Measurement Systems Analysis

Transcription

1 Measurement Systems Analysis

2 Since measurement systems represent a subprocess within a process They are subject to Variation. What could be the source of this variation? Why do Measurements Vary?

3 Possible Sources of Process Variation Observed Process Variation Actual Process Variation Measurement Variation Long-term Short-term Variation Variation due Variation due Process Variation Process Variation w/i sample to gage to operators Repeatability Accuracy Stability Linearity Reproducibility

4 Sources of Variation 4 Product Variability (Actual variability) Measurement Variability Total Variability (Observed variability)

5 Definitions 5 Bias the difference between the average measured value and a reference value Reference value agreed-upon standard, such as a standard traceable to a national standards body Attribute inspection: the ability of the attribute inspection system to produce agreement on inspection standards Controlled by calibration - process of comparing measurements to standards

6 Bias = accuracy Reference Value Observed Average Value

7 Some reasons for excessive bias: Instrument needs recalibrating Worn equipment Damaged master Improper calibration Temperature Humidity Cleanliness

8 Example 8 A standard with a known value of 5.4 is checked 10 times by one mechanical inspector using a dial caliper with a resolution of 0.05 mm. The readings obtained are: If this measurement system were to be used on a process with a tolerance of ±0.5mm, determine and interpret the bias.

9 Definitions 9 Repeatability Variation in measurements obtained with one measurement instrument when used several times by one appraiser, while measuring the identical characteristic on the same part Variation obtained when the measurement system is applied repeatedly under the same conditions is usually caused by conditions inherent in the measurement system Similar to precision

10 Definitions 10 Reproducibility Variation in the average of the measurements made by different appraisers using the same measuring instrument when measuring the identical characteristic on the same part Appraiser variation

11 Definitions 11 Stability 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 system is said to be stable if the results are the same at different points in time Also known as drift

12 Definitions 1 Linearity The difference in the bias values through the expected operating range of the gage measure of the consistency of Bias over the range of the measurement device

13 13 Measurement System Discrimination Discrimination/Resolution The ability of the measurement system to divide measurements into data categories Example: Resolution inch 1.000, , A measurement system should be able to divide the region of interest into at least five data categories When unacceptable discrimination exists, the range chart shows discrete jumps or steps

14 Gage and Measurement Systems Capability Analysis Total Variability = Variability in the Product + Measurement Error total product gage Determine how much of the observed variability is due to the gauge or measurement system Isolate the components of variability in the measurement system Assess whether the gauge is capable (suitable for the intended application)

15 Gage and Measurement Systems Capability Analysis Example: An instrument is to be used as part of a proposed SPC implementation. The quality improvement team involved in designing the SPC system would like to get an assessment of gage capability. Twenty units of the product are obtained, and the process operator who will actually take the measurements for the control chart uses the instrument to measure each unit of product twice.

16 Gage and Measurement Systems Capability Analysis

17 Gage and Measurement Systems Capability Analysis xchart Rchart 3 gage Shows the discriminating power of the instrument, that is, the ability of the gage to distinguish between units of product Shows the magnitude of measurement error, gage capability in control R chart operator having no difficulty in making consistent measurements out of control R chart operator having difficulty using the instrument Range in the variation of the individual measurement due to gage error

18 Gage and Measurement Systems Capability Analysis Estimating the Variance Components Other measures of Gage Capability product product M total gage total Signal-to-Noise Ratio (>5, capable) SNR p 1 Discrimination Ratio (>4, capable) p DR 1 p 1 p

19 Gage and Measurement Systems Capability Analysis Other measures of Gage Capability P/T (<0.1, capable) P / T 6 gauge USL LSL

20 Gage Repeatability and Reproducibility (GR&R) Components of Measurement Error Reproducibility - variability due to different operators using the gauge (or different time periods, or different environments, or in general, different conditions) Repeatability - basic inherent precision of the gauge itself measurementerror gauge repeatability reproducibility G R&R study - an experiment used to measure the components of gauge

21 Gage Repeatability and Reproducibility (GR&R) G R&R Studies are usually conducted with Factorial Experiments If there are a randomly selected parts and b randomly selected operators, and each operator measures every part n time, then the measurements ( i = part, j = operator, k = measurement) could be represented by the model y ijk P i 1,,..., p j 1,,..., o k 1,,..., n i O j ( PO) ij ijk Random effects model of The ANOVA Variance of any observations V ( y ijk ) P O PO

22 Gage Repeatability and Reproducibility (GR&R) SS Total SS P SS O SS PxO SS Error SS SS SS SS T ) i j k ijk x p o n i j k p on p o n i j k O pn p o n i j k PO n x x ( GrandTotal N i.. ) ( GrandTotal N. j. ) x ( GrandTotal N ij. ) SS P SS O ( GrandTotal N MS MS P MS MS PO Error o SSError po( n 1) SS p p 1 SSo o 1 SSPO ( p 1)( o 1)

23 Gage Repeatability and Reproducibility (GR&R) Estimation of the variance components ˆ MS Error ˆ PO ˆ O MS PO MS O MS n MS pn Error PO ˆ P MS P MS on PO

24 GR&R Example

25 GR&R Example

26 GR&R Example Reproducibility - sum of the operator and operator x part variance components Repeatability - ( O PxO ) gauge O PO Evaluate the adequacy of the measuring instrument in the Thermal Impedance Example if LSL = 18 and USL = 58.

27 Attribute Gauge Capability Sometimes the output of a gauge isn t numerical it s just pass/fail Nominal or ordinal data is also common Occurs frequently in service businesses Common situation do operating personnel consistently make the same decisions regarding the units they are inspecting or analyzing? Example a bank uses manual underwriting of mortgage loans The underwriter uses information to classify the applicant into one of four categories; decline or category 1,, 3 categories & 3 are low-risk and 1 is high risk Compare underwriters performance relative to a consensus evaluation determined by a panel of experts

28 Attribute Gauge Capability Thirty applicants, three underwriters Each underwriter evaluates each application twice The applications are blinded by removing names, SSNs, addresses, and other identifying information

29 Attribute Gauge Capability Determine the proportion of time that the underwriter agrees with him/herself this measures repeatability Determine the proportion of time that the underwriter agrees with the correct classification this measures bias Determine the proportion of time that all the underwriters agree on classification this measures reproducibility Minitab performs the analysis using the attribute agreement analysis routine

30 Attribute Gauge Capability