Measurement System Analysis

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<p>Measurement Systems AnalysisDefineMeasure</p> <p>Analyze</p> <p>Improve</p> <p>By: Mahender Kumar</p> <p>1 Control</p> <p>Learning Objectives Understand the language of Measurement. Show the importance of Measurement Measurement. Walk away knowing how to perform a Gage R&amp;R and how to interpret results results. Share some lessons learned.</p> <p>2</p> <p>Since Measurement systems represent y p a sub-process within a process... They are subject to Variation. What could be the source of this variation? Why do Measurements Vary?</p> <p>3</p> <p>Sources of Measurement Variation</p> <p>Equipment q p Part Operator Environment Procedure4</p> <p>Sources of Measurement VariationMeasurement System C&amp;E MatrixMeasurementsMechanical Integrety Wear Electrical Instability Algorithm Instability</p> <p>MaterialsCleanliness Temperature Dimension Weight Corrosion Hardness Conductivity Density</p> <p>MenProcedure P d Fatigue Attention Calibration Error Interpretation Speed Coordination Know ledge Dexterity Vision</p> <p>Measurement System ErrorTemp Fluxctuation Line Voltage Variation Vibration Cleanliness Humidity Operator Technique Standard Procedure Sufficient Work time Maintenance Standard Calibration Frequency Operator Training Ease of use Wear Stability Resolution Calibration Precision Design Temperature Cleanliness</p> <p>Environment</p> <p>Methods Sigma Champion Training Machines Six</p> <p>5</p> <p>Possible Sources of Process VariationObserved Process Variation</p> <p>Actual Process Variation</p> <p>Measurement Variation</p> <p>Long-term Process Variation</p> <p>Short-term Process Variation</p> <p>Variation w/i sample</p> <p>Variation due to gage</p> <p>Variation due to operators</p> <p>Repeatability</p> <p>Accuracy</p> <p>Stability</p> <p>Linearity</p> <p>Reproducibility</p> <p>We will look at repeatability and reproducibility as these are the primary contributors to measurement error. ese e e p y co bu o s o e su e e e o .6</p> <p>Why MSA</p> <p>RU = 0.0001 RU = 0.001</p> <p>U= 0.0001</p> <p>U : UNCERTAINITYNATIONAL STANDARD</p> <p>RANDOM UNCERTAINITY FOUND THRU CALIBRATION SYSTEM UNCERTAINITY OF MASTER TOTAL UNCERTAINITY SQRT( RU*RU + SU*SU)</p> <p>U= 0.001005</p> <p>LABORATORY STANDARD</p> <p>RU = 0.01</p> <p>U= 0.01005</p> <p>WORK STANDARD</p> <p>RU = 0.05</p> <p>U= 0.05099</p> <p>GAUGE FOR INSPECTION / TESTING</p> <p>Process CapabilityLower Spec. Limit Upper Spec. Limit</p> <p>6 Tolerance = T Process Capability = T / 6 Means, 6 &lt; (0.75*T) &gt; 1.33</p> <p>Impact of UncertaintyLower Spec. Limit</p> <p>ERROR identified through Calibration ProcessUpper Spec. Limit</p> <p>Uncertainty</p> <p>6P Process Tolerance = T</p> <p>Knowledge to be obtained How big is the measurement error? What are the sources of measurement error? Is the gage stable over time? Is the gage capable for this process? How do we improve the measurement system?11</p> <p>Sources of VariationProduct V i bilit P d t Variability(Actual variability)</p> <p>Measurement Variability</p> <p>Total Variability(Observed variability)</p> <p>12</p> <p>Effects of Measurement ErrorAveragesMeasurement System Bias Determined through Accuracy Study</p> <p> total = product + measurementVariability2 2 =2 + measurement total productMeasurement System Variability Determined through R&amp;R Study y</p> <p>13</p> <p>Terminology Location related terms: True value Bias Linearity</p> <p> Stability (over time) Variation related terms Repeatability Reproducibility14</p> <p>Definition of Terms Reference Value The theoretically or agreed upon correct value of the characteristic being measured, traceable to some standard</p> <p> Resolution The smallest increment, or unit of , measure, available from a measurement process Generally at least 1/10th of the specification range</p> <p>Definition of Terms Precision The degree of agreement (or variability) between individual measurements or test results from measuring the same specimen(s)</p> <p> Accuracy (Bias) y( ) The difference between the average of the measurement error distribution and the reference value of the specimen measured</p> <p>The Nature of Process Variation1 2 3 4 5</p> <p>Precise but not