n = number of observations at each location
Then the upper confidence limit for the sum of the between-location and within-location variance components (i.e., σ) is:
Given the sample within-location standard deviation (SE) and the sample between-location standard deviation (SM), one computes a confidence interval for σ using the Graybill–Wang method. Since the sample mean and mean squares for the
between-location and within-location standard deviations are independent, the overall confidence level (1– α) is the product
of the two individual confidence levels for μ and σ. Each individual confidence level is the square root of the overall confidence
level (μ is two-sided and σ is upper one-sided). One can generate an acceptance limit table by finding the largest combinations
of within- and between-location standard deviations for a fixed sample mean, such that the resulting confidence region remains
below the prespecified LBOUND.
Sample content uniformity acceptance limit tables
Tables assume that the target (i.e., the average of potency specification) is 100% and that the sampling plan is to test one
dosage unit from each of n separate locations throughout the batch. Passing the tabled limit ensures, with the chosen level of confidence, that there
is at least a 95% chance of passing the USP uniformity of dosage units test ‹905› for samples taken from that batch.
Click here to view sample tables
James S. Bergum, PhD,* is an associate director in the nonclinical biostatistics department of Bristol-Myers Squibb, One Squibb Dr., New Brunswick,
NJ 08903, tel. 732.227.5981, firstname.lastname@example.org
Hua Li, PhD, is a vice-president of management science at Merrill Lynch & Co.
*To whom all correspondence should be addressed.
Submitted: Feb. 16, 2007. Accepted: Aug. 20, 2007.