fill weight variation release and control of capsules, tablets, and sterile solids

American Society for Quality

Fill Weight Variation Release and Control of Capsules, Tablets, and Sterile SolidsAuthor(s): Charles RobertsSource: Technometrics, Vol. 11, No. 1 (Feb., 1969), pp. 161-175Published by: American Statistical Association and American Society for QualityStable URL: http://www.jstor.org/stable/1266772 .

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VOL. 11, No. 1

Fill Weight Variation Release and Control of Capsules, Tablets, and Sterile Solids

CHARLES ROBERTS1

Chas. Pfizer & Co., Inc.

The United States Pharmacopeia gives specifications for fill weight variation of capsules, tablets, and sterile solids to which the federal government expects the pharmaceutical industry to adhere. This paper makes probability statements about the USP weight variation test that could form the basis for a criterion for both final product release and in-process control, as far as fill weight variation is concerned. Use is made of the fact that the coefficient of variation, the standard deviation divided by the mean, efficiently describes fill weight variation. The effect of unintentional overfill on control is considered. A certain final product weight variation specification is examined and mention is made of sampling methods.

INTRODUCTION

There is considerable literature dealing with statistical methodology in the quality control of the pharmaceutical industry, and Olsen and Lee [1] give a survey of the literature. Of special importance are their references 12, 21, 26, 27, and 36. A more recent publication is that of French, et al. [2].

The United States Pharmacopeia [3] gives specifications for fill weight variation of capsules, tablets, and sterile solids to which the federal government expects the pharmaceutical industry to adhere. Unfortunately, the nature of the USP weight variation test (USPWVT) is such that it is possible, with almost any fairly large-sized lot, to fail to USPWVT and thereby cause recall of the entire lot. The USPWVT, as given by [3], is reprinted in the Appendix.

For example, the USPWVT for light tablets would involve taking only 20 tablets from the entire lot and then seeing how many of the 20 fall outside 10% limits on either side of the average of the 20. If 3 or more fell outside the 10% limits or there was one outside 20% limits, then the USPWVT would be failed and the pharmaceutical company must face the consequences of such failure. If the person sampling had carefully selected the 20 tablets from the entire lot of say 1 million tablets, it is easy to see that he could surely have caused USPWVT failure of the entire lot, based only on a small fraction of the lot.

A fairer test. A fairer test would be to have the entire lot at ones disposal and to randomly perform the USPWVT thousands of times, recording the fraction of times that the USPWVT is failed. Eventually this fraction ap- proaches a number defined to be the probability of failing a USPWVT. Al- though this test would be fairer, it would certainly be impractical.

Received February 1968; revised June 1968. 1Now at the Graduate School of Business Administration, New York University.

161

TECHNOMETRICS FEBRUARY 1969



162 C. ROBERTS

MODIFIED USPWVT

In the description of the USPWVT method, comparisons of each individual sampled weight are made with the average weight of the sample. The modified USPWVT (MUSPWVT) will involve comparisons of each individual sampled weight with the mean of the entire distribution of all the lot, not just the 20 or so sampled for the USPWVT. The size of the lot is assumed to be large. The mathematical model, which is developed in the Appendix, supposes that the desired lot average is MD, the actual lot average is M = (1 + B)MD, when the

product is momentarily produced with average weight MA = (1 - A)MD . The modified test not only simplifies computations but also gives a method

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WEIGHT VARIATION RELEASE AND CONTROL

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for determining when the production process is "in control". We can consider the probability of failing a MUSPWVT at the instant the machine starts pro- ducing an average that is larger or smaller than the average weight for this lot. If the probability of failing a MUSPWVT is too large at any moment, the process would be "out of control", and machine adjustment must be made.

The accuracy of the MUSPWVT in estimating the corresponding probability of failing a USPWVT is quite good either when the production is maintained near the lot average or when the entire finished lot is considered. For samples of 20 or more, the sample average is very near the average of the entire distribution, which results in corresponding accuracy. Because of the accuracy of the MUSPWVT when the production has been completed (A = 0), Figures 1, 2, and 3 do not mention "modified".

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PROBABILITY OF FAILING USPWVT

The coefficient of variation, often called the relative standard deviation, is defined to be the standard deviation divided by the mean. It is a measure of variation, which does not have units. In practice, fill weight release and control can be guided by the coefficient of variation, since the USP rules for allowable variation depend upon the average weight. This coefficient is often multiplied by 100, and expressed as a percent.