Accurate</p> <p>1</p> <p>2</p> <p>3</p> <p>4</p> <p>Accurate but not Precise</p> <p>Rule f thumb: R l of th b . . . . . .Test equipment MUST be a least 10 times more accurate &amp; precise then whats b i t t d t i th h t being tested17</p> <p>Measurement System Error</p> <p>Precise but not accurate</p> <p>Accurate but not precise</p> <p>Not accurate or precise</p> <p>Accurate and precise</p> <p>Precision vs. Accuracy vs</p> <p>Pr recision</p> <p>Accuracy</p> <p>Definition of Terms Repeatability p y The variation in repeated measurements of the same items with a single measurement system Within appraiser/system variation</p> <p> R Reproducibility d ibilit The variation in the average measurements by different appraisers or systems measuring th diff t i t i the same items Between appraiser/system variation</p> <p>Terms Linearity The degree to which bias changes with changes in the magnitude of the characteristic measured</p> <p> Stability y The dependability, or consistency of the measurement process over time p</p> <p>Measurement Systems Capability The variability resulting from measurement error must not exceed a significant proportion of the intended specifications said to be capable In addition, it is not desirable for measurement error to exceed a significant proportion of the total process variability Capability is not the same as acceptability, acceptability must be determined on a case b case b i by basis</p> <p>Measurement System Studies Potential Studies Assess potential of a measurement system to be capable over the long term 10 parts measured 23 times by one or more p y appraisers A quick and dirty study to find out if you are in y y y the ballpark Assesses repeatability and reproducibility Often called an R&amp;R study</p> <p> True value: Theoretically correct value unknown and unknowable y Reference standards NIST standards</p> <p> Bias Distance between average value of all measurements and true value Amount gage is consistently off target Systematic error or offset24</p> <p>BIAS Definition BIAS Is the difference between theobserved average of the measurement and the reference value. The referencevalue is the value that serves as an agreed-upon reference. The reference value can be determined by averaging several measurements with a higher level (e.g., metrology lab) of measuring equipment. Reference Value</p> <p>ACCURACY IS THE SAME AS BIAS</p> <p>Observed Average V l A Value25</p> <p>LinearityDifference in the accuracy values of a gage through the expected operating range of the gage Good LinearityRegression Plot</p> <p>Bad LinearityLinearity is N G ot ood</p> <p>55</p> <p>55</p> <p>45</p> <p>45</p> <p>Trials</p> <p>25</p> <p>Y=0.934227+0.994959X R -Squared=0.981</p> <p>Trials</p> <p>35</p> <p>35 Y=0.245295+0.99505X R -Squared=0.982</p> <p>25</p> <p>15</p> <p>15</p> <p>5 10 20 30 40 50</p> <p>5 10 20 30 40 50</p> <p>S tandard</p> <p>S tandard</p> <p>26</p> <p>Stability The distribution of measurements remains constant and predictable over time for both mean and standard deviation Total variation in the measurements obtained with a gage, on th same master or master parts, the t t t when measuring a single characteristic over an extended time period period. Evaluated using a trend chart or multiple measurement analysis studies over time27</p> <p>Stability (drift) DefinitionStability Is the total variation inthe measurement obtained with a measurement system (test / gage ) on the same master parts when measuring p g a single characteristic over an extended time period. Magnitude g Time-2</p> <p>Time-1 Ti 1</p> <p>Points to the frequency of Mean center Calibration</p> <p>time Stability28</p> <p> Total variation in the measurement system p Measure of natural variation of repeated measurements Terms: Random Error, Spread, Test/Retest error Repeatability and Reproducibility</p> <p>2 MS</p> <p>= +2 G</p> <p>2 O29</p> <p>Repeatability p y</p> <p>G</p> <p> The inherent variability of the measurement system Variation in measurements obtained with a gage when used several ti d l times b one operator while measuring a by t hil i characteristic on one part. Estimated by the pooled standard deviation of the distribution of repeated measurements RG =* d2</p> <p> Repeatability is less than the total variation of the measurement system</p> <p>30</p> <p>Repeatability Definition R t bilit D fi itiRepeatability The variation in measurements obtained with one measurement instrument when used several times by one appraiser while measuring the identical characteristic on same part.