Measurement Systems Analysis

Transcription

1 Measurement Systems Analysis Measurement Systems Analysis (MSA) Reference Manual, AIAG, ( Copyright, Pat Hammett, University of Michigan. All Rights Reserved. 1 Topics I. Components of Measurement System II. Sources of Measurement Error III. Types of Measurement System Studies A. Gage Accuracy Study B. Gage R&R Study 1

2 Decomposing Variation Measurement variation is inherent to a process! σ total σ inherent (random variation) σ special cause (special causes - these may be 0) σ product σ gage σ batch σ material σ? σ repeatability σ reproducibility σ static σ dynamic (load/unload between measurements) 3 I. Components of a Measurement System Equipment or Gage Type of Gage: Attribute: go-no go, vision systems (part present or not present) Variable: calipers, probe, tape measure, coordinate measurement machines, checking fixture with inspection device Discrimination of Measurement General Rules: At least 1/10 of tolerance (tol = 1 mm, measure to at least 0.1) Or, at least 1/10 of 6*process standard deviation (6σ) Operator & Operating Instructions Part locating or orientation scheme gage must be able to consistently locate the part being measured. 4

3 II. Sources of Measurement Error Systematic Variations 1. accuracy: improper calibration of equipment. reproducibility: different operators using same equipment with different techniques Random Variations 3. repeatability: (for example, inconsistent part locating) Periodic Variations 4. stability: wear, deterioration, environmental conditions 5 1. Accuracy difference between the true average and the observed average true average may be obtained using a more precise measuring tool Accuracy or Mean Bias True Average Observed Average 6 3

4 . Reproducibility variation in average of measurements made by different operators using the same gage measuring the same part. Reproducibility Operator C Operator A Operator B 7 3. Repeatability random variation in measurements when one operator uses the same gage to measure the same part several times. Observed Average Repeatability 8 4

5 4. Stability difference in the average of at least sets of measurements obtained with a gage as a result of time. Stability Time 1 Time 9 III. Types of Measurement Systems Analysis Methods A. Accuracy Gage Accuracy (Bias) Study B. Repeatability & Reproducibility Study Gage R&R (Methods: ANOVA or X-bar/Range) - Note: repeatability may be further decomposed into Static & Dynamic Repeatability 10 5

6 A. Gage Accuracy (Bias) Study Measure a master (reference) part using a more precise instrument. Repeatedly measure master part with gage. Reference Part (mm) 6.93 Measurement System Current Gage Trial Trial Trial Trial Trial Trial Trial Trial Trial Trial Average Difference 0.1 One-Sample T: Current Gage Test of mu = 6.93 vs mu not = 6.93 Variable N Mean StDev Current Gage Current Gage ( , ) p-value B. Gage R&R Study Gage R&R Study is used to identify if gage variation is sufficiently low relative to tolerance width and/or part variation. In this module, we will show how to conduct a Gage R&R study and interpret results using the Average and Range Gage R&R method. Note: Gage R&R also may be done using a Two- Factor Analysis of Variance. 1 6

7 Trials and Operators In conducting a Gage R&R study, we need to identify # parts, # trials per part, and # operators. We also need tolerance width for each feature. Tolerance Width = USL LSL USL ~ Upper Spec Limit and LSL ~ Lower Spec Limit. Common Applications (parts x trials x operators): 5 or 10 parts or 3 trials or 3 operators Example: 5x3x Two operators will measure each of 5 parts three times. 13 Data Sheet 10x3x3 Gage worksheet: gagerr.xls Gage R & R Study Worksheet Date: Gage Number: Gage Cert. Level: Gage Cert. Date: Gage Build Source: Part Number: Part Name: Characteristic: Engineering Level: Operator: A B No Operators: Tolerance Width: Study Variation: 5.15 # of standard deviation Number of Trials: Number of Parts: Trial Part Operator Number Average A 1 3 Average X-bar Range R-bar Trial Part Operator Number Average B 1 3 Average X-bar Range R-bar Trial Part Operator Number Average C 1 3 Average X-bar Range R-bar 14 7