The assumption is made that the distribution of the weights is normal. It is

necessary to specify the coefficient of variation of the distribution of individual

weights to use the eight figures accompanying this paper. Figures 1 (capsules), 2

(tablets), and 3 (sterile solids) give the probability of failing a USPWVT for




values of only the coefficient of variation for the entire lot. For example, when the coefficient of variation is 5.7%, the USPWVT of capsules (Figure 1) will be failed about once in every ten times the test is performed. When the coefficient of variation is 4%, the failure is about four in each one million times. The computations for Figures 1, 2, and 3 were made by direct use of the equations in Derivations 1, 2, and 3 of the Appendix, respectively.

It can be an easy matter to decide upon the release of a product, as far as weight variation is concerned, by use of these graphs. If a decision is made of what risk would be permitted in failing the USPWVT, like 0.01 or 0.001, then when the observed coefficient of variation is smaller than the value corresponding to the 0.01 or 0.001 probability, the product would be released. In the case of capsules (Figure 1), probabilities less than 0.01 and 0.001 correspond to coefficients of variation less than 5.02% and 4.64%, respectively.

The curves in this paper are for fill weights, and have not been adjusted for any tares. In the case of capsules, we want to know the fill coefficient of variation when we actually know only the coefficient of variation of the entire capsule. Due to empty capsule weight and weight variation, experience has shown that the coefficient of variation of the fill is approximately 10% larger than the coefficient of the filled capsule. As an example, if the coefficient of variation of the filled capsule is 3.50%, the coefficient for the fill is approximately 3.85%. Derivation 5 of the Appendix shows the computations involved.

A weight release specification. For capsules and sterile solids, Pfizer has made use of the pharmaceutical weight variation specification, "No more than 0.5% of the weights are outside 10% of the average", while referring to the entire lot. For all three products by Derivation 6 of the Appendix, this statement is equivalent to "The coefficient of variation is less than 3.56%. Such a specification is adequate for capsules, sterile solids, and light tablets, but would be disastrous for heavy tablets (see Figure 2) since a coefficient of variation of 3.56% would result in failure of the USPWVT about 66 of every 100 times.

We see, therefore, that there are three equivalent ways of expressing allowable weight variation of the lot. The first limits the proportion of the weights outside 10% of the average weight; the second puts an upper bound on the coefficient of variation; and the third limits the probability of failing a USPWVT. That is, the following three rules are equivalent.

Rule I: No more than 0.5% of the weights are outside 10% of the average. Rule II: The coefficient of variation is less than 3.56%.

Rule III:

Probability of failing a Product USPWVT is less than

Capsules 13 in 1 billion Light Tablets 14 in 100,000 Medium Tablets 32 in 1000 Heavy Tablets 66 in 100 Sterile Solids 52 in 100,000

165



- Con trol im/'f

Cen ter Po/in

- - Contro/ Limit

Graphical demonstration that overfill

gives a "tight control" above, but a "loose control" below.

FIGURE 4

Because we see that Rule III is good for capsules while it is very poor for heavy tablets, a satisfactory general rule would be Rule IV, "The probability of failing a USPWVT is less than 1 in 1000". This rule could then be applied to all three products whereas Rules I, II, and III cannot.

EFFECT OF UNINTENTIONAL OVERFILL

Here overfill does not mean the planned overfill which a manufacturer may put into his product so that he has some protection against subpotency. In this discussion, overfill will mean that extra average weight that is unintentionally added to the product fill weight because of the inability to adjust the machine better. This overfill is represented by the symbol B, meaning that the product average weight is M = (1 + B)MD where MD is the desired center point. By definition, a negative overfill is an underfill.

Figure 4 gives an example of a control procedure, where control limits are set above and below by, for example, i-3% of the proposed center point. If, as in the figure, the average fill weight is comfortably going along at +2% above center point, which would be within the ?3% control limits, it is evident that there is only 1% of freedom above (a tight control), while there is 5% below (a loose control). If the machine suddenly dropped weights almost 5%, failure of the USPWVT could be drastically affected although the production still would be "in control".

Figure 5 (capsules) demonstrates the effect of up to 2% unintentional over- fills and underfills, when the coefficient of variation is fixed at 3.5%. The curve for B = 0, or center point running, is the best that can be attained. That is, the curve for B = 0 is symmetrically located within the other curves. Note that on the left side, an overfill of +2% corresponds to probability of failing a

166 C. ROBERTS




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MUSPWVT below the B = 0 value, apparently indicating that overfill is better than center point operation. On the right side, however, an overfill of +2% puts the probability of failing a 1\IUSPWVT above the B = 0 value, indicating that overfill is actually less desirable than center point operation.

