Créer une présentation
Télécharger la présentation

Télécharger la présentation
## Measurement System Analysis

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Measurement System Analysis**Kevin B. Craner Boise State University October 6, 2003**Overview**• Purpose of measurement system analysis (MSA) • Organizational uses of MSA • Measurement system errors • Accuracy and Precision of measurements • MSA process flow • Real world application • Exercise**Measurement System Analysis (MSA)**• aka Gauge R&R • A tool used to evaluate the statistical properties of process measurement systems. • Purpose of MSA is to statistically verify that current measurement systems provide: • Representative values of the characteristic being measured • Unbiased results • Minimal variability**Organizational Uses**• Mandatory requirement for QS 9000 certification. • Identify potential source of process variation. • Minimize defects. • Increase product quality.**Measurement System Errors**• Accuracy: difference between the observed measurement and the actual measurement. • Precision: variation that occurs when measuring the same part with the same instrument.**Measurement System Error**Precise but not accurate Accurate but not precise Not accurate or precise Accurate and precise**Accuracy of Measurement**• Broken down into three components: 1. Stability: the consistency of measurements over time. 2. Accuracy: a measure of the amount of bias in the system. 3. Linearity: a measure of the bias values through the expected range of measurements.**Precision of Measurement**• Precision, aka Measurement Variation, can be broken down into two components: 1. 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.**MSA Process Flow**1. Preparation for study 2. Evaluate stability 3. Evaluate resolution 4. Determine accuracy 5. Calibration 6. Evaluate linearity 7. Determine repeatability and reproducibility**Preparation for Study**• Objective: establish process parameter for the study. • Process: 1. Determine which measurement system will be studied. 2. Establish test procedure.**Preparation for Study-Cont-**3. Establish the number of sample parts, the number of repeated readings, and the number of operators that will be used. 4. Choose operators and sample parts.**Evaluate Stability**• Objective: evaluate measurement system to determine if the system is in statistical control. • Procedure: 1. Choose sample standards. 2. Measure sample standards three to five times.**Evaluate Stability-Cont-**3. Plot data on a x-bar and R chart. • Analysis: 1. Determine if process is in control. 2. If process is unstable determine and correct the cause.**Evaluate Resolution**• Objective: determine if the measurement system can identify and differentiate between small changes in the given characteristic. • Process: 1. Choose a sample standard.**Evaluate Resolution-Cont-**2. Measure the sample standard three to five times. 3. Repeat the process 10 to 25 times. 4. Plot data on a R chart.**Evaluate Resolution-Cont-**• Analysis 1. The resolution is inadequate if: - There are only one, two, or three possible values for the range, or - There are only four possible values for the range when n >= 3.**Determine Accuracy**• Objective: determine the variation between the observed measurement and the actual measurement of a part. • Process: 1. Choose sample standards. 2. Measure sample standards 15 to 25 times using the same measuring device, the same operator, and the same setup.**Determine Accuracy-Cont-**3. Calculate x-bar 4. Calculate bias - Bias = Average – Reference Value 5. Calculate the upper and lower 95% confidence limit (CL).**Determine Accuracy-Cont-**• Analysis 1. If reference value is within the 95% CL then the bias is insignificant. 2. If reference value is outside the 95% CL then the bias is significant and measurement system must be recalibrated.**Calibration**• Objective: to ensure the instrument is accurate, and measurement bias is minimized. • Process: calibrate instrument IAW manufacturers instructions.**Evaluate Linearity**• Objective: determine the difference between the obtained value and a reference value using the same instrument over the entire measurement space. • Process: 1. Choose three to five sample standards that cover the measurement space.