8 Example: Car Door Suppose you conduct a Gage R&R study for a Car Door. 13 Features, 5 parts, 3 trials, Operators P6 P5 P4 P3 P7 P8 P9 P10 P11 P1 Measurements deviation from nominal. Spec 0 +/- 0.5 mm P P1 P13 15 Gage R&R Data Feature P1 (see gagerr.xls for data set) No Operators: Tolerance: 1 Number of Trials: 3 Number of Parts: 5 Trial Part Operator Number A Average Range Trial Part Operator Number B Average Range

9 Testing Range Stability? 1 st Step test if any range measurements are out-control (R i > UCL R ) If individual range measurements for a set of trials is out-of-control, than we may over-estimate gage variation. Note: Range tests help identify potential outliers. nd Step, if all measurements are in-control (stable), we may then compute the % Repeatability, % Reproducibility, and % Gage R&R. 17 Feature 1: Range Stability Test (from worksheet) R-Bar 0.03 X-Dif 0.0 UCLr 0.08 LCLr 0.00 Max Range 0.06 Range Stable? Yes Max Range Between Trials = 0.06 UCL r ~ 0.08 (calculated from data) Thus, the trials are in statistical control. 18 9

10 Gage R&R Calculations Most software will automatically compute: % Repeatability (% Equipment Variation) % Reproducibility (% Appraiser Variation) % R&R (% Repeatability and Reproducibility) We typically compute these value as: % of the tolerance width, and/or % of total variation in the parts measured. 19 Repeatability Calculations (use software) K = 5.15 or 6 (# of std deviations to use to estimate variation)* Repeatability Requires R-bar R-bar average range between trials EV σ = R d repeatabil ity = * K R d Trials d Note: K=6 (# of sigma s) - represents 99.73% of values if normal distribution K=5.15 (# of sigma s) - represents 99% of values if normal distribution 0 10

11 Reproducibility Calculations (use software) Reproducibility Requires X-bar diff X-bar Diff Range of Operator Means X diff = Max( Xi) Min( Xi) AV = σ X reproducibility diff * K ) = AV / K EV / nr) n number of parts r number of trials Trials d K (SV=5.15) K (SV=6) Note: 6σ - represents 99.73% of values if normal distribution 5.15 σ - represents 99% of values if normal distribution 1 Calculations - continued R&R Calculations (see attached worksheet for sample) # parts d K 3 (SV=5.15) K 3 (SV=6) R & R = EV σ R & R = R & R / PV = TV = Rp* K + AV K 3 R & R + PV

12 Gage R&R Ratio To determine acceptability, a ratio is typically formed comparing gage variation to either: Tolerance Width - % R&R Tolerance % R & R - Tolerance K * σ R R USL LSL = & Total Process Variation (TV) - % R&R TV Kσ R& R % R & R - TV = Kσ Note: K=6σ - represents 99.73% of values if normal distribution K= 5.15 σ - represents 99% of values if normal distribution TV 3 Repeatability and Reproducibility Ratios Similar ratios may be computed for repeatability and reproducibility. % Equipment Variation - Tolerance: % EV - Tolerance % Appraiser Variation Tolerance K *σ reproducib % AV - Tolerance = USL LSL Note: may compute ratios vs. Total Variation Observed σ σ repeatabiity reproducibility % EV - TV = % AV - TV = σ σ TV TV K *σ repeatabii = USL LSL ty ility 4 1

13 General Criteria for Gage R&R Measures: R&R % (Tolerance) or R&R% - TV if R&R% is: < 10% ~ measurement system is acceptable 10-30% ~ measurement system may be acceptable based upon importance of application, gage cost, cost of repairs.. > 30% ~ measurement system needs improvement 5 Repeatability Requirement Typically, manufacturers also have a requirement for EV (repeatability) % EV Tolerance < 18% OR, % EV Total Variation < 18% 6 13