As a further example in which Figure 5 is used, suppose that the entire lot up to present has an average overfill of + 1% and that the machine is continuing at this overfill level. This will correspond to the curve B = 1% and the control limit at - 1%. If the machine suddenly started to produce with a 3% underfill, the actual lot overfill B still is +1%, but the control limit would now be +3%, and the probability of failing a MUSPWVT would have jumped up to about 0.006 from having been below 0.00000001. Under ?3% control limits, center point operation could allow only a jump up to a probability of failure of 0.0002, indicating further the desirability of center point running.

Coefficien ts of Varia tion 4 0/, Ligh t Tab lt ) 3 C/. M ed i um Tablet) 2 % ( Heavy Tablet)

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169



170 C. ROBERTS

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CONTROL LIMITS

Because lighter tablets tend to have larger coefficients of variation, we now consider the example of 2% for heavy tablets, 3% for medium, and 4% for light. Figure 6 demonstrates that the same control limits of 3% cannot be used for the three sizes of tablets because of differing probabilities of failing the MUSPWVT. Figure 7 demonstrates that if one selects ?43% control limits for light tablets, the same probability curves are obtained for I2.25% limits and -t1.5% limits for medium and heavy tablets, respectively.

Sometimes production requests that wider control limits be allowed because of special characteristics of product-machine interaction. Figure 8 for light




tablets indicates that if a -33% control limit about the proposed center point is satisfactory with a 4% coefficient of variation, then it should be approximately equivalent to a ?=4.8% control limit with a 3% coefficient of variation. Note that if the coefficient of variation is 5%, the process could never be controlled with the assurance of the ?3% control limit with a 4% coefficient of variation.

SAMPLING METHODS

It is extremely important that the weights be sampled throughout the entire lot for estimation of the coefficient of variation. All high or low values of un- rejected material must be included in the computation of the coefficient of variation, because if these values are discounted, the result is that the standard ?deviation and hence the coefficient of variation will be inaccurately small, although the mean may remain unchanged.

Because of the relatively small weight of fills and the desirability of ex- amining several units, many times groups of 10 or 20 are the weighing unit. It is extremely important that the sampling from the machine be done in the proper way. For instance, on H & K encapsulating machines, there is a right side and a left side although the capsules come together later. The sampling should be from each side by having the person sampling put his hand under each head .outlet to collect the capsules. If the capsules from each head are not weighed separately, it is possible to have one side high, the other side low, and on the average appear in control, and not actually be in control.

Although extensive individual weighing can be very expensive, some syste- matic random sampling of individual units must be performed. Special equip- ment, like the Cahn balance, can greatly speed this operation.

171



172 C. ROBERTS

APPENDICES

Appendix 1.

USP WEIGHT VARIATION REQUIREMENTS

Capsules-Sterile Solids-Tablets

CAPSULES

Capsule mneet the requirements of the following test with respect to variation in weight of contents.

HARD CAPSI-LES-Weigh collectively 20 intact capsules, and calculate the average gros weight. Taking each cap- sile individually, balance it against weights representing !)0 per cent and 110 per vent of the average, respectively: if each c:pstile weighs between 90 per cent and 110 per cent of the average gross weight, the sample meets the requirements.

If not all of the capsules fall within the aforementioned limits, weigh the 20 capsules collectively and individually, and remove the contents of each capsule with the aid of a small brush or pledget of cotton. Weigh the emptied shells collectively and individually, and calculate for eachi capsule the net w-eight of its contents by subtracting the weight of the shell from the respective gross weight. D)etermine the average net weight by subtracting the weight of the 20 emptied Fhells fron the gross weight of the 20 iapsuiles. l)etermine the difference between the net weight and the average weight: the sample meets the requirements if (1) not more than two of the differences are greater than 10 per cent of the average and (2) in no case is the difference gre:ter than 25 per cent.

If more than 2 but less than 7 capsules deviate from the average between 10 per cent and 25 per cent, determine the net weights of an additionial 40 capsules, and determine the average content of the entire 60 capsules. Determine the 60 deviations from the new average: in not more than 6 of the entire 60 capsules does the difference exceed 10 per cent of the average, and in no case does the difference exceed 25 per cent.

SOFTr CAPSULES-For soft gelatin cap sules that do not meet the requirements of the test for gross capsule weight, determine the net weight of the contents of individual capstules as follows: Weigh the intact capsules individually to obtain their grss weights, taking care to preserve the identity of each capsule. Then cut open the capsules by means of a suitable clean, drv cutting instrument such as scissors or a sharp open blade, and remove the contents by washing in a suitable solvetnt. Allow the occluded solvent to evaporate fron the shells at room temperature over a period of about 30 minutes, taking precautions to avoid uptake or loss of moisture. Weigh the individual shells, and calculate the inet weight of the contents.