</p> <p>REPEATABILITY</p> <p>31</p> <p>Reproducibility p y</p> <p>O</p> <p> Operator variability of the measurement system Variation in the average of the measurements made b diff d by different operators using the same gage i h when measuring a characteristic on one part M t be adjusted f gage variation Must b dj t d for i ti Reproducibility is less than the total variation of the measurement systemO</p> <p>R = * d2</p> <p>32</p> <p>Reproducibility DefinitionOperator-B</p> <p>Reproducibility Is thevariation in the average of the measurements made by different appraisers using the same measuring instrument when measuring the identical characteristic on the same part.</p> <p>Ope ato C Operator-C</p> <p>Operator-A Reproducibility d ibili33</p> <p>Accuracy of Measurement Broken down into three components: 1. Stability: the consistency of y y measurements over time. 2. Accuracy: a measure of the amount of y bias in the system. 3. Linearity: a measure of the bias values y through the expected range of measurements.</p> <p>Precision of Measurement Precision, Measurement Variation, can be broken down into two components: p1. Repeatability (Equipment variation): variation in measurements under exact conditions. 2. Reproducibility (Appraiser variation): variation in the average of measurements when different operators measure the same part.</p> <p>Measurement System Discrimination yLeast count should be at most one-tenth of the total process capability or tolerance (6 sigma) Process capability 10 Max Least count 1 Part to Part variation must be greater than the smallest unit of measure it f</p> <p>36</p> <p>Types of R&amp;R Studies</p> <p> Variable Gage R&amp;R Numbers Units of measure</p> <p> Attribute Gage R&amp;R Subjective (cosmetic defects) Scatter of defects feel/visual37</p> <p>Basic TermsEV= Equipment Variation (Repeatability) AV AV= Appraiser Variation (Reproducibility) R&amp;R= Repeatability &amp; Reproducibility PV= Part Variation TV= Total Variation of R&amp;R and PV K1-Trial, K2-Operator, &amp; K3-Part Constants</p> <p>38</p> <p>Gage R&amp;R studyGenerally two or three operators Generally 10 units to measure Each unit is measured 2-3 times by each operator</p> <p>39</p> <p>Preparation for a Measurement p Study Determine if reproducibility is an issue. If it is, select the number of operators to participate. Operators selected should normally use the measurement system. Select samples that represent the entire operating range. Gage must have graduations that allow at least one-tenth of the expected process variation. Insure defined gaging procedures are followed followed. Measurements should be made in random order. Study must be observed by someone who recognizes the importance of conducting a reliable study.40</p> <p>Procedure for Performing R&amp;R g Study Calibrate the gage, or assure that it has been calibrated. Have the first operator measure all the samples once in random order. Have the second operator measure all the samples once in random order. Continue until all operators have measured the samples once p p (this is Trial 1). Repeat above steps for the required number of trials. Use GR&amp;R form to determine the statistics of the study. y Repeatability, Reproducibility &amp; %GR&amp;R Standard deviations of each of the above % Tolerance analysis</p> <p> Analyze results and determine action, if any.41</p> <p>Variable Gage R&amp;R g</p> <p>Guidelines% R&amp;R 10% 10% 30% Over 30%</p> <p>ResultsGage is OK Maybe acceptable based upon importance of application, and cost factor Gage system needs improvement/corrective action</p> <p>42</p> <p>Xbar Chart by Operator40 35 30</p> <p>Operator*Part No. InteractionABC-</p> <p>40 35 30</p> <p>Sample Mean n</p> <p>25 20 15 10 5 0</p> <p>Average</p> <p>25 20 15 10 5 0 1 2 3 4 5 6 7 8 9 10</p> <p>Part No.</p> <p>43</p> <p>Thanks</p> <p>For any query pl. mail me at mahender.kumar@yahoo.co.in pl mahender kumar@yahoo co in</p> <p>44</p>

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