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Intro to MSA of Continuous Data

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Intro to MSA of Continuous Data
This is the eighth in a series of articles about MSA. The focus of this article will be on assessing the measurement reproducibility between two measurement systems that must measure the same characteristic. Does the following scenario seem familiar? An operator performs an online test on a product. The test shows a failure to meet specifications. This is an expensive product, so the line supervisor takes the part to an online tester located on an adjacent line and retests it. This time it passes. The supervisor instructs the operator to go ahead and use the part. Both of them lose confidence in the first measurement device. But which one provided the correct result? There are several approaches that may be used to assess the reproducibility of two measurement devices. One approach that is commonly used when the measurement devices are fully automated is to perform a standard R&R study and replacing the Operators with the Measurement Devices. Reproducibility is now tester to tester reproducibility. The operator*part interaction becomes the tester*part interaction. While this approach does quantify the reproducibility of the two devices, it has the drawback of providing little additional information if a significant difference between the two is noted. It is also limited to fully automated gages. You do have the option of adding gage as a third factor (Parts, Operators, Gages) and analyzing the resulting designed experiment using Analysis of Variance (ANOVA). A second approach is known as the Iso-plot. This is a very simple graphical approach. An x-y plot is constructed with equal scales, and a 45º line is drawn through the origin. Parts are selected throughout the expected measurement range. Each part is measured using both gages. Each part is then plotted on the graph using the value measured by one gage on the x-axis and the value measured by the other gage on the y-axis. Ideally, the coordinates of all parts will lie on the 45º line. If the points fall consistently above or below the line, one gage is biased in respect to the other. The Iso-plot provides an excellent visual assessment of the reproducibility of the two gages, but does not provide quantifiable results. A linear regression analysis of the data used to create the Iso-plot will provide quantifiable results. Ideally, the regression constant should equal zero and the slope should equal one. The regression output will provide the relationship between the two gages as well as confidence and prediction limits. A third approach is the Bland Altman plot. Parts are selected throughout the expected measurement range. Each part is measured using both gages. Calculate the differences between the gages (Gage1 – Gage2), the mean of each pair of measurements and the mean of the differences. Plot the differences on an x-y plot with the differences on the y-axis and the mean of the paired measurements on the x-axis. Draw a horizontal line for the mean of the differences. Draw two more horizontal lines at + / - 1.96 standard deviations of the differences. Approximately 95% of the differences should fall within the limits. The mean line indicates the bias between the two gages. A trend indicates that the bias changes with the size (a linearity difference between the gages). An increase (or decrease) in the width of the pattern with size indicates that the variation of at least one of the gages is dependent on size. If the variation within the limits is of no practical importance, the two gages may be used interchangeably. Do not overlook the differences between gages when evaluating your measurement systems. Your operators will be quick to discover gages that inconsistently accept and reject product between the gages. They will then lose confidence in them and the test itself.

Within product variation (WPV)
This is the eleventh in a series of articles on MSA, and the first in advanced MSA topics. The focus of this article will be on how to handle within product variation (WPV). WPV is significant variation in the form of a product. Significant means that it detectable by your measurement device. Examples of variation in form include shaft diameter variation due to lobes, or a taper/barrel/hourglass shape; thickness variation due to parallelism and

