Determination of a two-tailed 100(1-alpha)% upper limit on the relative error in the laboratory-to-laboratory standard deviation obtained from an interlaboratory study.

For some classes of analytical methods, it is assumed that the error in the laboratory-to-laboratory standard deviation (S(L)) is appreciable. To demonstrate the magnitude of this error in S(L) for such methods, formulas were derived to obtain a two-tailed 100(1-alpha)% upper limit on the relative error in S(L) obtained from an interlaboratory study, assuming that the laboratory-to-laboratory variance (S(L)2) obtained in the validation of an analytical method is approximately normal and/or Chi-square distributed. This 100(1-alpha)% upper limit (delta(1-alpha/2)) is referred to as a margin of relative error in S(L) (MRE(S(L. Monte Carlo simulations were performed, and the results compared satisfactorily with the formula calculations. To aid in designing future interlaboratory studies in which concern is focused on the magnitude of the uncertainty in S(L), expressed as a proportion of the true value (sigma L), a formula was derived to determine the number of laboratories needed to attain a given MRE in S(L) for a stated number of replicates per laboratory.