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  • 1. Training Material for M EASUREMENT S YSTEM A NALYSIS
  • 2. Contents :
    • INTRODUCTION FOR MEASUREMENT SYSTEM ANALYSIS
    • GENERAL METHODS ILLUSTRATION FOR MEASUREMENT SYSTEM ANALYSIS
      • VARIABLE GAGE ANALYSIS METHOD
      • 1) THE AVERAGE-RANGE METHOD
      • 2) THE ANOVA METHOD
      • ATTRIBUTE GAGE ANALYSIS METHOD
      • 1) SHORT METHOD
      • 2) HYPOTHESIS TEST ANALYSIS
      • 3) SIGNAL DETECTION THEORY
      • 4) LONG METHOD
    • ACCEPTABILITY CRITERIA
    • CONCLUSION
    • FOUR METHODS COMPARISON
  • 3. Introduction: Basic requirements by QS-9000 & TS16949
    • Base on QS9000 & TS16949 requirements, all measurement system which were
    • mentioned in Quality Plan should be conducted Measurement System Analysis.
    MSA Requirement
  • 4. Introduction: The category of Measurement System
    • Most industrial measurement system can be divided two categories, one is variable
    • measurement system, another is attribute measurement system. An attribute gage
    • cannot indicate how good or how bad a part is , but only indicates that the part is
    • accepted or rejected. The most common of these is a Go/No-go gage.
    Variable Gage Attribute Gage (Go/No-go Gage)
  • 5. Introduction: What is a measurement process General Process Measurement Process Measurement: The assignment of a numerical value to material things to represent the relations among them with respect to a particular process. Measurement Process: The process of assigning the numerical value to material things. Operation Output Input Measurement Analysis Value Decision Process to be Managed
  • 6. Introduction: What are the variations of measurement process
  • 7. Introduction: What are the variations of measurement process Measurement(Observed) Value = Actual Value + Variance of The Measurement System 2 σ obs = 2 σ actual + σ variance of the measurement system 2
  • 8. Introduction: Where does the variation of measurement system come from?
    • The Five Characterizations of Measurement System:
    • 1. Location Variation: Bias; Stability; Linearity
    • Bias is the difference between the observed average of measurements and a
    • reference value. Bias is often referred to as accuracy. It is a systematic error
    • component of the measurement system
  • 9. Introduction: Where does the variation of measurement system come from?
    • The Five Characterizations of Measurement System:
    • 1. Location Variation: Bias; Stability; Linearity
    • Stability(Alias: Drift): Stability is the total variation in the measurements
    • obtained with a measurement system on the same master or parts when measuring
    • a single characteristic over an extended time period. A stable measurement process
    • is in statistical control with respect to location.
    Stability
  • 10. Introduction: Where does the variation of measurement system come from?
    • The Five Characterizations of Measurement System:
    • 1. Location Variation: Bias; Stability; Linearity
    • Linearity is the difference in the bias values through the expected operating range
    • of the measurement instrument. It is a systematic error component of the
    • measurement system.
    Linearity
  • 11. Introduction: Where does the variation of measurement system come from?
    • The Five Characterizations of Measurement System:
    • 2. Width Variation: Repeatability; Reproducibility; Gage R&R
    • Repeatability is the variation in measurements obtained with one measurement
    • instrument when used several times while measuring the identical characteristic
    • on the same part by an appraiser. It is a Within-system variation, commonly
    • referred to as E.V.---Equipment Variation.
    Repeatability
  • 12. Introduction: Where does the variation of measurement system come from?
    • The Five Characterizations of Measurement System:
    • 2. Width Variation: Repeatability; Reproducibility; Gage R&R
    • Reproducibility is the variation in the average of the measurements made by
    • different appraisers using the same gage when measuring the identical
    • characteristics of the same part. It is between-system variation, commonly
    • referred to as A.V.---Appraiser Variation.
    Reproducibility
  • 13. Introduction: Where does the variation of measurement system come from?
    • The Five Characterizations of Measurement System:
    • 2. Width Variation: Repeatability; Reproducibility; Gage R&R
    • Gage R&R means Gage repeatability and reproducibility, which combined
    • estimate of measurement system repeatability and reproducibility.