more. WPV can have a significant impact on the acceptability of a measurement system. While technically part of the product not the measurement system, it definitely impacts the measurement system. It cannot be isolated using the standard AIAG Gage R&R study, but requires a special approach. The AIAG MSA manual touches on this and presents a Range method for calculating the WIV effect. I show an ANOVA approach that allows an evaluation of all of the interactions with WPV. When I first decided to start this blog, I planned to demonstrate it using Minitab's General Linear Model (GLM). Fortunately, the new Minitab 16 made this easier with the Expanded Gage R&R Study feature. Note: Everything I show here can be duplicated with earlier versions of Minitab using GLM. The graphs must be created using the Graph commands and some creativity, and the metrics will have to be calculated by storing results and manually performing the calculations. You can follow along by opening the attached PDF file. • First, determine whether WPV is a potential issue. You may know this already from process knowledge, or suspect it from high Repeatability variation or an Operator*Part interaction. • Create a Gage Study worksheet. Either copy the format used in the attachment, or use Minitab to create a full factorial design for 3 factors. • Identify specific locations on the product to be measured by all operators. These can be selected at random or by design. If selected by design, this must be entered as a Fixed factor into Minitab. • Perform study • Analyze following the attached file. I recommend starting with all factors and 2-way interactions in the model. Review the p-values and remove all 2-way interactions with p-values greater than 0.05. If all interactions involving the Operator are removed, then look at the p-value for the Operator. If the Operator pvalue is greater than 0.05, remove it also. • Interpret the Session Window the same as a standard MSA for %SV, %Tol, etc. • Interpret Graph1 the same as a standard MSA. • Create Graph2 and interpret similar to Graph1. You will see two new graphs, the Measurement by WIV graph and the Part * WIV graph. The Measurement by WIV graph shows differences in the location measured on the part, and the interaction shows whether this location to location difference varies by part. Now that you understand the impact of WIV on your measurement system, what do you do with that knowledge? It depends. If the WIV varies randomly on the product (i.e., it is unpredictable), you cannot prevent it from affecting your measurement system. You can recognize it as part of your total variance equation (acknowledgements to bobdoering), but it will always affect your measurements. If the WIV is predictable by location, you can take this into account and improve your R&R results by specifying measurement locations in your work instructions. Last advice: Although it is possible to remove the effects of WIV from your R&R results, SPC

and capability results, it will still have an impact on function. For example, a shaft with lobes may not fit a bearing correctly, so beware. This is the tenth in a series of articles about MSA. The focus of this article will be on minimizing the number of MSA studies by creating families of gauges. A frequent question in the Cove is: “Must I perform an MSA on every gauge/part combination?” The answer is: “No. You may create families of gauges, and perform MSA studies by family.” Wait! Not so fast! What constitutes a family of gauges? Well, there are certain criteria that must be met: • • • Same gauges Same product characteristics Same tolerances or process variation depending on use of gauge

Another, less restrictive approach that could be used: • Similar gauges • Similar product characteristics • State the smallest tolerance or process variation (standard deviation) that the gage family may be used to measure and still achieve an acceptable R&R result Let’s cover each of these in more depth: Same/similar gauges: Conservative approach: Same brand and model of gauge Alternate approach: Similar gauges (brand or model not relevant) • • • • Same type (e.g., calipers, micrometers, 3 – point bore gage, etc.); Same range (e.g., 0 – 6 inch, 0 – 12 inch, etc); Same display (e.g., digital, dial, vernier, etc.); Same resolution (e.g., 0.0001, 0.05, etc.)

• Same technology, if relevant (e.g., scaled, rack and pinion gear, electrostatic capacitance technologies for calipers) • Same anvils, if relevant (e.g., outside, inside, step anvils for calipers)

Same/similar product characteristics: Conservative approach: Same features Alternate approach: Similar features (e.g., diameter, width, step etc.) within a specified range. Be cautious when establishing the range. You may need to perform a series of MSAs to establish how large this range may be. The impact of size will usually manifest itself through changes in the within-part variation, or by affecting the ease with which an operator can handle the part and gauge together. Same tolerances or process variation: Conservative approach:

• •

Same tolerance if gauges are used for inspection Same process variation if gauges are used for SPC

Alternate approach: • If gauges are used for inspection, state the smallest tolerance at which an acceptable % Tolerance may still be achieved • If gauges are used for SPC, state the smallest process variation standard deviation at which an acceptable % Study Variation may still be achieved

Once you have created a gauge family, document it. Create a record for each gauge family that clearly describes the gauges, characteristic and size range. The gauges could be identified by listing all serial numbers, gauge calibration ID numbers, or by clearly specifying the type, range, display, resolution and anvils. Perform the MSA and associate it with the gauge family record.

