Søren Bisgaard’s contributions to Quality Engineering: Design of experiments

Abstract

This article examines Søren’s impact on the design and analysis of experiment through three of his published articles in ASQ journals. These articles demonstrate Søren’s unique blend of engineer and statistician with the ability to see the big picture both of the solution to the specific problem and of the solution strategy for good practice. Søren was a giant in our field who was struck down too early in life by mesothelioma at the age of 58 years. His work, and more importantly his impact on his colleagues, has continued to influence the profession.     

A statistical engineering strategy for mixture problems with process variables

Experimenting with both mixture components and process variables, especially when there is likely to be interaction between these two sets of variables, is discussed. We consider both design and analysis questions within the context of addressing an actual mixture/process problem. We focus on a strategy for attacking such problems, as opposed to finding the best possible design or best possible model for a given set of data. In this sense, a statistical engineering framework is used. In particular, when we consider the potential of fitting parsimonious linear additive or nonlinear models as opposed to larger linearized models, we find potential to reduce the size of experimental designs. It is difficult in practice to know what type of model will best fit the resulting data. Therefore, an integrated, sequential design and analysis strategy is recommended. Using two published data sets and one new data set, we find that in some cases nonlinear models, or linear additive models —with no process/mixture interaction terms, enable reduction of experimentation on the order of 50%. In other cases, additive or nonlinear models will not suffice. We therefore provide guidelines as to when such an approach is likely to succeed, and propose an overall strategy for these types of problems.     

Near Minimal Resolution IV Designs for the sn Factorial Experiment

A fractional factorial design is of resolution IV if all main effects are estimable in the presence of two-factor interactions. For the sⁿ factorial experiment such a design requires at least N = s[(s – I)n – (s – 2)] runs. In this paper a series of resolution IV designs are given for the s” factorial, s = p ^α where p is prime, in N = s(s – I)n runs. A special case of the construction method produces a series of generalized foldover designs for the sⁿ experiment, s ≥ 3 and n ≥ 3, in N = s(s – I)n + s runs. These foldover designs permit estimation of the general mean in addition to all main effects and provide s degrees of freedom for estimating error. A section on analysis is included.     

Space-Filling Designs for Robustness Experiments

To identify the robust settings of the control factors, it is very important to understand how they interact with the noise factors. In this article, we propose space-filling designs for computer experiments that are more capable of accurately estimating the control-by-noise interactions. Moreover, the existing space-filling designs focus on uniformly distributing the points in the design space, which are not suitable for noise factors because they usually follow nonuniform distributions such as normal distribution. This would suggest placing more points in the regions with high probability mass. However, noise factors also tend to have a smooth relationship with the response and therefore, placing more points toward the tails of the distribution is also useful for accurately estimating the relationship. These two opposing effects make the experimental design methodology a challenging problem. We propose optimal and computationally efficient solutions to this problem and demonstrate their advantages using simulated examples and a real industry example involving a manufacturing packing line. Supplementary materials for the article are available online.     

Screening Designs for Poly-Factor Experimentation

A survey is given of the following types of screening designs: Incomplete 2 ^k designs, srlpersaturated and grollp-screening designs. These designs are compared with each other. Some new results for group-screening are derived.     

Using Experimental Design to Optimize the Process Parameters in Fluidized Bed Granulation

In this study many parameters were screened for a small-scale granulation process for their effect on the yield of granules between 75 and 500 μm and the geometrical granule mean size (d50). First a Plackett-Burman design was applied to screen the inlet air temperature, the inlet flow rate, the spray rate, the nozzle air pressure, the nozzle spray diameter, and the nozzle position. The Plackett-Burman design showed that the key process parameters were the inlet flow rate and the spray rate and probably also the inlet air temperature. Afterward a fractional factorial design (2^5?2) was applied to screen the remaining parameters plus the nozzle aircap position and the spraying time interval. The fractional factorial design showed that the nozzle air pressure was also important. As the target values for the granule yield (between 75 and 500 μm) and the geometric mean granule size (between 300 and 500 μm) were reached during the screening experiments, further optimization was not considered necessary.     

