RETRACTED ARTICLE: Development of censored data-based robust design for pharmaceutical quality by design
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ORIGINAL ARTICLE
Development of censored data-based robust design for pharmaceutical quality by design Byung Rae Cho & Yongsun Choi & Sangmun Shin
Received: 19 April 2009 / Accepted: 19 November 2009 / Published online: 9 December 2009 # Springer-Verlag London Limited 2009
Abstract Robust design techniques, which are based on the concept of building quality into products or processes, are increasingly popular in many manufacturing industries. In this paper, we propose a new robust design model in the context of pharmaceutical production research and development. Traditional robust design principles have often been applied to situations in which the quality characteristics of interest are typically time insensitive. In pharmaceutical manufacturing processes, time-oriented quality characteristics, such as the degradation of a drug, are often of interest. As a result, current robust design models for quality improvement which have been studied in the literature may not be effective in finding robust design solutions. To address such practical needs, this paper develops a robust design model using censored data, which is perhaps the first attempt in the robust design field. We then study estimation methods, such as the expectation–maximization algorithm and the maximum likelihood method, in the robust design context. Finally, comparative studies are discussed for model verification via a numerical example. B. R. Cho (*) Department of Industrial Engineering, Clemson University, Clemson, SC 29634, USA e-mail: [email protected] Y. Choi : S. Shin Department of Systems Management & Engineering, Inje University, Gimhae, Gyeong Nam 621-749, South Korea Y. Choi e-mail: [email protected] S. Shin e-mail: [email protected]
Keywords Robust design . Mixture experiments . Pharmaceutical formulations . Censored data . Expectation– maximization algorithm . Maximum likelihood estimation
1 Introduction Continuous quality improvement has become widely recognized by many industries as a critical concept in maintaining a competitive advantage in the marketplace. It is also recognized that quality improvement activities are efficient and cost-effective when implemented during the design stage. Based on this awareness, Taguchi [1] introduced a systematic method for applying experimental design, which has become known as robust design. The primary goal of this method is to determine the best design factor settings by minimizing performance variability and product bias, i.e., the deviation from the target value of a product. Because of the practicability in reducing the inherent uncertainty associated with system performance, the widespread application of robust design techniques has resulted in significant improvements in product quality, manufacturability, and reliability at low cost. Although the main robust design principles have been implemented in a number of different industrial settings, our literature study indicates that robust design has been rarely addressed in the pharmaceutical design process. In the pharmaceutical industry, the
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