%Tolerance for One-sided Specs
This is the ninth in a series of articles about MSA. The focus of this article will be on discussing the proper approach to evaluating Repeatability and Reproducibility as a % of Tolerance when the tolerance is onesided. The AIAG MSA manual is silent on this and no other "guru" that I am aware of has spoken on it. This is probably because there is no one, right answer. A recent post asked this question, and I recalled several prior posts that had all asked similar questions, with mixed responses. It forced me to really think the matter through from the perspective of what is the intent of the %Tolerance metric, not what is convenient or easy. Minitab users have two options. If they enter a natural boundary as the second specification (or the range between the boundary and the specification), Minitab will calculate %Tolerance the same way as if they entered a two sided specification (think Cp). If they leave the other specification blank, Minitab will calculate %Tolerance using 3 * the total R&R and the difference between the study mean and the specification (think Cpk). See the full explanation here. Lets look a few scenarios, and I will give you my but simply by thinking the problem through rationally. . This is not based on any research or statistics,

• Scenario 1, Maximum Flatness: Zero is a natural boundary and there is a maximum allowable flatness specification. Presumably, there is some incentive to drive for smaller and smaller levels of flatness, thus moving farther and farther away from the USL. In this situation, you will conceivably utilize the entire tolerance spectrum. This would tend to justify using the whole range, or entering 0 as a LSL. • Scenario 2, Minimum Hardness: I am using the example used by Minitab in the above link. In this scenario, you are not going to strive for infinite hardness. There will be practical and economical reasons for you to "hover" a safe distance above the LSL, and to not increase over

time. In this scenario, it would make more sense to use the Minitab approach. (I will casually overlook the fact that you cannot enter infinity into the USL field). • Scenario 3, Maximum activation force: The same logic could apply to a maximum activation force for a push button. If you strove for zero activation force on a conventional springloaded design, there would no force left to reopen the switch. Therefore, you will also “hover” a safe distance below the maximum force and not decrease over time. In this case, the Minitab approach of leaving the LSL field blank would also make sense. It may make more sense to forget about the %Tolerance entirely and use the Gauge Performance Curve approach (see my files MSA 3rd Ed.xls and MSA 3rd Ed ANOVA.xls in my earlier blogs. This approach provides the probability of accepting a product for each specific measurement as you near the specification. Bottom line, I recommend that you think carefully about your specific situation, and choose the appropriate approach based on the situation.

Technical Support Document How Minitab calculates %Tolerance

when a One-Sided Tolerance is entered for Gage R&R
Many processes operate with only a single specification limit. For example, a lumber mill cuts beams to be perfectly straight, but the beams often warp during manufacture. Measurements of this warping have an upper specification limit to distinguish acceptable and unacceptable degrees of warping. However, these measurements have no lower specification limit because they cannot take values less than zero. In fact, zero represents a perfectly straight beam with no warping. Likewise, some processes have a lower specification limit, but no upper specification limit. A cutlery manufacturer must ensure the hardness of its knife blades exceed 55 on the Rockwell C-scale. The lower specification limit is 55, but no upper specification limit exists. When evaluating Gage R&R for processes with only one specification limit, it is important for the analysis to reflect this property. One statistic that is directly affected by specification limits is the %Tolerance statistic, which compares the tolerance with the study variation. Ideally, the tolerance should amply encompass the study variation, ensuring the variability due to Gage R&R and part-to-part variation do not push the process output beyond the specification limits. When a process has two specification limits, the tolerance equals the difference between them, and %Tolerance equals the study variation of a given variation source divided by this tolerance. However, this method is invalid when you provide a single specification limit. For these cases, Minitab uses the following method: 1. Minitab calculates a one-sided process variation by dividing the Study Variation statistic by 2. 2. Minitab defines the one-sided tolerance as the absolute value of the difference between the single specification limit and the mean value of all measurements. 3. Minitab calculates the %Tolerance statistic by dividing the one-sided process variation by the onesided tolerance. ns observatioall of mean the is X and limit, ion specificatsingle the is L where 100 *L - X 2 Variation Study Tolerance %  If the mean of all observations is less than the lower specification limit, or greater than the upper specification limit, the measurements are deviating strongly from their acceptable range, and %Tolerance is not calculated.

