The operator must follow the documented procedure exactly for every trial. The data sheet must clearly record the raw measured value for each total measurement.
Calculating Equipment Variation (Repeatability)
Repeatability, or Equipment Variation (EV), quantifies the inherent variation observed when the same operator measures the same part multiple times under identical conditions. This variation is attributed to the gauge itself, reflecting its mechanical precision or short-term stability. The calculation typically uses the Average Range Method to isolate this component of error.
To calculate EV, the first step involves determining the range (R) for each set of repeated measurements taken by an operator on a single part. The average range ($\bar{R}$) is then calculated by averaging all these individual ranges across all parts and all operators in the study.
The Equipment Variation is derived using a statistical constant ($D_2^$) specific to the number of trials performed, which converts the average range into an estimate of the standard deviation. The formula is $EV = \bar{R} \times D_2^$. This value is expressed in the same units as the original measurement and represents the noise floor of the measurement device. A lower EV indicates a more precise and stable measuring instrument.
Calculating Appraiser Variation (Reproducibility)
Reproducibility, or Appraiser Variation (AV), quantifies the variation observed in the average measurements taken by different operators when measuring the same set of parts. This variation is attributed to human factors, such as differences in operator technique, training, or interpretation of the procedure. It differentiates the consistency between people, in contrast to EV which measures consistency within a single person’s repeated trials.
The calculation begins by finding the average measurement ($\bar{X}$) recorded by each individual operator across all their trials and parts. The range of the operator averages ($\bar{\bar{X}}_{Range}$) is then calculated by taking the difference between the highest and the lowest of these averages.
To translate this range into a standard deviation for reproducibility, the range is divided by a statistical constant specific to the number of operators. A refinement is applied by subtracting the contribution of the Equipment Variation (EV) from this raw value. This ensures the final AV calculation isolates only the variation stemming from the operators.
A high AV suggests that operator training is inconsistent or the measurement procedure is too subjective, leading to different techniques among personnel. This calculation isolates the human element of the measurement error.
Determining Total Gage R&R and Acceptability Standards
The total variation introduced by the measurement system, known as Total Gage R&R (GR&R), is found by statistically combining the Equipment Variation (EV) and the Appraiser Variation (AV). Since these sources are independent, they are combined using the root sum of squares method: $\text{GR\&R} = \sqrt{(EV^2) + (AV^2)}$. This value represents the overall variability of the entire measurement system.
The calculated GR&R value is compared against two primary benchmarks to determine acceptability: the total study variation and the specified engineering tolerance.
Percentage of Total Study Variation ($\%GR\&R$)
This metric is calculated by dividing the GR&R value by the total variation observed during the study, which includes both measurement error and the actual variation between the parts (Part Variation or PV). It indicates how much of the observed process spread is noise from the measurement system.
Percentage of Tolerance ($\%Tolerance$)
This is calculated by dividing the GR&R value by the total allowable engineering tolerance range. This benchmark is relevant when the system is used for determining product conformance to specifications. It indicates the proportion of the permissible error band consumed by the measurement system’s uncertainty.
Industry standards, such as those published by the Automotive Industry Action Group (AIAG), provide clear thresholds for acceptability. A system is generally considered acceptable if its $\%GR\&R$ is less than 10%. Results between 10% and 30% are marginal, suggesting improvement is required. Any result exceeding 30% is unacceptable, indicating the system cannot provide reliable data for process control or product acceptance decisions.
It is also important to consider the Part Variation (PV), which quantifies the actual differences between the parts selected for the study. The total study variation is the root sum of squares of the GR&R and the PV. A high Part Variation relative to the GR&R suggests the measurement system is sensitive enough to consistently distinguish between different parts.
Actions Based on Gage R&R Results
Once the Total Gage R&R study is complete, the resulting percentages determine the necessary corrective actions if the system is marginal or unacceptable. The remediation strategy must focus specifically on the component (EV or AV) contributing the most to the overall error, ensuring efficient use of resources.
Addressing Equipment Variation (EV)
If EV is the dominant source of error, the problem lies primarily with the measuring instrument. Corrective steps include placing the gauge on a more rigorous maintenance schedule, performing a formal recalibration, or replacing the device with a more precise model. Redesigning the fixturing to eliminate bending or temperature effects can also reduce the inherent variability of the equipment readings.
Addressing Appraiser Variation (AV)
If AV is unacceptably high, the focus shifts to standardizing the human element. This requires operator training to ensure all personnel follow the documented procedure identically. The measurement procedure itself may need revision to remove subjective steps, or the gauge design may need modification to make it less dependent on user interpretation.