MEASURE : Measurement System Analysis Dedy Sugiarto

Gage repeatability and reproducibility studies determine how much of your observed process variation is due to measurement system variation.

Minitab provides two methods for Gage R&R Crossed: Xbar and R, or ANOVA. The Xbar and R method breaks down the overall variation into three categories: part-to-part, repeatability, and reproducibility. The ANOVA method goes one step further and breaks down reproducibility into its operator, and operator by part, components. The ANOVA method is more accurate than the Xbar and R method, in part, because it accounts for the Operator by Part interaction

Example of a Gage R&R Study (Crossed) - (Xbar and R method) In this example, we do a gage R&R study on two data sets: one in which measurement system variation contributes little to the overall observed variation (GAGEAIAG.MTW), and one in which measurement system variation contributes a lot to the overall observed variation (GAGE2.MTW). For comparison, we analyze the data using both the and R method (below) and the ANOVA method. You can also look at the same data plotted on a Gage Run Chart. For the GAGEAIAG data set, ten parts were selected that represent the expected range of the process variation. Three operators measured the ten parts, two times per part, in a random order. For the GAGE2 data, three parts were selected that represent the expected range of the process variation. Three operators measured the three parts, three times per part, in a random order.

Step 1: Use the Xbar and R method with GAGEAIAG data 1 Open the file GAGEAIAG.MTW. 2 Choose Stat > Quality Tools > Gage R&R Study (Crossed). 3 In Part numbers, enter Part. In Operators, enter Operator. In Measurement data, enter Response. 4 Under Method of Analysis, choose Xbar and R. 5 Click OK. Step 2: Use the Xbar and R method with GAGE2 data 1 Open the file GAGE2.MTW.

GAGEAIAG.MTW)

Xbar and R Example - Session Window Output - GAGEAIAG.MTW Look at the %Contribution column in the Gage R%R Table. The measurement system variation (Total Gage R&R) is much smaller than what was found for the same data with the ANOVA method. That is because the and R method does not account for the Operator by Part effect, which was very large for this data set. Here you get misleading estimates of the percentage of variation due to the measurement system. According to AIAG, when the number of distinct categories is 5 it represents an adequate measuring system. However, as explained above, you would be better off using the ANOVA method for this data.

Xbar and R Example - Graph Window Output - GAGEAIAG.MTW In the Components of Variation graph, a low percentage of variation (6%) is due to the measurement system (Gage R&R), and a high percentage (94%) is due to differences between parts. In the Xbar Chart by Operator graph, although the and R method does not account for the Operator by Part interaction, this plot shows you that the interaction is significant. Here, the and R method grossly overestimates the capability of the gage. You may want to use the ANOVA method, which accounts for the Operator by Part interaction. Most of the points in the Chart are outside the control limits when the variation is mainly due to part-to-part differences.

GAGE2.MTW

Xbar and R Example - Session Window Output - GAGE2.MTW Look at the %Contribution column in the Gage R&R Table. A large percentage (78.111%) of the variation in the data is due to the measuring system (Gage R&R); little is due to differences between parts (21.889%). A 1 in Number of distinct categories tells you the measurement system is poor; it cannot distinguish differences between parts.

Xbar and R Example - Graph Window Output - GAGE2.MTW In the Components of Variation graph, a high percentage of variation (678%) is due to the measurement system (Gage R&R) - primarily repeatability, and the low percentage (22%) is due to differences between parts. Most of the points in the chart will be within the control limits when the observed variation is mainly due to the measurement system.

Step 1: Use the ANOVA method with GAGEAIAG data 1 Open the file GAGEAIAG.MTW. 2 Choose Stat > Quality Tools > Gage R&R Study (Crossed). 3 In Part numbers, enter Part. In Operators, enter Operator. In Measurement data, enter Response. 4 Under Method of Analysis, choose ANOVA. 5 Click OK. Step 2: Use the ANOVA method with GAGE2 data 1 Open the file GAGE2.MTW.

ANOVA Example - Session Window Output - GAGEAIAG.MTW Look at the p-value for the Operator*Part interaction in the ANOVA Table. When the p-value for Operator by Part is < 0.25, Minitab fits the full model (shown in the ANOVA Table With Operator *Part Interaction (p = 0.00016)). In this case, the ANOVA method will be more accurate than the and R method, which does not account for this interaction. Look at the %Contribution column in the Gage R&R Table. The percent contribution from Part-To-Part (89.33) is larger than that of Total Gage R&R (10.67). This tells you that most of the variation is due to differences between parts; very little is due to measurement system error. According to AIAG, 5 represents an adequate measuring system.

ANOVA Example - Graph Window Output - GAGEAIAG.MTW · In the Components of Variation graph (located in the upper left corner), the percent contribution from Part-To-Part is larger than that of Total Gage R&R, telling you that most of the variation is due to differences between parts; little is due to the measurement system. · In the By Part graph (located in upper right corner), there are large differences between parts, as shown by the non-level line. · In the By Operator graph (located in the middle of the right column), there are small differences between operators, as shown by the nearly level line. · In the Xbar Chart by Operator (located in lower left corner), most of the points in the and R chart are outside the control limits, indicating variation is mainly due to differences between parts. · The Operator*Interaction graph is a visualization of the p-value for Oper*Part - 0.00016 in this case - indicating a significant interaction between each Part and Operator.

Look at the p-value for the Operator Look at the p-value for the Operator*Part interaction in the ANOVA Table. When the p-value for Operator by Part is > 0.25, Minitab fits the model without the interaction and uses the reduced model to define the Gage R&R statistics. Look at the %Contribution column in the Gage R&R Table. The percent contribution from Total Gage R&R (84.36) is larger than that of Part-To-Part (15.64). Thus, most of the variation arises from the measuring system; very little is due to differences between parts. A 1 tells you the measurement system is poor; it cannot distinguish differences between parts.

In the Components of Variation graph (located in the upper left corner), the percent contribution from Total Gage R&R is larger than that of Part-to-Part, telling you that most of the variation is due to the measurement system - primarily repeatability; little is due to differences between parts. · In the By Part graph (located in upper right corner), there is little difference between parts, as shown by the nearly level line. · In the Xbar Chart by Operator (located in lower left corner), most of the points in the and R chart are inside the control limits, indicating the observed variation is mainly due to the measurement system. · In the By Operator graph (located in the middle of the right column), there are no differences between operators, as shown by the level line. · The Operator*Interaction graph is a visualization of the p-value for Oper*Part - 0.48352 in this case - indicating the differences between each operator/part combination are insignificant compared to the total amount of variation.

MSA (The Premise) Accurate & Precise The measurement of a processing unit by a random gage, used by a random operator, at a random point in time is both: Accurate & Precise From :

The Should-Be Condition! MSA (The Premise) The Should-Be Condition!

MSA (The Accuracies) Bias (defined as the absence of systematic error). Linearity (defined as the constant bias in the gage across the range of measurement). Stability (defined as the absence of special causes).

MSA (The Precision) Repeatability Reproducibility Reflecting the basic inherent precision of the gage itself. “Short-term” random error. Reproducibility Defined as the variability due to different conditions (operators, time periods, or environments) in the usage of the gage. “Long-term” random error

MSA (The Precision) Acceptable %P/T and %R&R is: Excellent: <10% Unacceptable: >30%