Linearity
This is the third in a series of articles about MSA. The focus of this article will be on measurement linearity. Linearity is simply measurement bias throughout the entire range of the measurement device. For this reason bias and linearity are often combined into a single study. A good calibration system will check the calibration of a measurement device at a minimum of three locations (both extremes and the middle of the measurement range). A thorough linearity study will check at least five locations (e.g., both extremes, and at 25%, 50% and 75% of the measurement range). Standards such as used in calibration should be used instead of actual parts unless the parts can be measured with less measurement variation with a different measurement device. Each standard is measured repeatedly at least ten times. All measurements must be made randomly to minimize the appraiser recalling previous results. The results can be analyzed using statistical software such as Minitab, or with the attached file as shown. • Calculate the bias for each individual measurement and the average bias for each reference standard (or part). • Plot the individual and average biases on the y-axis of a scatter plot versus the values of the standards on the x-axis. • Perform a regression analysis using the individual biases as the response and the reference values as the predictor variable. • Plot the regression line and the 95% confidence limits for the regression line on the scatter plot. • Plot the bias = 0 line for all reference values. • Verify that the Bias = 0 line lies within the +/- 95% confidence limits of the regression line. • The y – intercept and slope of the regression equation should each be approximately equal to zero. These values may be statistically evaluated if desired per the formulae in the AIAG MSA 3rd edition manual. For practical purposes the graphical analysis is sufficient. The statistical analysis is only necessary for borderline cases.

Ideally, linearity will be statistically equal to zero. However, this will not always be the case. There are several possible scenarios: • Constant bias – All measurements are offset by the same amount regardless of size. This is essentially a calibration issue. Calibrate the measurement device and repeat the linearity study. • Non-constant, linearly increasing/decreasing bias –The bias either increases or decreases as the location within the measuring range increases. Possible causes: measurement scale is proportionally small/large (gage issue), thermal bias (thermal expansion/contraction is proportional to the size of the dimension), pressure bias (deflection under pressure is proportional to size), etc. • Non-constant, nonlinear bias – The bias changes in a nonlinear fashion throughout the measurement range. Possible cause: measurement scale is nonlinear (gage issue, particularly with electronics), gage wear in one section of the measurement range, worn standards.

If the linearity is acceptable within the range actually used for measurement, the gage may be accepted for

a specified range of measurement. This must be clearly noted on the gage and the practice documented in the appropriate quality procedures.

