Designation: E2810 − 11 (Reapproved 2017)Standard Practice forDemonstrating Capability to Comply with the Test forUniformity of Dosage Units1This standard is issued under the fixed designation E2810; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice provides a general procedure for evaluat-ing the capability to comply with the Uniformity of DosageUnits (UDU) test. This test is given in General Chapter Uniformity of Dosage Units of the USP, in 2.9.40 Uniformityof Dosage Units of the Ph. Eur., and in 6.02 Uniformity ofDosage Units of the JP, and these versions are virtuallyinterchangeable. For this multiple-stage test, the procedurecomputes a lower bound on the probability of passing the UDUtest, based on statistical estimates made at a prescribedconfidence level from a sample of dosage units.1.2 This methodology can be used to generate an acceptancelimit table, which defines a set of sample means and standarddeviations that assures passing the UDU test for a prescribedlower probability bound, confidence level, and sample size.1.3 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety, health, and environmental practices and deter-mine the applicability of regulatory limitations prior to use.1.4 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E2363 Terminology Relating to Process Analytical Technol-ogy in the Pharmaceutical IndustryE2709 Practice for Demonstrating Capability to Complywith an Acceptance Procedure2.2 Other Documents:JP Japanese Pharmacopoeia3Ph. Eur. European Pharmacopoeia4USP United States Pharmacopeia53. Terminology3.1 Definitions—See Terminology E2363 for a more exten-sive listing of terms in ASTM Committee E55 standards.3.2 Definitions of Terms Specific to This Standard:3.2.1 acceptable parameter region, n—the set of values ofparameters characterizing the distribution of test results forwhich the probability of passing the lot acceptance procedureis greater than a prescribed lower bound.3.2.2 acceptance limit, n—the boundary of the acceptanceregion, for example, the maximum sample standard deviationfor a given sample mean.3.2.2.1 Discussion—The coefficient of variation (relativestandard deviation) may be substituted for the standard devia-tion where applicable.3.2.3 acceptance region, n—the set of values of parameterestimates (that is, sample mean and standard deviation) whereconfidence limits attain a prescribed lower bound on theprobability of passing a lot acceptance procedure.3.2.4 confidence level, C, n—the prescribed overall level forcalculating the uncertainty region of the parameters from thesample estimates.3.2.4.1 Discussion—The preset confidence level is stated asa percentage, for example, 100 (1 – α) = 95 %, where α is arisk that is allocated to the two parameters being estimated.3.2.5 lower probability bound, LB, n—the nominal probabil-ity of passing the UDU test for a given set of parameterestimates.1This practice is under the jurisdiction of ASTM Committee E55 on Manufac-ture of Pharmaceutical and Biopharmaceutical Products and is the direct responsi-bility of Subcommittee E55.03 on General Pharmaceutical Standards.Current edition approved Oct. 1, 2017. Published October 2017. Originallyapproved in 2011. Last previous edition approved in 2011 as E2810 – 11ɛ2. DOI:10.1520/E2810-11R17.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3Available from the Pharmaceuticals and Medical Devices Agency (PMDA),Shin-Kasumigaseki Building, 3-3-2 Kasumigaseki, Chiyoda-ku, Tokyo 100-0013,Japan, https://www.pmda.go.jp.4Available from the European Directorate for the Quality of Medicines andHealth Care (EDQM), Council of Europe, 7 allée Kastner, CS 30026, F-67081Strasbourg, France, http://www.edqm.eu.5Available from U.S. Pharmacopeial Convention (USP), 12601 TwinbrookPkwy., Rockville, MD 20852-1790, http://www.usp.org.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.13.2.6 multiple-stage acceptance procedure, n—a procedurethat involves more than one stage of sampling and testing agiven quality characteristic with one or more acceptancecriteria per stage.3.2.7 representative sample, n—a sample that consists of anumber of units that are drawn based on rational criteria suchas random sampling and intended to assure that the sampleaccurately portrays the material being sampled3.2.8 sampling plan, n—scheme for selecting dosage unitsfrom locations within a batch for testing purposes.3.2.8.1 Discussion—In this standard, a single dosage unit isselected from each batch location.3.2.9 uniformity of dosage units, UDU, n—the degree ofuniformity in the amount of the