Gage R&R.

Gage R&R

Gage R&R Training What is Gage R&R Why Gage R&R Definition of a Gage
Definition of Measurement Error Sources of Measurement Error / Variation Repeatability & Reproducibility A Gage R&R Study Analyzing the Results Understanding The Results Understanding the Graphs Further Analysis Making Use of The Results Summary

Gage R & R Gage R&R Training
It is a Study of the Variation in a measurement system. This includes the gage, operators, parts, characteristic and the environment in which it is measured. The output of the study is the estimated variation(Measurement Error) inherent in the measurement system.

Why Gage R & R Gage R&R Training
Measurement systems are extremely important in continuous process improvement & product confirmation. We must measure to know where we are. We use measurements to tell us if there is a problem in the process or if a process change has improved the process. For measurements to be effective, they must be timely, accurate, and precise. Since you cannot address something that cannot be measured precisely or the when the measurement precision is unknown, you must start with an assessment of the measurement system.

Figure 5-1 Effect of Gage Precision on Quality
Gage R&R Training Why Gage R & R The Effect of the Measurement System Precision on Product acceptance or Rejection.

Why Gage R & R Gage R&R Training
Figure 5-1 Effect of Gage Precision on Quality Gage R&R Training Why Gage R & R The Effect of the Measurement System Precision on Process Control and Improvement. Graph and Table of Actual Cp for Combination of Observed Cp and % R&R OBSERVED CP % R&R %R&R

What is a Gage (Gauge) Gage R&R Training
Definition: Any instrument or apparatus for measuring the state of a phenomenon/characteristic, and or for ascertaining its numerical value at a particular moment

Measurement/Observational Error
Gage R&R Training Measurement/Observational Error Observational error is the difference between a measured value of quantity and its true value. A measurement error is not a "mistake". Variability is an inherent part of things being measured and of the measurement process. 100

Measurement/Observational Error
Gage R&R Training Measurement/Observational Error Every time we repeat a measurement with a sensitive instrument, we obtain slightly different results. The common statistical model we use is that the error has two additive parts: systematic error which always occurs (always the same value) when we use the instrument in the same way, and random error which may vary from observation to observation 100 Random errors - arise from random fluctuations in the measurements Quantified by Gage R&R Studies Can be reduced by repeating measurement many times to obtain a mean value. Systematic/bias errors are consistent and repeatable (constant offset) Controlled by Regular Calibration and Confirmation / Resetting by use of Masters

Sources of Measurement Error
Gage R&R Training Sources of Measurement Error Environment, temperature, lighting, humidity etc. Setting Masters, Visual Aids etc. Condition and suitability of actual measurement equipment. Fixtures, jigs, tables etc. CMM software, excel sheets, calculators etc. Actual person making the measurement. Actual part being measured. Definition of characteristic to be measured. Measurement procedure detail, method, training. Physical constraints, difficultly of access of characteristic to be measured, destructive testing etc.

Variation Due to Operators
Gage R&R Training Sources of Variation Every observation contains both the actual process variation and measurement variation Observed Process Variation Actual Process Variation Calibration Repeatability Variation Due to Gage Variation Due to Operators Long Term Process Variation Variation Within Sample Measurement Variation Short Term Process Variation Stability Linearity

Gage Variability Gage R&R Training
Calibration – Is the gage accurate Stability – does the gage change over time Repeatability – variation of the gage when used by one operator in a brief interval Linearity – is the gage more accurate when used at low values than at high values (How accurate is it across its entire range) Variation within a sample should be included in the process variation – Yet it is also often mixed with measurement variation

Repeatability & Reproducibility
Gage R&R Training Repeatability & Reproducibility Repeatability is the variation observed when an operator measures the same sample with the same gage several times. Reproducibility is the additional variation observed when different operators use the same gage to measure the same sample. Repeatability Reproducibility R&R + =