Bias
This is the second in a series of articles about MSA. The focus of this article will be on measurement bias, sometimes referred to as accuracy. Bias is the difference between the actual value of a part and the average measured value of that part. In other words, a measurement device that has bias will consistently over or under state the true value of the part. In most cases, a separate study of measurement bias is not performed if the measurement device has been calibrated. The reason for this is simple. Calibration is intended to detect and correct any measurement bias found. As I stated in Part 1, calibration and measurement uncertainty are outside of the scope of this series and is better left to experts in those fields. However, I will state that all calibration programs are not created equal. Some less equal calibration programs may take a single measurement of a standard and then make a determination on whether there is measureable bias in the gage. This overlooks the fact that taking a second or third measurement could provide different results than found in the first measurement. There are also other less obvious sources of bias from which a calibration system, no matter how well designed and implemented, will not protect you. I will go through a few examples of bias that you could encounter: • Measurement device bias – As we discussed in Part 1, all measurements vary to some extent. if the device has sufficient resolution to see it. The failure mode of a weak calibration system is to base the calibration on a single measurement. The solution is to take multiple measurements of the standard and compare the average of these measurements to the standard before making a determination of the magnitude of the bias and making an adjustment. Even better, a 1-sample t-Test may be used to determine the statistical significance of the bias provided the required sample size is established in advance using the maximum allowable bias and desired alpha and beta risks. • Temperature bias – Many products will change size with changes in temperature. The magnitude of this change in size may or may not add significant bias depending on the materials involved. What may be less commonly known is that the measurement device will also change size with temperature. How often does the appraiser carry the measurement device in a pocket or in their hand warming it up to body temperature? Temperature not only affects mechanical dimensions, but also electrical. Resistance changes with temperature affecting many electrical measurements. An extremely important aspect of calibration performed by internal lab is normalizing both the standard and the gage at standard temperatures before calibration. • Humidity bias – Certain materials will swell or shrink with changes in moisture content. Critical measurements should be made at standard humidity conditions after a lengthy normalization time. • Pressure bias – Materials that are compressible such as rubber or foam are notoriously difficult to measure due to the deformation of the part under pressure. But did you realize that the steel shaft diameter that you are measuring may also be understated depending on whether you used the ratchet thimble on the micrometer or not? • Cosine error bias – Not just for CMMs! Test indicators, less commonly used these days, are also susceptible to cosine error. Did you realize that the ball on the tip of a CMM probe can introduce potential bias? All touches made with the tip must be made perpendicular to the surface

of the part. When this is not done the diameter of the sphere will introduce what is called cosine error. The larger the sphere used, the larger the cosine error. • Measurement procedure bias – Your measurement procedure can also introduce bias. How do you measure the diameter of a shaft (randomly, max, min, average of max-min, using CMM)? What about the location on the shaft (middle, end, multiple locations)? The effect of this bias depends on the application of the part. Does the shaft need to slip into a hole? The average diameter reported by a CMM will understate the effective diameter of the shaft. It may measure in specification and not fit into a ring gage.

Stability
This is the fourth in a series of articles about MSA. The focus of this article will be on measurement stability. Stability is simply measurement bias throughout an extended period of time. This is where calibration falls short from an MSA perspective. Calibration is a series of snapshots widely spaced in time taken under controlled environmental conditions. A stability study is a series of repeated measurements taken under actual usage conditions. The purpose is to verify that the bias of the gage does not change over time due to environmental conditions or other causes. A stability study is performed by selecting a measurement standard (ideal) or a master sample part that is midrange of the expected measurement range. Note: This may be enhanced by adding standards/master parts at the low and high ends of the expected measurement range. On a periodic basis, measure the standard 3 – 5 times. The period should be based on knowledge of what may influence the measurement system. For example, if ambient temperature variation is expected to be the major source of variation, make hourly checks throughout the day. If the source of variation is expected to be long term drift, take daily or weekly measurements. Analyze the data using Xbar/R or Xbar/s control charts (use separate charts if you measured at the low/middle/high ends of the expected measurement range). The subgroups are comprised of the 3 -5 measurements and measure short term repeatability of the measurement device. If the control chart is in a state of statistical control throughout the study period, the gage stability is acceptable. There is no numerical acceptance criterion. If the control chart is out of control, analyze the patterns. • For example, the influence of temperature would be expected to appear as cyclical trends that coincides with the ambient temperature. • If the gage operates on plant utilities (e.g., air pressure) abrupt shifts could occur based on plant demand on the utilities (e.g., air pressure). • Single points out of control could be the result of a gage that is overly sensitive to operator technique. • Runs could be the result of different measurement methods

A stability study will also provide an estimate of the within operator repeatability of the gage. StdDevrepeatability = Rbar/d*2 (d2 may be used if the number of subgroups is greater than 20).

