Home / Lean Six Sigma / Measurement system analysis (MSA)
Assess a measuring gage with parts of known value: repeatability and bias on one reference part (Cg, Cgk) or bias across the operating range (linearity). Run it before a gage R&R or when a new gage arrives: you need the readings and the reference value; you get whether the gage is capable (Cg and Cgk ≥ 1.33), whether it reads with a systematic error and where to correct it.
Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.
Key: Bias = mean of readings − reference (systematic error); T and P = bias t-test (P below 0.05: the error is real, not chance); Cg = repeatability only; Cgk = repeatability and bias together; both should be ≥ 1.33. %Var = how much of the allowed band the gage uses (should be ≤ K).
Each reading in order, with the reference, the band Ref ± K/2 of tolerance and the mean.
How to read: horizontal axis = reading order; vertical axis = value read. Green line = part reference value; red dashed = band allowed to the gage; dotted = mean. Red points are outside the band. Good: points tight around the reference, not rising or falling over time.
Distribution of the readings with the normal curve, the reference and the band Ref ± K/2 of tolerance.
How to read: bars = how many readings fell in each value bin; curve = normal distribution with the mean and SD of the readings. Vertical lines: reference, mean (X̄) and the limits of the allowed band. Good: the whole curve fits between the limits and the mean sits on the reference.
Key: Slope = how much the error changes per unit of reference (P below 0.05: real linearity); Constant = error at reference zero; %Linearity = slope × 100; Bias by reference = average error on each part, with the t-test P (below 0.05: that part is read wrong).
Bias of each reading, average bias per reference, regression line with 95% CI and the bias = 0 line.
How to read: horizontal axis = reference value of each part; vertical axis = error (reading − reference). Grey points = each reading; squares = average error of the part; blue line = fitted bias, with the dashed 95% band. Good: the "bias = 0" line stays inside the band all along; a sloped line = the error changes along the scale.
Linearity and average bias as % of process variation.
How to read: each bar shows how much of the process variation is taken by linearity and by average bias. Short bars are good; above 10% the gage error already weighs on part decisions.
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It is the first test of a new or repaired gage: one operator measures the same reference part of known value 25 to 50 times. The study separates gage repeatability (Cg) from bias against the reference value (Cgk) before involving several operators in a gage R&R. It is required by German automotive standards (VDA 5, Bosch Booklet 10) and widely used in PPAP.
Cg = (K/100 × tolerance) ÷ (L × s) and Cgk = (K/200 × tolerance − |bias|) ÷ (L/2 × s), with K = 20% and L = 6 by default. In the default example (50 readings, reference 12.306 and tolerance 0.05), s = 0.00485, bias is 0.0015 and Cg = 0.34 and Cgk = 0.24: the gage is not capable for that tolerance.
The usual one is Cg ≥ 1.33 and Cgk ≥ 1.33, equivalent to %Var (repeatability) and %Var (repeatability and bias) up to 15% with K = 20%. Bias is also checked with a t-test: p < 0.05 means a real bias, to be fixed with a zero adjustment. Resolution should be at most 5% of the tolerance.
It compares the mean of the readings with the reference value: t = bias ÷ (s ÷ √n), with n − 1 degrees of freedom. In the example, t = 2.18 and p = 0.034: the 0.0015 bias is small but real. The confidence interval of the bias appears in the table, to compare with the uncertainty of the reference part.
It checks whether gage bias changes across the operating range. Per the MSA manual, pick at least 5 reference parts covering the range and measure each 10 times or more. The calculator fits the bias vs reference line and shows %linearity (100 × |slope|) and the bias at each reference with a t-test. In the manual example (references 2 to 10, 12 readings), the slope is −0.1317 (p < 0.001) and %linearity is 13.2%.
Grey dots are the bias of each reading, squares are the average bias per reference and the line is the regression with its 95% confidence interval. If the bias = 0 line fits entirely inside the interval, the MSA manual accepts the linearity. If the slope is significant, judge bias reference by reference: in the example, references 2, 8 and 10 show bias and 4 and 6 do not.
A type 1 study uses one reference part and one operator and measures repeatability and bias at one point. Linearity extends bias to the whole range. Gage R&R uses real parts and several operators and measures reproducibility and how well the system sees process variation. A calibration check compares the instrument with a standard at several points and decides pass or fail by the instrument tolerance.
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