    • This combined measurement error then is compared with the process output
    • variability to compute the gage percentage R&R (%R&R ) . The %R&R is the
    • basis for making a judgment of whether the measurement system is good enough
    • to measure the process.
  • 14. Analysis Techniques:
    • Currently there are three techniques for variable measurement system and four
    • techniques for attribute measurement system analysis were recommended by
    • AIAG MSA Reference Manual.
    • Range Method
    • Average - Range
    • Method
    • ANOVA
    • Short Method
    • Long Method
    • Hypothesis Test Analyses
    • Signal Detection Theory
    • Followings are some practical examples to illustrate how to perform four
    • methods respectively.
    Variable Gage Attribute Gage
  • 15. Analysis Techniques: Preparation before MSA
    • The approach to be used should be planned.
    • The number of appraisers, number of sample parts, and number of repeat
    • readings should be determined in advance.
    • The appraisers should be selected form those who normally operate the
    • instrument.
    • The sample parts must be selected from the process and represent its entire
    • operating range.
    • The instrument must have a discrimination that allows at least one-tenth of
    • the expected process variation of the characteristic to be read directly.
    • The measurement procedure should be defined in advance to ensure the
    • consistent measuring method.
  • 16. Analysis Techniques: Variable Gage Analysis
    • General Gage R&R Study:
    The Average and Range Method The ANOVA Method The common step for conducting Gage R&R study: 1. Verify calibration of measurement equipment to be studied. 2. Obtain a sample of parts that represent the actual or expected range of process variation. 3. Add a concealed mark to each identifying the units as numbers 1 through 10. It is critical that you can identify which unit is which. At the same time it is detrimental if the participants in the study can tell one unit from the other (may bias their measurement should they recall how it measured previously). 4. Request 3 appraisers. Refer to these appraisers as a A, B, and C appraisers. If the measurement will be done repetitively such as in a production environment, it is preferable to use the actual appraiser that will be performing the measurement.
  • 17. For extreme cases, a minimum of two appraisers can be used, but this is strongly discouraged as a less accurate estimate of measurement variation will result. 5. Let appraiser A measure 10 parts in a random order while you record the data noting the concealed marking. Let appraisers B and C measure the same 10 parts Note: Do not allow the appraisers to witness each other performing the measurement. The reason is the same as why the unit markings are concealed, TO PREVENT BIAS. 6. Repeat the measurements for all three appraisers, but this time present the samples to each in a random order different from the original measurements. This is to again help reduce bias in the measurements. Analysis Techniques: Variable Gage Analysis …… 10 Parts 3 Appraisers 3 Trials
  • 18.
    • The Average and Range Method:
    • A range control chart is created to determine if the measurement process is stable
    • and consistent. For each appraiser calculate the range of the repeated measurements
    • for the same part.
    Analysis Techniques: Variable Gage Analysis
  • 19. Analysis Techniques: Variable Gage Analysis The average range for each operator is then computed. The average of the measurements taken by an operator is calculated. A control chart of ranges is created. The centerline represents the average range for all operators in the study, while the upper and lower control limit constants are based on the number of times each operator measured each part (trials).
  • 20. Analysis Techniques: Variable Gage Analysis The centerline and control limits are graphed onto a control chart and the calculated ranges are then plotted on the control chart. The range control chart is examined to determine measurement process stability. If any of the plotted ranges fall outside the control limits the measurement process is not stable , and further analysis should not take place. However, it is common to have the particular operator re-measure the particular process output again and use that data if it is in-control.
  • 21. Analysis Techniques: Variable Gage Analysis Repeatability - Equipment Variation (E.V.) The constant d 2 * is based on the number of measurements used to compute the individual ranges(n) or trials, the number of parts in the study, and the number of different conditions under study. The constant K 1 is based on the number of times a part was repeatedly measured (trials). The equipment variation is often compared to the process output tolerance or process output variation to determine a percent equipment variation (%EV).