drug substance among dosageunits.3.2.9.1 Discussion—The requirements of the UDU test ap-ply to each drug substance in dosage units containing one ormore drug substances, unless otherwise specified. The unifor-mity improves as the variability decreases.4. Significance and Use4.1 The methodology was originally developed (1-4)6foruse in drug content uniformity and dissolution but has generalapplication to any multistage test with multiple acceptancecriteria. Practice E2709 summarizes the statistical aspects ofthis methodology. This practice applies the general methodol-ogy of Practice E2709 specifically to the UDU test.4.1.1 While other methods can be used to estimate theprobability of passing the UDU test, they are outside the scopeof this practice.4.2 The UDU test procedure describes a two-stage samplingtest, where at each stage one can pass or continue testing, andthe decision to fail is deferred until the second stage. At eachstage there are acceptance criteria on the test results as outlinedin Table 1.4.3 The UDU test is a market standard. The USP GeneralNotices include the following statement about compendialstandards. “The similarity to statistical procedures may seem tosuggest an intent to make inference to some larger group ofunits, but in all cases, statements about whether the compendialstandard is met apply only to the units tested.” Therefore, theUDU procedure is not intended for inspecting uniformity offinished product for lot/batch release or as a lot inspectionprocedure.4.3.1 The UDU test defines a product requirement to be metat release and throughout the shelf-life of the product.4.3.2 Passing the UDU test once does not provide statisticalassurance that a batch of drug product meets specified statis-tical quality control criteria.4.4 This practice provides a practical specification that maybe applied when uniformity of dosage units is required. Anacceptance region for the mean and standard deviation of a setof test results from the lot is defined such that, at a prescribed6The boldface numbers in parentheses refer to a list of references at the end ofthis standard.TABLE 1 Uniformity of Dosage Units Test ProcedureNOTE 1—All measurements of dosage units and criteria values are inpercentage label claim (%LC).At each stage calculate the sample average,X—, and the sample standard deviation, s.StageNumberTestedPass Stage If:S110 |M – X¯|+2.4s ≤ 15.0, where M isdefined below.S220 (1)|M – X¯|+2.0s ≤ 15.0, using all30 results (S1+S2).(2) No dosage unit is outside themaximum allowed range of0.75 * M to 1.25 * M.M is defined as follows:If T is less than or equal to 101.5 %LC, and(1)IfX¯is less than 98.5 %LC, thenM = 98.5 %LC.(2)IfX¯is between 98.5 and101.5 %LC, then M = X¯.(3)IfX¯is greater than 101.5 %LC,then M = 101.5 %LC.If T is greater than 101.5 %LC, and(1)IfX¯is less than 98.5 %LC, thenM = 98.5 %LC.(2)IfX¯is between 98.5 and T, thenM = X¯.(3)IfX¯is greater than T, thenM = T.T is the target content per dosage unit at the time of manufacture, ex-pressed as %LC. Unless otherwise specified in the individual monograph, Tis 100.0 %LC.E2810 − 11 (2017)2confidence level, the probability that a future sample from thelot will pass the UDU test is greater than or equal to aprespecified lower probability bound. Having test results fall inthe acceptance region provides assurance that a sample wouldpass the UDU test with at least the specified lower boundprobability. This procedure does not account for any decreasein potency during the shelf life, which could affect the abilityto meet the UDU test requirements.4.5 This practice can be used as an element for processdemonstration or validation, continuous process verification,in-process testing, or lot release (acceptance). As the circum-stances and available information vary in these differentapplication areas, this practice does not prescribe a specifictarget, sample size, lower probability bound, or confidencelevel. These must be prospectively selected by the user andmay be different from those used in the acceptance limit tablesprovided in this practice.5. Procedure5.1 Generating The Acceptance Limit Table:5.1.1 The general procedure that generates the acceptancelimit tables is described in Practice E2709 and the specificprocedure for application to the UDU test is described in theliterature (4). A simplified description on the construction anduse of these tables is given in this section.Acomputer programis required to generate the tables given a target T as apercentage of label claim (LC), a lower probability bound LB,a confidence level