Journal of Pharmaceutical and Biomedical Analysis 20 (1999) 875–887 Nested designs in ruggedness testing Y. Vander Heyden a , K. De Braekeleer a , Y. Zhu b , E. Roets b , J. Hoogmartens b , J. De Beer c , D.L. Massart a, * a ChemoAC, Pharmaceutical Institute, Vrije Uni6ersiteit Brussel, Laarbeeklaan 103, 1090 Brussels, Belgium b Laboratory for Pharmaceutical Chemistry and Drug Analysis, Katholieke Uni6ersiteit Leu6en, Van E6enstraat 4, 3000 Leu6en, Belgium c Wetenschappelijk Instituut Volksgezondheid —Louis Pasteur, Juliette Wytmanstraat 14, 1050 Brussels, Belgium Received 8 August 1998; received in revised form 8 December 1998; accepted 1 January 1999 Abstract Nested designs were performed in order to execute a ruggedness test according to the United States Pharmacopeia definition for ruggedness, in which mainly non-procedure related factors are examined. Several nested designs have been executed on a high performance liquid chromatography assay to determine tetracycline and related substances in bulk samples of tetracycline. Factors such as different laboratories, analysts, instruments, columns, days and batches were examined. The interpretation methods described in the literature were found to cause problems. In these methods the variances of the examined factors are estimated from the calculated mean square values and from the equation for the expected mean squares. Very frequently, negative variance estimates were obtained. Their absolute values were found to be dependent on the influence of the factor examined below it in the design, on the examined response. Therefore an alternative interpretation method for nested designs, based on pooled variances, was proposed and found to be appropriate to use for ruggedness testing purposes. Both approaches, the one from the literature and the one proposed here, were tested on simulated data coming from a nested design with four factors and on the experimentally measured data. © 1999 Elsevier Science B.V. All rights reserved. Keywords: Nested designs; Ruggedness test www.elsevier.com/locate/jpba 1. Introduction In the United States Pharmacopeia (USP) [1,2] ruggedness is defined as ‘‘The degree of reproduci- bility of test results obtained by the analysis of the same sample under a variety of normal test condi- tions, such as different laboratories, different ana- lysts, different instruments, different lots of reagents, different elapsed assay times, different assay temperatures, different days, etc.’’ This defi- nition is different from that originally introduced by Youden and Steiner [3] under the term rugged- ness, which in analytical chemistry is mainly called robustness and in which one evaluates the influence of small changes in the operating condi- tions. The use of two-level screening designs such * Corresponding author. Tel.: +32-2-477-4737; fax: +32- 2-477-4735. E-mail address: fabi@vub.vub.ac.be (D.L. Massart) 0731-7085/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII:S0731-7085(99)00112-0