  • 22. Analysis Techniques: Variable Gage Analysis Reproducibility - Appraiser Variation(A.V.) X diff is the difference between the largest average reading by an operator and the smallest average reading by an operator. The constant K 2 is based on the number of different conditions analyzed. The appraiser variation is often compared to the process output tolerance or process output variation to determine a percent appraiser variation (%AV).
  • 23. Analysis Techniques: Variable Gage Analysis Repeatability and Reproducibility( Gage R&R) The gage error (R&R) is compared to the process output tolerance to estimate the precision to tolerance ratio (P/T ratio). This is important to determine if the measurement system can discriminate between good and bad output. The basic interest of studying the measurement process is to determine if the measurement system is capable of measuring a process output characteristic with its own unique variability. This is know as the Percent R&R (P/P ratio, %R&R), and calculated as follows:
  • 24. Analysis Techniques: Variable Gage Analysis Process or Total Variation: If the process output variation (  m ) is not known, the total variation can be estimated using the data in the study. First the part variation is determined: Rp is the range of the part averages, while K 3 is a constant based on the number of parts in the study. The total variation (TV) is just the square root of the sum of the squares of R&R and the part variation
  • 25. Analysis Techniques: Variable Gage Analysis
    • The ANOVA Method:
    • A weakness with the Average-Range method of using the range to determine
    • gage R&R is that it does not consider the variation introduced into a measurement
    • through the interaction between different conditions (appraiser) and the gage.
    • Consequently, to account for this variation an analysis of variance method (ANOVA)
    • is utilized. In addition, when the sample size increases, use of the range to estimate
    • the variation in not very precise. Furthermore, with software packages readily
    • available, the ANOVA method is a viable choice.
    • The total variation in an individual measurement equals:
    • The part to part variation is estimated by  p 2 ; the operator variation is estimated by
    •  o 2 ; the interaction effect is estimated by  op 2 ; while repeatability is estimated by  r 2
  • 26. Analysis Techniques: Variable Gage Analysis Part: Operator: Interaction: Repeatability:
  • 27. Analysis Techniques: Variable Gage Analysis Total: The gage R&R statistics are then calculated as follows: Measurement Error: Part: Operator: Interaction: Reproducibility : Repeatability : Measurement Error : Total :
  • 28. Analysis Techniques: Variable Gage Analysis
    • Acceptability Criteria:
    • The gage repeatability and reproducibility: %R&R (P/P ratio: % total of total
    • variance; P/T ration:% total of tolerance):
    • Less than 10% Outstanding
    • 10% to 20% Capable
    • 20% to 30% Marginally Capable
    • Greater than 30% NOT CAPABLE
    • For the P/P ratio and the P/T ratio, either or both approaches can be taken
    • depending on the intended use of the measurement system and the desires of the
    • customer. Generally, If the measurement system is only going to be use to inspect
    • if the product meets the specs, then we should use the %R&R base on the tolerance
    • (P/T ratio). If the measurement system is going to be use for process optimization
    • /characterization analysis, then we should use the %R&R base on total variation
    • (P/P ratio).
  • 29. Analysis Techniques: Variable Gage Analysis
    • Acceptability Criteria:
    • For a Gage deemed to be INCAPABLE for it’s application. The team must review
    • the design of the gage to improve it’s intended application and it’s ability to
    • measure critical measurements correctly. Also, if a re-calibration is required, please
    • follow caliberation steps.
    • If repeatability is large compared to reproducibility, the reasons might be:
    • 1) the instrument needs maintenance, the gage should be redesigned
    • 2) the location for gaging needs to be improved
    • 3) there is excessive within-part variation.
    • If reproducibility is large compared to repeatability, then the possible causes
    • could be:
    • 1) inadequate training on the gage,
    • 2) calibrations are not effective,
    • 3) a fixture may be needed to help use the gage more consistently.
  • 30. Analysis Techniques: Variable Gage Analysis
    • The Measurement Bias:
    • Using a certified sample, and a control chart of repeated measurements, the bias of
    • a measurement process can be determined. Bias is the difference between the known
    • value and the average of repeated measurement of the known sample. Bias is
    • sometimes called accuracy.