Using experimental design to optimize the process parameters in fluidized bed granulation

In this study many parameters were screened for a small-scale granulation process for their effect on the yield of granules between 75 and 500 μm and the geometrical granule mean size (d50). First a Plackett-Burman design was applied to screen the inlet air temperature, the inlet flow rate, the spray rate, the nozzle air pressure, the nozzle spray diameter, and the nozzle position. The Plackett-Burman design showed that the key process parameters were the inlet flow rate and the spray rate and probably also the inlet air temperature. Afterward a fractional factorial design (2^5-2) was applied to screen the remaining parameters plus the nozzle aircap position and the spraying time interval. The fractional factorial design showed that the nozzle air pressure was also important. As the target values for the granule yield (between 75 and 500 μm) and the geometric mean granule size (between 300 and 500 μm) were reached during the screening experiments, further optimization was not considered necessary.     

Use of Strip-Strip-Block Design for Multi-Stage Processes to Reduce Costs of Experimentation

A strip-strip-block design is proposed for use in investigating the effects of factors, and their interactions, in three-stage industrial processes. Consideration is given, more generally, to the question of how to generate such designs, what theoretical properties they should have, and how to analyze the results of such designs. A case study is used as an illustration.     

Elementary Statistics

Fractional two-level factorial designs are often used in the early stages of an investigation to screen for important factors. Traditionally, 2 ^n-k fractional factorial designs of resolution III, IV, or V have been used for this purpose. When the investigator is able to specify the set of nonnegligible factorial effects, it is sometimes possible to obtain an orthogonal design with fewer runs than a standard textbook design by searching within a wider class of designs called parallel-flats designs. The run sizes in this class of designs do not necessarily need to be powers of 2. We discuss an algorithm for constructing orthogonal parallel-flats designs to meet user specifications. Several examples illustrate the use of the algorithm.     

Quality risk management in pharmaceutical development

The objective of ICH Q8, Q9 and Q10 documents is application of systemic and science based approach to formulation development for building quality into product. There is always some uncertainty in new product development. Good risk management practice is essential for success of new product development in decreasing this uncertainty. In quality by design paradigm, the product performance properties relevant to the patient are predefined in target product profile (TPP). Together with prior knowledge and experience, TPP helps in identification of critical quality attributes (CQA’s). Initial risk assessment which identifies risks to these CQA’s provides impetus for product development. Product and process are designed to gain knowledge about these risks, devise strategies to eliminate or mitigate these risks and meet objectives set in TPP. By laying more emphasis on high risk events the protection level of patient is increased. The process being scientifically driven improves the transparency and reliability of the manufacturer. The focus on risk to the patient together with flexible development approach saves invaluable resources, increases confidence on quality and reduces compliance risk. The knowledge acquired in analysing risks to CQA’s permits construction of meaningful design space. Within the boundaries of the design space, variation in critical material characteristics and process parameters must be managed in order to yield a product having the desired characteristics. Specifications based on product and process understanding are established such that product will meet the specifications if tested. In this way, the product is amenable to real time release, since specifications only confirm quality but they do not serve as a means of effective process control.     

Implementation of quality by design approach in manufacturing process optimization of dry granulated,immediate release,coated tablets – a case study

The aim of this study was to optimize the process of tablets compression and identification of film-coating critical process parameters (CPPs) affecting critical quality attributes (CQAs) using quality by design (QbD) approach. Design of experiment (DOE) and regression methods were employed to investigate hardness, disintegration time, and thickness of uncoated tablets depending on slugging and tableting compression force (CPPs). Plackett–Burman experimental design was applied to identify critical coating process parameters among selected ones that is: drying and preheating time, atomization air pressure, spray rate, air volume, inlet air temperature, and drum pressure that may influence the hardness and disintegration time of coated tablets. As a result of the research, design space was established to facilitate an in-depth understanding of existing relationship between CPPs and CQAs of intermediate product (uncoated tablets). Screening revealed that spray rate and inlet air temperature are two most important factors that affect the hardness of coated tablets. Simultaneously, none of the tested coating factors have influence on disintegration time. The observation was confirmed by conducting film coating of pilot size batches.