Preparing for a Gage R&R Study
Gage R&R Training Preparing for a Gage R&R Study 1. Determine the number of parts, the number of appraisers to use and the number of trials. There are several issues that must be considered when planning a gage R&R study. The first is the number of appraisers and the number of parts to use. The number of parts (n) must be greater than or equal to 5. The number of appraisers (k) must be greater than 2. The number of trials (r) must be greater than or equal to two. This represents how often each appraiser will measure a part. In addition, the n*k should be greater than 15. This gives more confidence in the results. If possible, include all the appraisers who operate the gage in the study 2. Select the parts for the study The next step is selecting the parts to include in the study. There are two ways to determine the % gage R&R. One is to compare the gage variation to the variation of the parts used in the study. In this case, the parts should be selected to reflect the range of variation in the process. In other words, don't just take 10 parts off the line right in a row. You need to select the parts so they reflect the variation seen in the manufacturing process. Use this method if the gage is used for process control. The other way to determine the % gage R&R is to compare the results to the specification range. The parts should be selected to cover the entire specification range and if possible some parts outside of the specification range should be used. Use this method if the gage is used for product verification.

Preparing for a Gage R&R Study
Gage R&R Training Preparing for a Gage R&R Study 3. Label the parts from 1 to n and designate the appraisers A, B, etc. 4. Conduct the Measurements The parts must be run in random order. Start with appraiser A. Appraiser A measures the parts in random order. The results are recorded. This process continues for each appraiser without the appraisers being able to see the results from other appraisers. This cycle is continued until you have completed all trials. Be sure that an appraiser cannot see his/her results from previous trials. 5. Use the actual gage that will be used in production. 6. The study must be conducted in the same area, environment, fixtures and conditions that will be used in production. 7. Prepare a worksheet to record all measurements – See example on the next slide..

Gage R&R Training Worksheet Example Random Sequence

Analyzing the Results Gage R&R Training
To demonstrate how to analyze the results, we will use the following example. Suppose you want to determine if a certain gage is capable of measuring the length of a certain part. You decide to do a basic gage R&R study (Average& Range). You select three appraisers (A, B, and C). You select ten parts that represent typical variation in the length output. You have each appraiser measure each part three times. The measurement results are given below. All Measurements in mm.

First we calculate the averages and ranges for each part & for each appraiser/operator Part Average = (Trial 1 + Trial 2 + Trial 3)/3 Ave = ( )/3 = mm Range = Max measurement of part #1 – Min Measurement from part #1 Range = – = mm Repeat for all parts. Calculate the Average of all parts which is identified as Xa (“X” for average and “a” for appraiser A) Calculate the Average Range of all Parts which is identified as Ra (“R” for range and “a” for appraiser A)

5. Repeat calculations of Averages and Ranges for all appraisers/operators.

6. Calculate the part averages for all 10 parts For part #1 = ( )/3 = 3.608

7. Calculate the average of the part averages Add all part averages / 10 = which is identified as Xbar Calculate the Range of the part averages. a) Max part average – Min part average = – = 0.848mm which is identified as Rp

7. You then determine the average range (Rdbar) for the three appraisers. Rdoublebar = (A Rge. + B Rge. + C Rge)/3 = ( )/3 = 8. Then determine the difference between the maximum appraiser average and the minimum appraiser average (Xdiff). A has the maximum average (3.927). C has the minimum average (3.922). Xdiff = = mm

The various contributors to the measurement system variation can now be calculated. There are eight that need to be calculated. There are 2 main methods to calculate Gage R&R are Average & Range and the other is ANOVA. The difference is that ANOVA analyse any interactions between the repeatability and reproducibility. I will describe the Average and Range method in this presentation as the calculations are easier to follow. Equipment variation (EV) Appraiser variation (AV) Repeatability and reproducibility (GRR) Part variation (PV) Total variation (TV) Number of Distinct Categories (NDC) Interclass Correlation (IC) Probable Error (PE)

