Article

Mandel, John; Lashop, Theodore W. *(1987, ASQC)* *National Bureau of Standards*

*Journal of Quality Technology*Vol. 19 No. 1- QICID: 5579 January 1987 pp. 29-36
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Repeatability and reproducibility are usually defined by the relation R = 2sr divided by k, where R stands for repeatability or reproducibility, and sr is the corresponding standard deviation. It is then stated that the probability is C that a difference between two test results will lie between (-R) and (+R). For C = 0.95, which is the usual choice, the values that have been proposed for the multiplier k are 1.96, 2, or Student's t. However, C is actually a random variable with a highly skewed distribution. It is shown that regardless of the above choice of k, the probability that C will lie in the "vicinity of 0.95," such as for example 0.92 to 0.97, is very small, unless the number of participating laboratories is large (30 or more). Nevertheless, for any given interval defining a "vicinity of 0.95," a value of k exists that maximizes the probability that C lies in that interval. For a number of reasonable choices for "vicinity of 0.95" the optimal k is close to 1.96.

Statistical tests,Repeatability and reproducibility studies (R&R),Interlaboratory comparisons

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