R&R

This is the fifth in a series of articles about MSA. The focus of this article will be on measurement repeatability and reproducibility commonly referred to as a gage R&R study. This article will deal solely with the AIAG MSA methodology. The AIAG methodology is the methodology required by many customers, particularly in the automotive industry. Whether you agree with it or not, it is a standard approach and has widespread acceptance. Most suppliers have no option other than to comply. I will deal with other approaches in a later article. This is where calibration completely separates from MSA. There is no equivalent in calibration to R&R. Calibration, bias studies, linearity studies and stability studies have all focused on measurement bias. R&R studies focus on measurement variation. Let’s first start with definitions. What is Repeatability? What is Reproducibility? What is an Operator by Part interaction? Repeatability is the measurement variation observed when a single operator measures one part multiple times. Reproducibility is the measurement variation observed when multiple operators measure one part multiple times. Depending on the measurement system, AND how the MSA study is designed Reproducibility may also be the measurement variation observed when multiple measurement stations or devices measure one part multiple times. For example, a measurement device may consist of a fully automated measurement device comprised of multiple stations. Each station is dimensionally unique and the difference contributes to measurement variation. Another example is multiple, fully automated measurement devices that measure the same characteristic. Each device has a slightly different measurement bias and contributes to the measurement variation. Yet another example is a semi-automated measurement device that is manually loaded. The resulting measurement is influenced by the manner in which the product is loaded into the fixture. Each operator that loads the product has a slightly different technique for loading that influences the measurement variation. Operator by Part Interaction is a situation where the result of an operator’s measurement technique is influenced by the part itself. For example, two operators measure a shaft diameter using techniques that are identical in all respects except one. Operator A takes measurements at the midpoint of the shaft length. Operator B measures at one end of the shaft. Two shafts out of ten have burrs on the ends. Operator A’s measurements are not affected by the burr. Operator B’s measurements are affected by the burr. This will result in an interaction between the operator and the part itself. Part Selection The first step in an effective R&R study is to determine the use of the gage itself. Will it be used for part inspection to a tolerance, for process control, for statistical studies (e.g., a hypothesis test, capability study, DOE, etc.), or for a combination of these? This is very important because it influences the selection and quantity of parts needed for the R&R study. If the gage is used solely for part inspection, the selection of parts is not critical because the part variation is not included in the calculation of the R&R metric, %Tolerance (i.e., P/T Ratio). Some will recommend that parts representing the full spread of the tolerance be used. While this does not hurt, it is not really necessary. If a gage linearity study has been performed, the change in bias over the tolerance spread is known. If a gage linearity study has not been performed and there is a linearity issue an R&R study will not detect it. If the gage is used for part inspection or for statistical tests, the selection of parts is critical because the part variation is part of the calculation of the R&R metric, % Study Variation (i.e., %GRR). It is vital that the parts selected for the study reflect the actual variation of the process. That is, the StdDev of the parts equals the StdDev of the process. Some statistical packages, such as Minitab, allow the entry of the historical StdDev of the process. If your software has this option, use it, entering the process StdDev from a capability study or calculated from SPC charts. If the software does not have the feature, manual calculations using the