Analyzing the Results Gage R&R Training = R
Repeatability: Equipment Variation (EV) This is the "within appraiser" variation. It measures the variation one appraiser has when measuring the same part (and the same characteristic) using the same gage more than one time. The calculation is given below. EV = Rdbar x K1 where K1 is a constant that depends on the number of trials. For 2 trials, K1 is For 3 trials, K1 is For this example: EV = Rdbar x K1 = x = Average of Ra,Rb,Rc = R K1 = Constant (explained later)

Reproducibility: Appraiser Variation (AV) This is the "between appraisers" variation. It is the variation in the average of the measurements made by the different appraisers. The calculation is given below. AV = SQ. ROOT ((X DIFF X K2)SQUARED - (EV SQUARED/NR)) where N = number of parts and R = number of trials The bias correction factor for ranges used here is the bias correction factor for estimating variances which is commonly known as K2 AV =Sqrt(( x ) ^2 – (( ^2)/(10x3))) AV= SQRT ABS( – ) = X1 = SQ. ROOT ((X DIFF X K2)SQUARED = Variance of measurement system X2 = (EV SQUARED/NR)) = Variance of gauge So AV = X1 – X2 = Variation between the appraisers.

Repeatability and Reproducibility (GRR)
Gage R&R Training Analyzing the Results Repeatability and Reproducibility (GRR) The next calculation combines the two above to determine GRR, which is given by: GRR = SQRT(EV^2 + AV^2) For this example, GRR = SQRT( ^ ^2) = For this example the Equipment has a greater effect to variance than the operators Repeatability Reproducibility R&R + =

Analyzing the Results Gage R&R Training Part Variation (PV)
The part variation is determined by multiplying the range of the part averages (Rp) by a constant K3. K3 depends on the number of parts. For 10 parts, K3 = The part variation is then given by: PV = Rp x K3 = x = 0.267mm Total Variation (TV) This is the total variation from the study. It is determined by the following equation: TV = SQRT(GRR^2 + PV^2) TV =SQRT( ^ ^2) = mm

Number of Distinct Categories (NDC).
Gage R&R Training Analyzing the Results Number of Distinct Categories (NDC). This is a measure of the number of distinct categories that can be distinguished by the measurement system. It is similar to looking at how many possible values there are on a range control chart. The calculation is: NDC= 1.41(PV/GRR) = 1.41(0.267/ ) = 13.5 If the number of categories is less than two, the measurement system is of minimal value because it is difficult to distinguish one entity from another. If the number of categories is two, the measurement system can only divide the data into two groups low and high. If the number of categories is three, the measurement system can divide the data into three groups low, medium, and high. A measurement system that is acceptable and useful for process improvement activities must have five or more distinct categories; ten or more is ideal.

The Results Gage R&R Training But What Do The Results Mean
This is the Typical Result of a Gage R&R Study But What Do The Results Mean

The Results Gage R&R Training 11.76% 109.78%
The GR&R Result Does Not Indicate the % of the Variance or Tolerance Consumed by The Measurement system WHY THESE “PERCENTAGES” DO NOT ADD UP The %EV and %AV do not add up to the %GRR because they are not proportions. Likewise, the %GRR and the %PV do not add up to 100% because they are not proportions. They are instead trigonometric functions. 11.76% 109.78%

The Results Gage R&R Training
The GR&R Result Does Not Indicate the % of the Variance or Tolerance Consumed by The Measurement system PV TV AV EV R&R In this diagram we can begin to see why these quantities do not add up. While they are dressed up to look like proportions, and while they were interpreted as proportions, they are, and always have been, nothing more than trigonometric functions. And trigonometric functions do not satisfy the conditions needed for a set of ratios to be interpreted as proportions.

