An anticipatory approach to optimal experimental design for model discrimination

The problem of model discrimination arises when several models are proposed to describe one and the same process. To identify the best model from the set of rival models, it may be necessary to collect new information about the process, and thus additional experiments have to be performed. This paper deals with the experimental design methodologies that are used to find the experimental conditions that allow to discriminate among rival models with the least experimental effort. For this, the expected experimental results should be predicted differently by the rival models, and the uncertainty on the measurements and on the model predictions should not be too large. These aspects were included in the approach developed by Buzzi-Ferraris and co-workers [G. Buzzi-Ferraris, P. Forzatti, G. Emig, H. Hofmann, Sequential experimental design procedure for model discrimination in the case of multiple responses. Chemical Engineering Science (1) (1984) 81–85], but in their approach the uncertainties are estimated from the information content of the already performed experiments. This work presents a modification of the Buzzi-Ferraris approach in which the expected information content of the newly designed experiment is considered, even before the experiment is performed (anticipatory design). In this way, a better estimate of the uncertainties is achieved, and an experiment with an increased discriminatory potential is obtained. The approaches were illustrated and compared by applying them to a case study in which two rival models are proposed to describe the in vitro kinetics of an enzyme.     

Separation in D‐optimal experimental designs for the logistic regression model

The D‐optimality criterion is often used in computer‐generated experimental designs when the response of interest is binary, such as when the attribute of interest can be categorized as pass or fail. The majority of methods in the generation of D‐optimal designs focus on logistic regression as the base model for relating a set of experimental factors with the binary response. Despite the advances in computational algorithms for calculating D‐optimal designs for the logistic regression model, very few have acknowledged the problem of separation, a phenomenon where the responses are perfectly separable by a hyperplane in the design space. Separation causes one or more parameters of the logistic regression model to be inestimable via maximum likelihood estimation. The objective of this paper is to investigate the tendency of computer‐generated, nonsequential D‐optimal designs to yield separation in small‐sample experimental data. Sets of local D‐optimal and Bayesian D‐optimal designs with different run (sample) sizes are generated for several “ground truth” logistic regression models. A Monte Carlo simulation methodology is then used to estimate the probability of separation for each design. Results of the simulation study confirm that separation occurs frequently in small‐sample data and that separation is more likely to occur when the ground truth model has interaction and quadratic terms. Finally, the paper illustrates that different designs with identical run sizes created from the same model can have significantly different chances of encountering separation.     

Application of mixture experimental design to simvastatin apparent solubility predictions in the microemulsifion formed by self-microemulsifying

Self-microemulsifying drug delivery systems (SMEDDS) are useful to improve the bioavailability of poorly water-soluble drugs by increasing their apparent solubility through solubilization. However, very few studies, to date, have systematically examined the level of drug apparent solubility in o/w microemulsion formed by self-microemulsifying. In this study, a mixture experimental design was used to simulate the influence of the compositions on simvastatin apparent solubility quantitatively through an empirical model. The reduced cubic polynomial equation successfully modeled the evolution of simvastatin apparent solubility. The results were presented using an analysis of response surface showing a scale of possible simvastatin apparent solubility between 0.0024 ∼ 29.0 mg/mL. Moreover, this technique showed that simvastatin apparent solubility was mainly influenced by microemulsion concentration and, suggested that the drug would precipitate in the gastrointestinal tract due to dilution by gastrointestinal fluids. Furthermore, the model would help us design the formulation to maximize the drug apparent solubility and avoid precipitation of the drug.     

Simulated experimental design used to define the characteristic curves of car shock‐absorbers

This paper introduces a special ‘quality’ parameter on automotive perspective, i.e. the quality index in order to measure the customer satisfaction with car manoeuvrability. In particular, it describes how the characteristic setting curves of a car shock‐absorber can be optimized using subjective customer assessment of three categories of perception: handling, steering quality and ride‐comfort. These, called manoeuvrability indices, were used to represent the assessment of customer satisfaction with car manoeuvrability. The characteristic curves for each shock‐absorber setting were defined using parameters which uniquely determined their shape. Subsequent analysis was carried out using simulated experimental design which adopts a numeric model of vehicle simulation thereby enabling experimental costs to be reduced. This analysis made it possible to ascertain which setting parameter values provided the best compromise among the three categories of required performance. A codified method of optimization was then developed. This method, which includes the three categories of perception, will be extended to all new projects. Copyright © 2001 John Wiley & Sons, Ltd.     