**Evaluate Linearity-Cont-**2. Measure sample standards 15 to 25 times. 3. Calculate the average of the readings. 4. Calculate bias. 5. Plot reference values on x-y graph. 6. Calculate slope of the linear regression line. 7. Calculate linearity and percent linearity. 8. Calculate R2.**Evaluate Linearity-Cont-**• Analysis 1. The closer the slope is to zero, the better the instrument. 2. R2 gives indication of how well the “best-fit” line accounts for variability in the x-y graph.**Determine Repeatability and Reproducibility**• Objective: determine variation in a set of measurement using a single instrument that can be credited to the instrument itself, and to the entire measurement system. • Process 1. Generate random order for operators and parts to complete the run.**Determine Repeatability and Reproducibility -Cont-**2. Repeat process for subsequent runs. 3. Have operators take measurements. • Analysis: 1. Plot data 2. Run ANOVA (analysis of variance) on data.**Determine Repeatability and Reproducibility -Cont-**3. Calculate total variance. 4. Calculate % Contribution and determine if acceptable. 5. Calculate % Contribution (R&R) 6. Calculate Process to Tolerance ratio (P/T) for repeatability. 7. Determine if P/T is acceptable.**Real World Application**• Case study performed by Tirthankar Dasgupta and S.V.S.N Murthy, Indian Statistical Institute, 2001. - Gauge R&R study of automobile radiator manufacturer. - After studying four characteristics of radiator components the following results were obtained:**Table 1. Results of Preliminary Study**Source: Dasgupta & Murthy, Total Quality Management, Vol. 12, No. 6, 2001**Real World Application-Cont-**• Any system having greater than 30% gauge R&R is considered inadequate. As seen in Table 1, all four characteristics’ %R&R is inadequate. • Investigation of the measurement system led to a subsequent reduction of %R&R in three of the four characteristics to between 12% and 23%.**Real World Application-Cont-**• Further investigation of the fourth characteristic, inlet hole diameter, led the examiners to a manufacturing problem. The team discovered high ovality in the inlet hole, which was caused by the cutting tool. The tool was modified to reduce ovality.**Real World Application-Cont-**• Benefits of the study 1. Reduced measurement variation. 2. Increased operator confidence regarding their aptitude for conducting gauge R&R studies. 3. Paved the way for further studies within the firm.**An Exercise – Calculating EV, AV, R&R, and TV**• Given: EV = 5.15(s0) , AV = 5.25(s1) R&R = (EV2 + AV2) TV = (EV2 + AV2 + PV2) • Where: s0 = gauge standard deviation = 0.05 s1 = true appraiser standard deviation = 0.1 PV = part-to-part variation = 0.02**An Exercise – Calculating EV, AV, R&R, and TV**• Calculate R&R and TV • Is the calculated R&R acceptable?**Summary**• MSA studies are required for QS 9000 certification. However, MSA can prove beneficial to any firm that uses measurement systems whether they are seeking QS 9000 certification, or not. • MSA studies are a tool that aid in ensuring quality at all levels of a process.**Summary-Cont-**• According to David C. Crosby, “If you don’t know the capability of your measurement system, you don’t know if your measurements, or your products, are good or bad.”**References**• Crosby, David C. A Managers Guide to Gauge R&R, Rubber World 218 (1998): 16-17. • Goyal, Niraj. Selecting Appropriate Metrics.www.isixsigma.com/library/content.c020930a.asp. 4 Oct 2003. • Hemanth, S. Anomoly In Normality. www.isixsigma.com/library/content/c02820a.asp. 4 Oct 2003. • Niles, Kim. Characterizing the Measurement Process.www.isixsigma.com/library/content/c020527a.asp. 4 Oct 2003. • Measurement Systems Analysis Overview. http://mathstat.carleton.ca/~help/minitab/QCMEASYS.pdf. 4 OCT 2003. • Measurement System Analysis Resolution and Granularity. www.isixsigma.com/library/content/c000903a.asp. 4 Oct 2003.**References**• Measurement System Capability Manual. www.6sigma.us/MSASymbolsandNotation.html. 3 Oct 2003. • Dasgupta, Tirthankar & Murthy, S.V.S.N. Looking beyond audit-oriented evaluation of gauge repeatability and reproducibility: A case study. Total Quality Management. 12 (2001): 649-655.