C, and a sample size n.5.1.2 The first step is to determine the acceptable parameterregion. On a two-dimensional content space consisting of thetrue mean (µ) on the horizontal axis and standard deviation (σ)on the vertical axis the upper boundary of this region is definedby a contour, a curve that is concave downward and depictedby the solid curve in Fig. 1. The contour is determined by theLB probability and the Target under the assumption that thedosage unit content is normally distributed. The acceptableparameter region is the set of points on or below the contour.Any (µ, σ) pair in the acceptable region would pass the UDUtest with a probability of at least the LB.5.1.3 The second step is to generate the acceptance limitcurve. The sample mean (X¯) and sample standard deviation (s)estimate the population parameters µ and σ within C %confidence limits as chosen by the user. The joint confidenceregion for µ and σ (5) has the shape of an inverted trianglearound a (X¯, s) pair as depicted in Fig. 1 with the lowest vertexat (X¯, 0). A value of X¯is selected starting with s = 0, then theNOTE 1—All points below the lower bound contour have higher than a 95 % chance of passing UDU test if mean and standard deviation are known.All points below the acceptance region contours pass the associated acceptance limit table for n = 100 and n = 10.ULS is the upper confidence limit for σ.Z is a standard normal critical value.FIG. 1 Example of Simultaneous Confidence Interval with 95 % Lower Bound and Acceptance RegionsE2810 − 11 (2017)3confidence region is expanded by increasing s until one of theupper vertices just touches the acceptable parameter region.The size of the confidence region is determined by C and n.This value of s defines a point on the acceptance limit curve at(X¯, s). Additional selections of X¯then generate the acceptancelimit curve, as depicted as dotted lines in Fig. 1. Acceptancelimit curves are shown for n = 10 and n = 100, illustrating thatthe acceptance limits approach the acceptable parameter regionwith increasing sample size.5.1.4 Computer programs have been developed for generat-ing acceptance limit tables, but these may not be available toall practitioners. This practice contains four acceptance limittables for many practical use situations.5.2 Using the Acceptance Limit Tables in This Practice:5.2.1 In each table acceptance limits on the standard devia-tion are given for means ranging 90–110 % of LC in incre-ments of 0.2 %LC for sample sizes ranging from n =10 ton = 500. In all tables the target is set at T = 100 %LC, so theacceptance limits for standard deviations are symmetricalaround 100 %LC. This target is also required for interchange-ability across the ICH regions (6).5.2.1.1 At the confidence level of C = 95 % used often inthe regulatory arena, three levels of the probability lowerbound are provided: LB =90%(Table 2), LB =95%(Table 3)and LB =99%(Table 4). These provide 90 %, 95 %, and 99 %TABLE 2 Acceptance Limits on Sample Standard Deviation (%LC) forT = 100 %LC, C =95%,LB =90%LCSample Average(%LC)Sample Size (n)10 30 40 50 60 80 100 120 150 200 500100.0 2.91 4.36 4.65 4.84 4.99 5.19 5.33 5.43 5.54 5.66 5.9399.8 or 100.2 2.88 4.31 4.59 4.79 4.94 5.14 5.28 5.38 5.50 5.62 5.9199.6 or 100.4 2.84 4.26 4.54 4.74 4.89 5.09 5.24 5.34 5.45 5.58 5.8899.4 or 100.6 2.81 4.21 4.49 4.69 4.83 5.04 5.18 5.29 5.40 5.53 5.8499.2 or 100.8 2.77 4.16 4.43 4.63 4.77 4.98 5.13 5.23 5.35 5.48 5.7999.0 or 101.0 2.74 4.10 4.38 4.57 4.72 4.92 5.07 5.17 5.29 5.43 5.7498.8 or 101.2 2.70 4.05 4.32 4.52 4.66 4.86 5.01 5.11 5.23 5.37 5.6998.6 or 101.4 2.67 4.00 4.27 4.46 4.60 4.80 4.94 5.05 5.17 5.30 5.6398.4 or 101.6 2.63 3.95 4.21 4.40 4.54 4.74 4.88 4.99 5.10 5.24 5.5698.2 or 101.8 2.60 3.89 4.16 4.34 4.48 4.68 4.82 4.92 5.04 5.17 5.4998.0 or 102.0 2.56 3.84 4.10 4.28 4.42 4.62 4.75 4.86 4.97 5.10 5.4397.8 or 102.2 2.53 3.79 4.05 4.22 4.36 4.55 4.69 4.79 4.90 5.03 5.3597.6 or 102.4 2.49 3.74 3.99 4.17 4.30 4.49 4.62 4.72 4.84 4.97 5.2897.4 or 102.6 2.46 3.68 3.93 4.11 4.24 4.43 4.56 4.66 4.77 4.90 5.2197.2 or 102.8 2.42 3.63 3.88 4.05 4.18 4.36 4.50 4.59 4.70 4.83 5.1397.0 or 103.0 2.39 3.58 3.82 3.99 4.12 4.30 4.43 4.53 4.63 4.76 5.0696.8 or 103.2 2.35 3.53 3.77 3.93 4.06 4.24 4.37 4.46 4.56 4.69 4.9996.6 or 103.4 2.32 3.48 3.71 3.87 4.00 4.18 4.30 4.39 4.50 4.62 4.9196.4 or 103.6 2.28 3.42 3.65 3.81 3.94 4.11 4.23 4.33 4.43 4.55 4.8496.2 or 103.8 2.24 3.37 3.60 3.76 3.88 4.05 4.17 4.26 4.36 4.48 4.7796.0 or 104.0 2.21 3.32 3.54 3.70 3.82 3.99 4.10 4.19 4.29 4.41 4.6995.8 or 104.2 2.17 3.26 3.48 3.64