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*Using the Bergum Method and the MS Excel software program, the author determines the probability of passing the USP dissolution test.*

James S. Bergum introduced a method for computing the probability that a sample taken from a production lot will pass *United States Pharmacopeia (USP)* multiple-stage tests such as the content uniformity and dissolution tests. In this article, the author discusses the probability of passing the *USP* dissolution test according to Sampling Plan 1 in Bergum's paper and its computation using Microsoft Excel (1, 2). A previous article discussed the use of Microsoft Excel to determine the probability of passing the *USP* content uniformity test (3).

**Dissolution test**

As described in the *USP*, the short procedure to determine the dissolution test result is as follows (4, 5):

- Acceptance criteria for stage 1. Test six units (result is the percent of active ingredient released at a specified dissolution time point). Pass if the following criterion is met: each unit is not less than
*Q*+ 5%; in which*Q*is the quantity of dissolved active ingredient specified in the original monograph, expressed as a percentage of the labeled content.

- Acceptance criteria for stage 2. Test six additional units. The mean of 12 units must not be less than
*Q*%, and no unit may be less than*Q*– 15%.

- Acceptance criteria for stage 3. Test 12 additional units. The mean of 24 units must not be less than
*Q*%; no more than two units may be less than*Q*– 15%; and no unit may be less than*Q*– 25%.

Formula for MS Excel calculation for dissolution.

**Probability bound.** From Bergum's Validation Report, Appendix E, the probability (*P*) of passing the *USP* dissolution test is expressed in the equations at left (6).

v

A complete MS Excel formula for the dissolution test is derived in the sidebar, "Formula for MS Excel calculation for dissolution."

**Evaluation of sample data**

The two population parameters, the mean and sigma (the population standard deviation), are estimated as discussed in the previous article, using a simultaneous confidence interval in MS Excel as follows:

When the *Q* value, SD, UB, and lower confidence limit for mean were substituted into the formula (see sidebar, "Formula for MS Excel calculation for dissolution), the probability result will be obtainable.

Table I. Comparison of the probability, calculated using Bergum's CuDAL Software (6) and Excel, of passing stage 1 of the USP dissolution test (n = 56).*

Tables I and II provide a comparison of the results obtained using Bergum's CuDAL Software and Excel methods, for stages 1 and 3, respectively. The two tables demonstrate that the probability by Excel also will guarantee that, when using the same CV values as Bergum software,~95% of future samples will meet the specifications outlined in the *USP* test. All the CV values computed by Bergum software to guarantee at least 95% off future samples meet *USP* tests.

Table II. Comparison of the probability, calculated using BergumÃÂ´s CuDAL Software (6) and Excel, of passing stage 3 of the USP dissolution test (n = 24).*

**Conclusion**

Bergum's method is very helpful for constructing acceptance limits and determining the probability of passing multiple-stage USP tests such as the dissolution test. For computing the probability of passing the dissolution test (or, described in a previous article, the content uniformity test), the MS Excel formula derived in this article can be used to obtain the same results as those generated by Bergum's validated SAS program. However, it is recommended that the MS Excel results be verified in comparison with the SAS results before using the results in official documentation. The equation can be downloaded from www.pharmtech.com

** Appendix **

www.pharmtech.com/pharmtech/data/articlestandard/pharmtech/082006/308833/article.xls

**Acknowledgement**

The author is very grateful to the reviewer of this paper for his very helpful comments.

**Pramote Cholayudth** is the managing director of the Professional Conference Center Ltd., 6/756 Number One Complex, Bangkok-Ram 2 Road, Pravate District, Bangkok, 10250, Thailand, fax 1662 740 9586, cpramote2000@yahoo.com

**References**

1. J. S. Bergum, "Constructing Acceptance Limits for Multiple Stage Tests," *Drug Dev. Ind. Pharm.***16** (14), 2153–2166 (1990).

2. J. S. Bergum and M.L. Utter, "Statistical Methods for Uniformity and Dissolution Testing," in *Pharmaceutical Process Validation: An International Third Edition, Revised and Expanded,* R.A. Nash and A.H. Wachter (Marcel Dekker, Inc, New York, 2003), pp. 667–697.

3. P. Cholayudth, "Use of the Bergum Method and MS Excel to Determine the Probability of Passing the USP Content Uniformity Test," *Pharm. Technol.*** 28** (9), 86–98 (2004).

4. "Chapter ‹711› Dissolution," in *United States Pharmacopeia *24–*National Formulary* 19 (US Pharmacopeial Convention, Rockville, MD, 1999).

5. S.C. Chow and J.P. Liu, "USP Tests and Specifications: Dissolution Testing," in *Statistical Design and Analysis in Pharmaceutical Science: Validation, Process Controls, Practical and Clinical Applications,* (Marcel Dekker, Inc, New York, NY, 3d ed., 1995), pp. 165–167.

6. J.S. Bergum's SAS Programs, "Appendix E: Lower Bound Calculations," Content Uniformity and Dissolution Acceptance Limits (CuDAL), version: 1.0, dated July 26, 2003.