The Results as True Ratios
Gage R&R Training The Results as True Ratios So what is additive in a Gauge R&R Study? Look at the structure of the formula for TV. The Total Variance is the sum of the Repeatability Variance, the Reproducibility Variance, and the Product Variance. TV = SQRT(GRR^2 + PV^2) = TV = SQRT(EV^2 + AV^2 + PV^2) Therefore by ^2 both sides TV^2 = EV^2 + AV^2 + PV^2 So the proportion of the Total Variation is - %EV = 100*(EV^2/TV^2) = 100*( / ) = 1.0% %AV = 100*(AV^2/TV^2) = 100*( / ) = 0.1% %R&R = 100*(R&R^2/TV^2) = 100*( / ) = 1.1% %PV = 100*(PV^2/TV^2) = 100*( / ) = 98.9% % R&R + %PV = Total Variation. = 100% Therefore the Measurement System Error = 1.1% of the Total Variance of the Study. To Calculate the %Tol substitute (Tol/5.04)^2 for TV^2 %R&R =%R&R = 100*(R&R^2/ (Tol/5.04)^2 )= 100*( / ) = 0.52%

Understanding The Results
Gage R&R Training Understanding The Results As you can see from the results below there is a vast difference in the % reported. The AIAG MSA uses an assumption of additively which is a violation of the Pythagorean Theorem, and is what makes it impossible to make sense of the ratios %EV, %AV, %R&R & %PV. It is why the “percentages” do not add up, and this is why many engineers can not figure out exactly what the final numbers in a Gauge R&R Study represent. They are confusing because they are trigonometric functions being interpreted as proportions when they are not proportions. The Wheeler method reports the results as an actual proportion of the variance or tolerance. This makes the results easier to interpret and gives a real meaning to the results.

Understanding The Graphs
Gage R&R Training Understanding The Graphs Step 1 Measurement Stability A stable measurement system shows no out of control points or "non-random" patterns or trends in the range chart Step 2 Resolution / Discrimination Adequate resolution or discrimination means that the measurement units (inches, tenths of inches, thousandths of inches,…) are sufficiently small enough to be able to "see" variation. - Stratification on a range chart is a good indication that there is a problem with inadequate resolution. - The number of stratified levels on the Range Chart is an indicator of the degree of the problem. - Fewer "levels" means less adequate resolution: - A rule of thumb: There should be approximately 5 levels of resolution between the control limits on the Range Chart and less than 25% of the ranges equal to zero to be considered adequate.

Gage R&R Training Understanding The Graphs Step 3 Bias Bias in a measurement study is a "shift" in the pattern on the X-bar chart between operators (i.e., the same part pattern is evident, but one operator reads consistently higher or lower than the others). Step 4 Measurement Capability Measurement capability is the comparison of Measurement Variation to Product Variation to determine whether the current measurement process can see part to part differences. More than 50% of the part measurements should be out-of-control to be considered marginally acceptable.

Gage R&R Training Understanding The Graphs Step 5 Operator Bias Operator Bias is the comparison of Between-Operator variation to Within-Operator variation. An out-of-control chart indicates that a Bias does exist between operators, while a chart exhibiting control indicates that no Bias exists between operators.

Gage R&R Training Understanding The Graphs Step 6 Operator Inconsistency Operator Inconsistency is the comparison of Within-Operator variation for a specific operator to the overall Within-Operator variation. An out-of-control chart indicates that a Inconsistency does exist between operators, while a chart exhibiting control indicates that no Inconsistency exists between operators.

Understanding the Results
Gage R&R Training Understanding the Results Step 7 Interclass Correlation & Discrimination Ratio The major axis reflects product variation, and the minor axis reflects measurement error. The Discrimination Ratio is the ratio of the major axis to the minor axis. IC >0.9 = First Class Monitor DR > 4 Gage appears to have adequate discrimination

Futher Analysis Gage R&R Training
Interclass Correlation; Signal Attenuation & Discrimination Ratio We use the Interclass Correlation to characterize the ability of a measurement system to capture meaningful information about a production stream. The proportion of the total variance that is consumed by the part variation is an estimate of the Interclass Correlation Coefficient. IC = PV^2/TV^2 IC = 0.267^2 / ^2 = 0.989 The Discrimination Ratio is the ratio of the major axis to the minor axis. DR = See ANOVA worksheet for calculations. The amount by which a signal coming from the production process is attenuated by the effects of measurement error may be estimated by: Production Process Signal Attenuation = 1 – sqrt IC = 1 – Sqrt = 0.55%