    Process Variation = 6 Sigma Range Percent Bias = BIAS Process Variation
  • 31. Analysis Techniques: Variable Gage Analysis
    • Linearity :
    • Linearity of a measurement process is the difference in the bias or precision values
    • through the expected operating range of the gauge. To evaluate linearity, a graph
    • comparing the bias or precision to the expected operating range is created.
    • A problem with linearity exists if the graph exhibits different bias or precision for
    • different expected operating ranges.
    • By using the following procedure, linearity can be determined.
    • 1) Select five parts whose measurements cover the operating range of the gage.
    • 2) Verify the true measurements of each part.
    • 3) Have each part be randomly measured 12 times on the gage by one operator.
    • 4) Calculate the part average and the bias for each part.
    • 5) Plot the bias and the reference values.
    • 6) Calculate the linear regression line that best fits these points.
  • 32. Analysis Techniques: Variable Gage Analysis 7) Calculate the goodness of fit statistic:
  • 33. Analysis Techniques: Variable Gage Analysis 8) Determine linearity and percent linearity: Linearity = Slope x Process variation(  m ) %Linearity = 100[linearity/Process Variation] The acceptability criteria of Bias, Linearity depend on Quality Control Plan, characteristic being measured and gage speciality, suggested criteria of ESG is as following: Under 5% - acceptable 5% to 15% - may be acceptable based upon importance of application, cost of measurement device, cost of repairs, etc., Over 15% - Considered not acceptable - every effort should be made to improve the system The stability is determined through the use of a control chart. It is important to note that, when using control charts, one must not only watch for points that fall outside of the control limits, but also care other special cause signals such as trends and centerline hugging.Guideline for the detection of such signals can be found in many publications on SPC.
  • 34. Analysis Techniques: Attribute Gage Study
    • Short Method:
    • A Short Method example for battery length go/no-go gage study: The Short
    • method need to be conduct by selecting 20 parts which have been measured by
    • a variable gage in advance, some of the parts are slightly below and above both
    • specification limits . Two appraisers then measure all parts twice randomly.
    Measurement Result table 1
  • 35. Analysis Techniques: Attribute Gage Study Acceptability criteria: If all measurement results (four per part) agree, the gage is acceptable. If the measurement results do not agree, the gage can not be accepted, it must be improved and re-evaluated. Conclusion: Because table 1 listed measurement results are not whole agreement, at part 15# and 17#, appraiser’s decisions are not agree. so the battery length gage can not be used and must be improved and re-evaluated.
  • 36. Analysis Techniques: Attribute Gage Study
    • Hypothesis Test Analysis:
    • Short method should know the variable reference value of samples in advance.
    • However, in some situations it is hard to realize to get all samples variable
    • reference value. So in this case, Hypothesis test analysis shall be applied for gage
    • study.
    II II Target I I III USL LSL
  • 37. Analysis Techniques: Attribute Gage Study
    • Hypothesis test analysis depends on cross tabulation method which needs to take
    • a random sample of 50 parts from the present process and use 3 appraisers who
    • make 3 measurements on each part and decide if the part is acceptable or not.
    • Appraisers measure the parts and if the part is within limits they give “1” and if not
    • they give “0” and write those results in a table. In order to eliminate any bias
    • produced, the labeled samples are mixed before giving to appraisers for identification
    • in each trails. Following table 2 listed filler gage measuring results for the battery
    • welding gap:
    …… 50 Samples 3 Appraisers 3 Trials
  • 38. Table 2 Filler gage measuring result
  • 39. Table 2 Filler gage measuring result
  • 40. Table 2 Filler gage measuring result Analysis Techniques: Attribute Gage Study In order to determine the level of agreement among the appraisers, we applied Cohen’s Kappa which is used to assess inter-rater reliability when observing or otherwise coding qualitative/categorical variables. It can measure the agreement between the evaluations of two raters when both are rating the same object.