STERILE SOLIDS

The following tests and specifications apply to fill tolerances of sterile solids packaged as dosage fornm, with or without diluents, in suitable containers and intended for parenteral use when suitably dissolved or suspended.

Select a representative sample of 60 filled containers. Itemove all paper labels from 201 of the containers, and cleanse and dry them thoroughly. Re- move the closure front or break the top from each container, and without delay weigh each container and its contents. Empty each conltainer by gentle tap- ping, and then rinse it with water and with alcohol. Dry each emptied container at 10)5 for 1 hour (or at a lower temperature to constant weight, if the nature of the container precludes heat- ing at 105'), cool in a deeiccator, and weigh: the weight of the contents is the difference between the two weights.

Calculate the average net weight of the contents of the 2) containers: the sample meets the reqluirelnenlts if (1) not more than 2 of the net weights deviate by nlore than 10 per cent from the average net weiglit, and (2) no net weight deviates by more than 15 per cent from the average net weight.

If more than 2 but less than 7 of the net weights deviate from the average by between 10 per cent and 15 per cent, determine the weights of the contents of the 40 additional filled containers. Calculate the average net weight of the contents of the entire 60 containers: the sample meets the requirements if (1) not more than 6 of the net weights of the 60 individual containers deviate by more than 10 per cent from the average net weight, and (2) not more than 1 of the net weights of the 60 individual containers deviates by more than 15 per cent from the average net weight.

Container Content- FOR STERILE SOLIDS WITHOUT DILUENTS

-The average net weight, determined as directed in the foregoing paragraphs, is not less than 93 per cent and not more than 107 per cent of the labeled amount of the article in each container, calcu- lated on the dried basis if a test for Loss on Drying or Water is provided in the individual monograph.

FOR STERILE SOLIDS WITH DILUENTS- The average content, determined on the pooled contents, accurately weighed, of' not less than 10 containers, determined as directed in the Assay provided in the individual monograph, falls within the tolerances provided in the monograph.

TABLETS Uncoated tablets conform to the

weight tolerances given in the accompanying table.

Weigh individually 20 whole tablets, and calculate the average weight: the weights of not more than 2 of the tablets ditfer from the average weight by nmore than the percentage listed and no tablet differs by more than double that percentage.

Weight Variation Tolerances for Un.oated Tablets

Average Weight Percentage of Tablet, ms. Difference

130 or less 10 Froni 130 through 324 7.5 More than 324 5

Appendix 2. Probability of Failing a Modified USP Weight Variation Test

It is assumed that the mean of the distribution of weights is M, standard deviation S, and that C = S/M is the coefficient of variation. The quantity MI is the desired average weight and MA is the instantaneous mean. The numbers A and B are defined by A = (MD - MA)/MD and B = (M - MD)/MD. The quantity A is the underfill of the process at an instant, while B is the overfill




of the entire lot. The computations that will be made will depend only on A, B, and C.

The weights are assumed to be normally distributed. In practice, this is not always the case, although normality does characterize a standard situation. In some instances normality can be relaxed, and in others similar results can be obtained by Monte Carlo methods, although these two topics will not be dis- cussed here.

Capsules

Let us define:

P = probability that any one weight lies within 10% of the overall mean.

Q = probability that any one weight lies outside 10% but within 25% of the overall mean.

Pi = probability of i in sample of 20 inside "Q" limits with 20-i inside "P" limits.

Ri = probability of i in sample of 40 inside "Q" limits with 40-i inside "P" limits.

By [3], since we have trinomial processes, the probability of passing a MUSPWVT is

Po + Pl + P2 + P3(Ro + R, + R2 + R) + P4(Ro + R, + R2) +

P5(Ro + R,) + PeRo,

where

20! 40! Pi 20- p20-piQ and Ri p- 40-iQi

P= -

(20 - i)!! and = (40- i)!i! -

Letting F denote the standard normal cumulative distribution,

Prob (0.9M < X < 1.1M)

Prob (0.9M < X < 1.1M)

= Prob {[0.9M - (1 - A)MD]/S

< [X - (1 - A)MD]/S < [1.1M - (1 - A)MD]/S}

= F[(0.1 + 1.lB + A)/(1 + B)C] - F[(-0.1 + 0.9B + A)/(1 + B)C]

and by collecting terms, the following derivation is proved.