Futher Analysis Gage R&R Training
Probable Error PE (Average Error of a single Measurement) Use the estimated Repeatability and Reproducibility Variance Component R&R to find an estimate of the Probable Error PE= X R&R PE = X =

Making Use of the Results Measurement Increment (Gage Resolution)
Gage R&R Training Making Use of the Results Measurement Increment (Gage Resolution) The diagram below shows how the size of the measurement increment will affect the median error of a measurement. Inspection of diagram shows that as long as the measurement increment is less than one Probable Error, there is virtually no inflation in the error of a measurement. However, as the measurement increment exceeds the Probable Error, the inflation begins to increase in a non-linear manner. This non-linear relationship leads to a preference that the measurement increment should be approximately the same size as the Probable Error. When the measurement increment is greater than 2.0 PE you will be loosing information due to the round-off. When it is less than 0.2 PE you will be writing down meaningless digits.

Making Use of the Results
Gage R&R Training Making Use of the Results Measurement Increment (Gage Resolution) Thus, the Probable Error provides us with an objective way to determine how many digits to record for any measurement. When the number of digits recorded is discretionary, we should seek to have a measurement increment that satisfies the following: 0.2 Probable Error < measurement increment < 2 Probable Errors Smallest Effective Measurement Increment = 0.2 X PE = 0.2 X = Largest Effective Measurement Increment = 2 X PE = 2 X = The measurement increment (gage resolution) should be between the smallest and largest effective measurement increment. So a gage resolution of 0.05 NG 0.01 is OK 0.001 NG

Gage R&R Training Making Use of the Results Watershed Specifications While the minimum acceptable value is considered to be in-spec, a value that is one measurement increment below the minimum acceptable value will be out-of-spec. Thus the actual watershed point between an acceptable value and an unacceptable value is halfway in between these two values, and the Lower Watershed Specification Limit is: LWSL = minimum acceptable value – one-half of a measurement increment Specification = 0.7 to 1.2 mm Gage Resolution = 0.1 LWSL = 0.7 – 0.05 = 0.65 and therefore the UWSL = = 1.25

Gage R&R Training Making Use of the Results Manufacturing Specifications The idea behind manufacturing specifications is to define those measurement values which correspond to conforming items. That is, when the measurement falls within the manufacturing specifications we want to be able to say that the product is within the customer specifications. In the absence of measurement error we could achieve this objective by simply using the customer specifications as the manufacturing specifications. But when we have to make allowance for measurement error there will need to be some gap between the manufacturing specifications and the customer specifications. How to determine the size of the gap, D,

Making Use of the Results Manufacturing Specifications
Gage R&R Training Making Use of the Results Manufacturing Specifications If we choose a large value for D we can be very confident that the product is conforming, but we could end up with very tight manufacturing specifications. When this happens there will be an increased risk of rejecting conforming product. By choosing a small value for D we will not have as much confidence that the product is conforming, but we will have looser manufacturing specifications with a correspondingly smaller risk of rejecting conforming product.

Gage R&R Training Making Use of the Results Manufacturing Specifications The minimum probability of a conforming item is shown as a function of the capability index. This graph shows that, without adjustment, using the Watershed Specifications as the Manufacturing Specifications will result in anywhere from a 64% chance of conforming product to an 83% chance as the capability varies from 0.10 to 2.00. The Minimum Probability of Conforming Product When The Observed Measurement = Maximum / Minimum Acceptable Value

Gage R&R Training Making Use of the Results Manufacturing Specifications The probabilities in graph below range from 85% to 95% depending upon the capability. If you want to have at least a 85 percent chance that the measured item is in spec when the measurement falls within the Manufacturing Specifications, then you will need to tighten up the Watershed Specification Limits by one Probable Error, or 0.675σe on each end, and use these tightened specs as your 85% Manufacturing Specifications. For two-sided specifications this adjustment for measurement error consumes 1.35σe of the Watershed Tolerance.

