Question

1. A part has a specification of 200+/- 30. a gauge R&R study involves 2 operators. 10 parts are measured twice by each operator. Operator 1 measured an average range of 2 and an x-bar bar of 201 for the measurements. Operator 2 measured an average range of 3 and has x bar bar of 205 for the measurements. what is the gauge reproducibility

a)2.36 b)3.55 c)1.48 d)2.22

Answer 1

No. of Trails = 2

No. of Operators = 2

No. of Parts = 10

Operator 1

R1-bar = 2

X1-bar = 201

Operator 2

R2-bar = 3

X2-bar = 205

X-bar Diff = X2-bar - X1-bar = 205-201

X-bar Diff = 4

R-bar bar = (R1-bar + R2-bar)/No. of Operators = (2+3)/2 = 2.5

Repeatability or Equipment Variation (EV) = (Rbarbar) x (K1)

Here K1 is the constant which depends on the number of trials in the study. For 2 trials K1 = 0.8862

Repeatability or Equipment Variation (EV) = (2.5) x (0.8862)

Repeatability or Equipment Variation (EV) = 2.22

Reproducibility - Appraiser Variation (AV) Percent Appraiser Variation = SQRT{(Xbar diff x K2)^2 - (EV^2/[(# parts) x (# trials)])}

Here K2 is the constant which depends on the number of operators in the study. For 2 operators K2 =0.7071

Reproducibility - Appraiser Variation (AV) Percent Appraiser Variation = SQRT{(4 x 0.7071)^2 - (2.22^2/[(10) x (2)])}

Reproducibility or Appraiser Variation (AV) Percent Appraiser Variation = 2.78

Repeatability & Reproducibility (GRR) = SQRT[ (EV^2) + (AV^2) ]      

Repeatability & Reproducibility (GRR) = SQRT[ (2.22^2) + (2.78^2) ]      

Repeatability & Reproducibility (GRR) = 3.56