  • 41. Step 1. Organize the score into a contingency table. Since the variable being rated has two categories, the contingency table will be a 2*2 table: Table 3 Analysis Techniques: Attribute Gage Study A*B Cross-Tabulation Table 3
  • 42. Analysis Techniques: Attribute Gage Study Step 2. Compute the row totals (sum across the values on the same row) and column totals of the observed frequencies. Step 3 Compute the overall total (show in the table 3). As a computational check, be sure that the row totals and the column totals sum to the same value for the overall total, and the overall total matches the number of cases in the original data set. Step 4 Compute the total number of agreements by summing the values in the diagonal cells of the table. Σa = 53+ 89 = 142 Step 5 Compute the expected frequency for the number of agreements that would have been expected by chance for each coding category. ef = = = 21.6 Repeat the formula for other cell, we got other expected count (show in the table 3). row total * col total overall total 59 * 55 150
  • 43. Step 6 Compute the sum of the expected frequencies of agreement by chance. Σef = 21.6+57.6 = 79.2 Step 7 Compute Kappa K = = = 0.89   Step 8 Evaluate Kappa - A general rule of thumb is that values of kappa greater than 0.75 indicate good to excellent agreement; values less than 0.4 indicate poor agreement.   Repeat above step, we can got following kappa measures for the appraisers: Table 4 Analysis Techniques: Attribute Gage Study Σ a- Σef N - Σef 142 - 79.2 150 - 79.2 Table 4
  • 44. Using the same steps to calculated the kappa measure to determine the agreement of each appraiser to the reference decision: Table 5 Total summary on Table 6: Analysis Techniques: Attribute Gage Study Table 5
  • 45. Analysis Techniques: Attribute Gage Study
  • 46. Analysis Techniques: Attribute Gage Study The AIAG MSA reference manual edition 3 provides acceptability criteria for each appraisers results: Definition: False Alarm – The number of times of which the operator (s) identify a good sample as a bad one. Miss – The number of times of which the operators identify a bad sample as a good one.
  • 47. Analysis Techniques: Attribute Gage Study So summarizing all the information of the example with this table: Table 7 Number of correct decisions Total opportunities for a decision Effectiveness = Number of False Alarm Total opportunities for a decision False Alarm Rate = Number of False Alarm Total opportunities for a decision Miss Rate =
  • 48. Analysis Techniques: Attribute Gage Study Conclusion: The measurement system was acceptable with appraiser B, marginal with appraiser A, and unacceptable for C. So we shall determine if there is a misunderstanding with appraiser C that requires further training and then need to re-do MSA. The final decision criteria should be based on the impact to the remaining process and final customer. Generally, the measurement system is acceptable if all 3 factors are acceptable or marginal. Minitab also can perform attribute gage analysis, but it didn’t declare the acceptability criteria, so it is not recognized by QS9000 standard.
  • 49. Analysis Techniques: Attribute Gage Study
    • Signal Detection Theory is to determine an approximation of the width of the
    • region II area so as to calculate the measurement system GR&R.
    • Also used filler gage as example to perform Signal Detection approach. The
    • tolerance is 0.45 ~0.55mm. The process needs to take a random sample of 50
    • parts from the practical process and use 3 appraisers who make 3 measurements
    • on each part, and then got following table: Table 8
    II II Target I I III USL LSL
  • 50. Table 8 Signal Detection Table for Filler Gage
  • 51. Table 8 Signal Detection Table for Filler Gage
  • 52. Analysis Techniques: Attribute Gage Study
    • Above table 8 shows the 50 parts measurement result, “0” standard rejected, “1”
    • standard acceptable, code “-” standard region I, code “x” standard region II,
    • code “+” standard region III.
    • And then base on the part reference value to arrange in order from Max. to Min.,
    • meanwhile to show the code: Table 9
    Region III Region I Region I Region II Region II
  • 53. Analysis Techniques: Attribute Gage Study
    • Next step we should find Xa value which located region I , but is the nearest to
    • region II. Xb value which located region III, but is the nearest to region II.
    • And then calculate the distance of region II.
