A Bayesian-like estimator of the process capability index by Pearn W. L., Lin G. H.

By Pearn W. L., Lin G. H.

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2) 1 n If this expression is divided by 1 yi2 , then we have the square of the cosine of the angle between vectors Xj and Y . If the mean has been subtracted from each variable, then the cosine is the correlation between variables Xj and Y . Let the first variable selected be denoted by X(1) ; this variable is then forced into all further subsets. The residuals Y − X(1) b(1) are orthogonal to X(1) , and so to reduce the sum of squares by adding further variables, we must search the space orthogonal to X(1) .

0 The vector Rβ contains the expected values of the first k projections, where k is the number of columns in X. The remaining (n − k) projections have zero expected values. The stochastic part of the projections is Q . Q INTERPRETATION OF PROJECTIONS 29 = σ 2 I. That is, the elements of Q are uncorrelated and all have variance σ 2 . This part of the result is distribution-free. If the are normally distributed, then the elements of Q , being linear combinations of normal variables, will also be normally distributed.

Then if the variable in the top row of the submatrix RB is added next, the 2 reduction in the residual sum of squares (RSS) is r1y . To find the reduction in RSS if the variable in the second row is added next instead, a planar rotation can be used to bring this variable into the top row and then the reduction in RSS is equal to the square of the value which is then in the top position of ryB . There is no need to perform the full planar rotation of whole rows to calculate the effect of bringing a variable from row i to row 1 of RB .

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