In 2006, FDA CMC Statistics team evaluated the statistical properties of the USP, EU, and JP procedures outlined above with the operating characteristics curves. We proposed that a lot is accepted if only a small proportion of units in the lot have the dose contents below a lower specification or above an upper specification limit. Our proposed procedure is a two-tier sampling plan based on the two one-sided tolerance intervals. We further adapt Pocock’s group sequential boundaries to control the confidence levels at the two tiers. Our proposed DCU testing procedure (Tsong and Shen 2007) is described as follows.

In order to harmonize the acceptance sampling plans across the United States, Europe, and Japan regions, a harmonization procedure (U.S. Pharmacopoeia XXV 2010) was developed to replace USP XXIV and EP III plans. The two-stage harmonized procedure is derived based on a sequential procedure using the two-sided tolerance interval combined with an indifference zone for the sample mean and zero tolerance criteria for the observed dose content of each unit.

The two-stage harmonized procedure for DCU is described in (U.S. Pharmacopoeia XXV 2010).

For the first stage, the sample mean () and the sample standard deviation (s) of the 10 units are calculated. The indifference zone (M) at the first stage is defined as M = 98.5 % if <98.5 %; M = 101.5 % if >101.5 %; and M =  if . The two-sided tolerance interval is calculated as ( −2.4s, +2.4s), where the constant 2.4 can be interpreted as the tolerance coefficient with approximately 87.5 % coverage and a confidence level of 90.85 % for a sample size of 10. The dose content uniformity is accepted if all 10 samples are within (75 %, 125 %)M and ( −2.4s, +2.4s) is covered by (M-15 %, M+15 %). If the lot fails to be accepted, go to the second stage.

In Stage 2, additional 20 samples are randomly collected. With a total of 30 samples, a tolerance coefficient of 2.0 is used for calculation. The constant 2.0 can be interpreted as the tolerance coefficient with 87.5 % coverage and 95.14 % confidence level for a sample size of 30. The lot is accepted if all 10 samples are within (75 %, 125 %)M and ( −2s, +2s) is covered by (M-15 %, M+15 %). Otherwise, the lot fails the DCU test.

FDA CMC Statistics team evaluated this harmonized USP procedure. Based on our evaluation, it is biased toward the lot with the true mean deviating from 100 % label claim. In other words, the probability of passing the lot with an off-target mean is higher than that of the lot with an on-target mean (100 % LC) based on simulations (Shen and Tsong 2011).

Since 2007, the pharmaceutical industry has expressed an interest in conducting large sample testing for dose content uniformity due to the availability of near-infrared spectroscopy in the manufacturing process. With this NIRS technology, continuously testing of the dose content without destroying the units becomes possible. Thus, the pharmacopeia acceptance sampling procedure for small samples should be extended to large samples. Many statistical testing procedures have been proposed for this purpose. The approach proposed by the FDA CMC Statistics team is a large sample DCU testing procedure based on the two one-sided tolerance intervals (TOSTI). Our proposed approach maintains a high probability to pass the USP compendia by restricting the TOSTI OC curves for any given sample size to intersect with the USP OC curve for a sample size of 30 at the acceptance probability of 90 % when the individual unit is assumed to be normally distributed with an on-target mean of 100 %LC (Shen et~al. 2014). The derivation of the tolerance coefficient K for any large sample size n was provided in Shen et~al. (2014), Dong et~al. (2015), and Tsong et~al. (2015). We denote this extension as PTIT_matchUSP90 method in the remaining section.

The large sample dose uniformity tests with two options were published in European Pharmacopeia (Council of Europe 2012). EU option 1 is a parametric approach based on a two-sided tolerance interval approach with an indifference zone and a counting limit for the number of dosage units outside 75 %M −125 %M, with M defined the same way as that in the USP Harmonized procedure. EU option 2 is a non-parametric approach developed for non-normally distributed contents of dosage units. The EU option 2 is actually a counting procedure with two acceptance criteria. The number of dosage units outside of and are required to be no more than C1 and C2, respectively, where L1, L2, C1, and C2 are defined in Table 2.9.47.-2 of European Pharmacopeia (Council of Europe 2012).