Gage R&R Training Making Use of the Results Manufacturing Specifications The graph below represent the cases where the watershed specifications have been tightened by 2, 3 & 4 Probable Errors. Thus, if you want at least a 99.9 percent chance that you are shipping good stuff, your 99.9% Manufacturing Specifications will be the Watershed Specification Limits tightened by four Probable Errors, or 2.70σe, on each end. For two-sided specifications this adjustment for measurement error consumes 5.40σe of the Watershed Tolerance. 4PE 3PE 2PE

Gage R&R Training Making Use of the Results Manufacturing Specifications Example of analysis in Diagram Below. Based on the process capability and the use of the gage you need to determine the manufacturing specifications for production control and inspection specifications for product acceptance. i.e. Watershed Limits adjusted by 1,2,3,4,or more PE

Common Mistakes in a Gage R&R Study
Gage R&R Training Common Mistakes in a Gage R&R Study Not following the instructions for conducting the study. Failing to have standardized measuring method that everybody is trained on, & following. Using only one part or a master. If you only use one part, THERE CAN'T BE ANY PART VARIATION, so people and equipment are the ONLY source of variation. Collecting parts that are too close together and do not represent the total variation. Process Control Collecting parts that are too close together and do not represent the total tolerance range. Product Control. Using a gage that measures in too much or too little resolution. Not Randomizing all samples, test subjects, and trials so you don't have confounding of factors in the data. Using the result of 1 Gage R&R study on 1 characteristic to read across to other parts or characteristics that use the same or same type of gage. Conducting the study in Lab conditions and not at the station where the measurements are actually taken in production. Not understanding and doing nothing with the results. Not repeating the Gage R&R study on a minimum 12 month basis.

How to Decrease Measurement Error
Gage R&R Training How to Decrease Measurement Error Source Check / Improve Environment, temperature, lighting, humidity etc. Setting Masters, Visual Aids etc. Condition and suitability of actual measurement equipment. Fixtures, jigs, tables etc. CMM software, excel sheets, calculators etc. Ensure that the environment is correct for the measurement, is the lighting adequate to read the gage, do changes in temperature or humidity effect the result. Are the masters correct, in specification, easy to use, are the visual aids correct and controlled and calibrated. Is the measurement equipment in calibration, is the stability understood, is it maintained, easy to use and read. Is it controlled and stored correctly. Are all fixtures, jigs tables etc in good repair are they maintained, are the inspection / measurement stations ergonomic. Are you sure all of your calculation methods are correct, all equations have been check, are there updated versions.

How to Decrease Measurement Error
Gage R&R Training How to Decrease Measurement Error Source Check / Improve Actual person making the measurement. Actual part being measured. 8. Definition of characteristic to be measured. Measurement procedure detail, method, training. Physical constraints, difficultly of access of characteristic to be measured, destructive testing etc. 6. Are they capable of making the measurement, eye sight etc. Have they been trained, continual improvement. 7. Is the part easy to measure, handle, The Within Part Variation is quantified and measurement methods developed to take this into account. 8. Is the characteristic being measured well defined and understood. 9. Are the measurement procedures correct, have enough detail, is the training material and methods adequate. Is the characteristic difficult to access, does the act of measurement change the characteristic.

Summary Gage R&R Training Average & Range ANOVA
Understanding your measurement system and its impact on your manufacturing process and your product quality is important. The goal is to constantly improve process control, reducing the variability of the process and product. In order to address the actual process variability the variability due to the measurement system must be identified and separated from that process. Studies of measurement variation are a waste of time unless you use that information to reduce process variation, increase process control and assure product confirmation. Fortunately there is no need to go through the laborious task of the calculations shown in the presentation as the 2 files attached below do this automatically for you. So Please use Gage R&R correctly – Understand what the results are telling you and take actions based on the results. Gage R&R is not just an annoying PPAP requirement it is a tool for improvement. Average & Range ANOVA

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