historical value are still possible as follows" % Study Variation = 100 * [StdDevR&R / StdDevTotal Variation] StdDevTotal Variation = SQRT[StdDevR&R^2 + StdDevPart Variation^2] Manually substitute the StdDev from a capability study for StdDevPart Variation How many operators, trials and parts do I use? The recommended standard is to have three operators measure ten parts three times each. Is this always the best approach? What flexibility do we have in modifying this? To answer this question, we need to look at how the data are used by the ANOVA calculations. Source of Variation degrees of freedom (n-1) Reproducibility (3 operators) 2 Parts (10 parts) 9 Pure Error (Repeatability) 78 Total Variation (90 measurements) 89 The 10/3/3 approach provides very good estimates of the total variation and the repeatability. The least reliable estimate of variation will be the Reproducibility because it has the smallest degrees of freedom. If concessions must be made, it is better to run fewer trials in order to maintain or increase the number of operators. The total number of measurements should be maintained near 90. The number of parts may be reduced, if (and only if) an independent estimate of part variation (such as from a capability study) is available and used as described in the previous section. Selection of Operators Always use the actual operators that will perform the measurement. Do not use personnel that will not perform the measurement task. Select the operators randomly. Do not handpick the best operators. If only one operator performs the measurement task (e.g., complex analytical equipment), perform the study with that operator only. There is no Reproducibility component in that situation Measurement of Parts Parts should be introduced randomly to each operator by an independent party that is not involved in the actual measurements. This is to prevent potential measurement bias caused by an operator remembering a previous measurement and consciously or unconsciously adjusting the next measurement to match. Parts should be measured using the same method that will normally be used. If Reproducibility is adversely affected by the use of different methods, you need to know that. If there is significant within-part variation in form that adversely affects Repeatability, you need to know that also. What method do I use? In the MSA manual, there are two optional methods: the Range method and the ANOVA method. Both methods will provide very similar results. The Range method uses simpler math, but the ANOVA method can detect a potential Operator x Part interaction. If you have software available, use the ANOVA method. It provides additional information. The only compelling reason for using the Range method is if you must perform manual calculations. continued in next blog entry

Comparison of Two Gages
This is the eighth in a series of articles about MSA. The focus of this article will be on assessing the measurement reproducibility between two measurement systems that must measure the same

characteristic. Does the following scenario seem familiar? An operator performs an online test on a product. The test shows a failure to meet specifications. This is an expensive product, so the line supervisor takes the part to an online tester located on an adjacent line and retests it. This time it passes. The supervisor instructs the operator to go ahead and use the part. Both of them lose confidence in the first measurement device. But which one provided the correct result? There are several approaches that may be used to assess the reproducibility of two measurement devices. One approach that is commonly used when the measurement devices are fully automated is to perform a standard R&R study and replacing the Operators with the Measurement Devices. Reproducibility is now tester to tester reproducibility. The operator*part interaction becomes the tester*part interaction. While this approach does quantify the reproducibility of the two devices, it has the drawback of providing little additional information if a significant difference between the two is noted. It is also limited to fully automated gages. You do have the option of adding gage as a third factor (Parts, Operators, Gages) and analyzing the resulting designed experiment using Analysis of Variance (ANOVA). A second approach is known as the Iso-plot. This is a very simple graphical approach. An x-y plot is constructed with equal scales, and a 45º line is drawn through the origin. Parts are selected throughout the expected measurement range. Each part is measured using both gages. Each part is then plotted on the graph using the value measured by one gage on the x-axis and the value measured by the other gage on the y-axis. Ideally, the coordinates of all parts will lie on the 45º line. If the points fall consistently above or below the line, one gage is biased in respect to the other. The Iso-plot provides an excellent visual assessment of the reproducibility of the two gages, but does not provide quantifiable results. A linear regression analysis of the data used to create the Iso-plot will provide quantifiable results. Ideally, the regression constant should equal zero and the slope should equal one. The regression output will provide the relationship between the two gages as well as confidence and prediction limits. A third approach is the Bland Altman plot. Parts are selected throughout the expected measurement range. Each part is measured using both gages. Calculate the differences between the gages (Gage1 – Gage2), the mean of each pair of measurements and the mean of the differences. Plot the differences on an x-y plot with the differences on the y-axis and the mean of the paired measurements on the x-axis. Draw a horizontal line for the mean of the differences. Draw two more horizontal lines at + / - 1.96 standard deviations of the differences. Approximately 95% of the differences should fall within the limits. The mean line indicates the bias between the two gages. A trend indicates that the bias changes with the size (a linearity difference between the gages). An increase (or decrease) in the width of the pattern with size indicates that the variation of at least one of the gages is dependent on size. If the variation within the limits is of no practical importance, the two gages may be used interchangeably. Do not overlook the differences between gages when evaluating your measurement systems. Your operators will be quick to discover gages that inconsistently accept and reject product between the gages. They will then lose confidence in them and the test itself.

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