MEASUREMENT SYSTEM ANALYSIS

Qualification of a measurement system for use by quantifying its accuracy, precision, and stability

–Understand the quality characteristics of measurement

–Understand the method for establishing measurement capability

–Define the requirements of the measurement system

The Qualities of Measurement

Resolution

•Accuracy (Bias)

•Linearity

•Repeatability

•Reproducibility

•Stability

Resolution is the incremental ability of a measurement system to discriminate between measurement values. The measurement system should have a minimum of 20 measurement increments within the product tolerance (e.g, for a full tolerance of 1, minimum resolution is .05)

Accuracy—or bias—is a measure of the distance between the average value of the measurement of a part and the True, certified, or assigned value of a part.

Linearity   is the consistency of accuracy (bias)over the range of measurement; a slope of one (unity) between measured and true value is perfect.

Repeatability   is the consistency of a single appraiser to measure the same part multiple times with the same measurement system; it is related to the standard deviation of the measured values.

Reproducibility is the consistency of different appraisers in measuring the same part with the same measurement system; it is related to standard deviation of the distribution of appraiser averages.Stability is the ability of a measurement system to produce the same values over time when measuring the same sample As with statistical process control charts, stability means the absence of “Special Cause Variation” which is indicated by an “in control” condition, leaving only "Common Cause” or random variation.

   Generally, precision is the principle concern; inaccuracy due to linearity or constant            bias can typically be corrected through calibration•

  Measurement Error is the statistical summing of the error generated by Repeatability(the     variation within an appraiser) and Reproducibility (the variation between appraisers)–            σerror= √(σ repeability)2+ (σ reproducibility)2

•Total Measurement Error spans the interval that contains 99% of probable  measurement values from a measurement system, using a single part–Total  Measurement Error = 5.15 * σerror• Measurement system precision is defined by  the Precision/Tolerance Ratio, the ratio between Total Measurement Error and    the part tolerance–P/T Ratio = 5.15 * σerror/ (Upper Spec Limit –Lower Spec Limit)

Error Independence is defined by the lack of a relationship between measurement error and the measurement value; error generated by the measurement process should be independent of the measured value

•Stability is defined by the randomness of the measurement error; purely random measurement error is evidence of good stability

•Linearity is defined by the slope of measured value vs. true value; a slope of 1 (a 1:1 relationship) is perfect

•Bias Offset is defined by the average difference between the measured value and the true value at the specification target; a value of zero is perfect

–The combination Bias Offset and Linearity define the amount of systematic measurement error across the entire measurement range; they are typically corrected through calibration