14 Car Door Example: Feature 1 Note: feature 1 has tolerance +/- 0.5 mm. No Operators: Tolerance: 1 Number of Trials: 3 Number of Parts: 5 Trial Part Operator Number Average A Average X-bar 0.01 Range R-bar 0.04 Trial Part Operator Number Average B Average X-bar 0.03 Range R-bar Results From Worksheet Calculations from Excel File: gagerr-v3.xls Are the repeatability data? Is this gage acceptable? %EV-Tol 9.7% %EV-TV 38.6% R-Bar 0.03 %AV-Tol 5.8% %AV-TV 3.0% X-Dif 0.0 %RR-Tol 11.3% %RR-TV 44.9% UCLr 0.08 %PV-TV 89.3% LCLr 0.00 Pass/Fail Pass Pass/Fail Fail Max Range 0.06 Range Stable? Yes 8 14

15 Interpretation: Feature 1 % R&R (tolerance) = 11% Relative to the tolerance, this measurement system meets R&R criteria. % R&R TV = 45% Note: although fail 30% criteria, the variation in the parts for the study is quite small. 5.15σ TV = 0.6 which is approx ¼ tolerance width of 1 mm 9 % TV Versus % Tolerance Industry Debate: % TV versus % Tolerance Opinion 1: purpose of gage is to separate gage variation from product variation. Thus, use % TV requirement Opinion : purpose of gage is to measure relative to a tolerance. Thus, use % Tolerance Instructor Opinion: Measure Both. If fail % TV, make sure that you have taken parts with sufficient variation relative to the tolerance range

16 Minitab Gage R&R Analysis also may be done in minitab. Under Stat >> Quality Tools Types of Gage R&R Studies in Minitab Crossed design (when each part is measured multiple times by each operator may use either ANOVA or Average/Range Method) Nested design (when each part is measured by only one operator, such as in destructive testing. In destructive testing, the measured characteristic is different after the measurement process than it was at the beginning. Crash testing is an example of destructive testing. 31 Minitab: Feature #1 STAT >> Quality Tools >> Gage R&R (Crossed) Part Numbers PartNo Operator Operator Measurement Data Value Method Analysis X-bar/Range Options >> Process Tolerance =

17 Results Using Minitab Minitab (if set K (study variation sigma) = 5.15 and X-bar / Range method option, results should be ~ same) Quality Tools >> Gage R&R Study Crossed StdDev Study Var %Study Var %Tolerance Source (SD) (5.15*SD) (%SV) (SV/Toler) Total Gage R&R.18E Repeatability 1.86E Reproducibility 1.13E Part-to-Part 4.37E Total Variation 4.88E Results from Minitab If use Minitab Gage tool, range chart is automatic output Gage R&R (Xbar/R) for Value Gage name: Date of study: Reported by: Tolerance: Misc: Components of Variation Response by PartNo 100 %Contribution 0.10 Percent 50 %Study Var %Tolerance Range Chart Sample Range Gage R&R Repeat Reprod Part-to-Part R Chart by Operator A B UCL= R=0.03 LCL=0 PartNo Response by Operator 5 Operator A B 0.10 Xbar Chart by Operator A B 0.10 Operator*PartNo Interaction Operator A Sample Mean UCL= Mean=0.0 LCL= Average B PartNo

18 Is it the R or the R? If we fail Gage R&R study, we often look at equipment and appraiser variation estimates individually. So, if % EV is higher than % AV we consider repeatability a greater concern than reproducibility. 35 Improving Gage Capability How do we improve reproducibility? operator training, OR more clearly define measurement scales (easier to read). How do we improve repeatability? gage maintenance, OR may need to redesign the gage or the gage locating scheme which affects how a part is held during measuring