    • dLSL = Xa,LSL - Xb,LSL = 0.446697 – 0.470832 = 0.024135
    •  
    • dUSL = Xa,USL - Xb,USL = 0.566152 – 0.542704 = 0.023448
    0.023791 0.55 – 0.45 %GR&R = = = 0.277 = 27.7% GR&R USL -LSL
    • Conclusion: The %GR&R is larger than 10%, but less than 30%, it may be
    • acceptable based upon importance of application, cost of measurement device,
    • cost of repairs, etc.
    GR&R = = = 0.023791 dUSL +dLSL 2 0.023448 + 0.024135 2
  • 54. Analysis Techniques: Attribute Gage Study
    • Long Method is used the concept of the Gage Performance Curve (GPC) to
    • develop a measurement system study. It focuses on assessing the repeatability
    • and bias of the measurement system. The purpose of developing a GPC is to
    • determine the probability of either accepting or rejecting a part of some
    • reference value.
  • 55.
    • The first step of Long Method is the part selection. It is necessary to know the
    • part reference value which was measured with variable measurement system. The
    • approach should select 8 parts as nearly equidistant intervals as practical . The
    • Maximum and minimum values should represent the process range . The 8 parts
    • must be measured 20 times with the attribute gage. We use “m” to represent the
    • measuring times, use “a” to represent the number of accepts.
    • For the smallest (or largest) part, the value must be a=0; For the largest (or smallest)
    • part, the value must be a=20; For the 6 other parts, the value 1≤a≤19.
    Analysis Techniques: Attribute Gage Study 1 Appraiser 20 Trials …… 8 Samples
  • 56. Analysis Techniques: Attribute Gage Study Example: We use a filler gage to measure the fitting gap between battery and hand phone which specification is 0~0.2mm. The number of accepts for each part are: Table 10 Table 10
  • 57. Analysis Techniques: Attribute Gage Study
    • The second step is the acceptance probabilities calculation for each part using the
    • binomial adjustments:
    Table 11 P'a = < if a + 0.5 m a m 0.5, a ≠0 > if a - 0.5 m a m 0.5, a ≠ 2 0 0.5 if a m 0.5 =
  • 58. Analysis Techniques: Attribute Gage Study
    • The third step: Plot Gage Performance Curve with part reference value XT as
    • X axis, and the probability of acceptance P' a as Y axis
    Gage Performance Curve
  • 59. Analysis Techniques: Attribute Gage Study
    • The fourth step: Base on Gage Performance Curve to find XT value at P a = 0.5%
    • and P a = 99.5% (using normal probability paper can get more accurate estimates).
    • We also can use Statistical Forecast calculation to get the XT value.
    •  
    • XT = 0.264 at P a = 0.5% XT = 0.184 at P a = 99.5%
    •  
    • Bias = XT (at P a = 0.5%)-USL = 0.264 – 0.2 =0.064
    •  
    • The repeatability is determined by finding the differences of the XT value
    • corresponding to P a = 99.5% and P a = 0.05% and dividing by an adjustment factor
    • of 1.08.
    Repeatability = XT(at P a = 0.5%) - XT(at P a = 99.5%) 1.08 = = 0.074 0.264 – 0.184 1.08
  • 60. Analysis Techniques: Attribute Gage Study
    • Conclusion: Because the filler gage repeatability is 7.4% , Bias is 6.4%. Both of
    • them are less than 10%, so the gage can be accepted to use.
  • 61. Four Methods Comparison
    • The four methods for attribute measurement study have respective feature. The
    • Short method look like simple, but it need to select enough parts which are slightly
    • below and above both specification limits, and must measure variable reference
    • value in advance. Hypothesis Test didn’t need to measure the variable reference
    • value, so it is feasible for manufacturing, but it need large sample size. Signal
    • Detection method can determine an approximation of the width of the region II
    • area so as to calculate the measurement system GR&R. Long method is used the
    • concept of the Gage Performance Curve (GPC) to assess the repeatability and bias
    • of the measurement system. When the importance of the measurement system
    • need to be highly assured, the Signal Detection method and Long method would
    • be necessary. Although the statistical calculation process for above methods is
    • complex, now we are designing a software to be able to perform the four methods
    • process and calculation.