Derivation 1: For capsules, the probability of passing a MUSPWVT is

pl8(p2 + 20PQ + 190Q2) + P54Q3(1140P3 + 50,445P2Q +

1,098,504PQ2 + 15,701,220Q3)

173



174 C. ROBERTS

where

P = F[(O.1 + 1.1B + A)/(l + B)C] - FL(-O.l + O.9B + A)/(1 + B)C]

Q = F[(0.25 + 1.25B + A)/(l + B)CI - F[(-0.25 + 0.75B + A)/(l + B)C] - P

and F is the standard normal cumulative distribution.

Tablets and Sterile Solids

Similar to the capsule case, we have

Derivation 2: For tablets, the probability of passing a MUSPWVT is

pI8(p2 + 2OPQ + 190Q2)

where

(i) tablets less than 130 mg. (light tablets)

P = F[(O.1 + 1.1B + A)/(1 + B)C] - FV(-0.l + 0.9B + A)/(l + B)C]

Q = F[(0.2 + 1.2B + A)/(l + B)C] - F[(-0.2 + 0.8 + A)/(1 + B)C] - P

(it) tablets between 130 and 3!24 mg. (medium tablets)

P = F[(0.075 + 1.075B + A)/(l + B)C]

- F[(-0.075 + 0.925B + A)/(l + B)CJ

Q = F[(0.15 + 1.15B + A)/(l + B)C]

- F[(-0.15 + 0.85B + A)/(l + B)C] - P

(iii) tablets greater than &924 mg. (heavy tablets)

P = FII(O.05 + 1.05B + A)/(l + B)C] - F[(-0.05 + 0.95B + A)/(l + B)C]

Q = FII(0.1 + 1L1B + A)/(l + B)C] - F[(-0.l + 0.9B + A)/(1 + B)C] - P.

Derivation 3: For sterile solids, the probability of passing a MUSPWVT is

p18(p2 + 2OPQ + 190Q2)

+ p,54Q3(l1140P3 + 50,445p2Q + 1,098,504PQ2 + 15,701,220Q3)

+ P54 Q3T(45,600p2 + 1,972,200PQ + 41,967,960Q2)

where

P = F[(0.1 + 1.1B + A)/(l + B)C1] - FL(-0.l + 0.9B + A)/(1 + B)G]

Q = F[(0.15 + 1.15B + A)/(1 + B)C]

- F[(-0.15 + 0.85B + A)/(l + B)C] - P

T= 1- P -Q.




Derivation 4: It is possible to always choose B = 0 by selection of A = B(1 - A)/(1 + B), while keeping C fixed.

Proof: Follows easily by application of Derivations 1 through 3.

Tare Weight and Variation

Let M, , S, , Mf, S, be the means and standard deviations of the tare and the fill, respectively.

Derivation 5: The coefficients of variation of the fill and the filled product, Cf and C, respectively, satisfy

Cf = C(1 - b)/(1 - a), where a = M,/M and b = S2/S2.

Proof: Since S2 = S, + S and M = Mf + M,, then

C = (Sf + S2)/(M, + M,)

= S,(1 + S2/S)J/M,(1 + M,/M,) = C(1 + S2/S2)J/(1 + M,t/M).

Because Cf = Sf/M,, (1 - b)- = 1 + S2/S, and (1 - a)-' = 1 + Mt/M,, the proof is complete.

A Specification Derivation 6: The statements (i) No more than 0.5% of the weights are outside 10% of the average

and

(ii) The coefficient of variation is less than 3.56% are equivalent.

Proof: It is necessary to have

Prob (X > 1.1M) + Prob (X < 0.9M) < 0.005

which is equivalent to

1 - F(O.1M/S) + F(-0.1M/S) ? 0.;005 or

F(-O.1M/S) < 0.0025.

Therefore, M/S > 28.08 which is equivalent to the coefficient of variation less than 0.0356.

REFERENCES

[1] OLSEN, T. N. T. and LEE, I., 1966. Application of statistical methodology in quality control functions of the pharmaceutical industry, a survey, J. Pharm. Sci., 55, No. 1, 1-14.

[2] FRENCH, W. N., MATSUI, F., COOK, DENYS, and LEVI, LEO, 1967. Pharmacopeial stand- ards and specifications for bulk drugs and solid oral dosage forms, similarities and differences, J. Pharm. Sci., 56, No. 12, 1622-1641.

[3] The United States Pharmacopeia 1965. 17th Revision, pages 926-927.

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fill weight variation release and control of capsules, tablets, and sterile solids

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