Computational design strategy: an approach to enhancing the transdermal delivery of optimal capsaicin-loaded transinvasomes

Abstract

The aim of this study was to design and develop simultaneous optimal transinvasome formulations (OTV) to enhance the transdermal delivery of capsaicin. Using a central composite experimental design with duplicate centroids, 10 model formulations of transinvasomes (TVs) were demonstrated. The lipid compositions of the TV formulations were determined as formulation factors (X_n) and response variables (Y_n), respectively. TV formulations containing a constant concentration of phosphatidylcholine, cholesterol, 0.15% capsaicin, and various percentages of d-limonene (X₁) and cocamide diethanolamine (X₂) were prepared. The physicochemical characteristics, e.g. the vesicle size, size distribution, zeta potential, entrapment efficiency, and skin permeability, of the TV formulations were experimentally investigated. The relationship among the formulation factor, the response variables, and the OTV was predicted using Design Expert^® software. The accuracy and reliability of the OTV predicted using computer software were experimentally confirmed and investigated as an experimental transinvasome formulation (ETV). The results indicated that the skin permeability of the ETV was close to the OTV and was significantly higher than that of conventional liposomes and commercial products. The response surfaces estimated by the computer software were helpful in understanding the complicated relationship among the formulation factor, the response variables, and the stability of the TV formulation.     

Integrating biopharmaceutics risk assessment and in vivo absorption model in formulation development of BCS class I drug using the QbD approach

Objective: Clinically relevant critical quality attributes (CQA’s) were identified for the development of generic drug products containing fluconazole and potential design spaces relevant to the clinical application of the drug candidate was explored.

Significance: A simplified scoring system for the biopharmaceutics risk assessment roadmap (BioRAM) is proposed to guide product development.

Methods: Factorial design of experiments was employed to study the effect of formulation and process variables on CQA’s. The in vivo model was developed for predicting the fraction of drug absorbed and to identify the effect of formulation components on drug absorption.

Results: BioRAM yielded low scores for fluconazole absorption with respect to severity (risks of sub and supra-bioavailable drug products), probability of incidence of bioinequivalent results and capacity of detection. The results demonstrated that dissolution was highly influenced by the active pharmaceutical ingredient (API) polymorphism and the ratio of diluents. Process variables (mixing time, lubricant concentration, lubrication time and filling speed) did not impact the clinical outcome of the formulation with respect to dissolution and content uniformity.

Conclusions: Understanding the clinical implications of the adopted formulation approach led to the construction of purposeful design space and control strategy.     

Box–Behnken experimental design for preparation and optimization of the intranasal gels of selegiline hydrochloride

Selegiline hydrochloride (SL) is chosen as an adjunct for the control of clinical signs of Parkinsonian patients. The aim of the present work is to develop and optimize thermosensitive gels using Pluronic (F-127) for enhancing transport of SL into the brain through the nasal route. SL gels were prepared using a cold method and the Box–Behnken experimental design methodology. Drug (SL), gelling agent (F-127), and emulsifier (Propylene glycol, PG) were selected as independent variables, while the gelation temperature, gel strength, pH, gel content, and gel erosion were considered as dependent variables. For further understanding of the interaction between the various variables, contour plots and surface plots were also applied. Selected formulations, like S10 (contain 25?mg SL, 20?g F-127, and 1?g PG) and S14 (contain 50?mg SL, 18?g F-127 and 1?g PG), had a clear appearance in the sol form, with gelling temperature of the nasal gel ranging between 33 and 34, respectively. The gel strength of the formulations varied from 4.67 and 0.68?mm and the drug content was 100%. The pH of the formulations ranged between 6.71 and 7.11. Detachment force was acceptable (63.69–244.16 N/cm²) to provide prolonged adhesion. In vitro, drug release studies showed that the prepared formulations could release SL for up to 8?h. Permeation flux for the S10 gel was 0.0002?mg/min/cm². Results demonstrated that the potential use of SL gels can enhance the therapeutic effect of SL through the intranasal administration.     

Robust optimisation approach to the design of service networks for reverse logistics

In this paper we discuss a typical service network of a company providing repair and refurbishment services for its products. To optimise the network we propose a mixed-integer linear programming (MILP) model that minimises the total cost subject to flow balance and logical constraints. The solution of the model determines which facilities are to be used in the network and the associated flows. The model is validated against data obtained from a computer manufacturer and real-life sources. The optimal network configuration depends on several factors such as the number of products returned, percent of faulty products and warranty fraction of modules, which are uncertain in nature. We also address the issue of identifying these uncertain parameters, and their levels to be considered. A min-max robust optimisation model is then developed and solved to address these uncertainties.     

An approach to identify the optimal configurations and reconfiguration processes for design of reconfigurable machine tools

A reconfigurable machine tool (RMT) is a special machine that can deliver different machining functions through reconfiguration processes among its configurations during the machine utilisation stage. In this research, a new approach is developed to identify the optimal configurations and the reconfiguration processes for design of the RMTs. In this work, a generic design AND-OR tree is used to model different design solution candidates, their machine configurations and parameters of these configurations. A specific design solution is created from the generic design AND-OR tree through tree-based search and modelled by different machine configurations. For a reconfiguration process between two machine configurations, a generic process AND-OR graph is used to model reconfiguration operation candidates, sequential constraints among operations and operation parameters. A graph-based search is used to generate all feasible reconfiguration process candidates from the generic process AND-OR graph. The optimal design is identified by multi-level and multi-objective hybrid optimisation. A case study is developed to show how this new approach is used for the optimal design of a RMT.     

Simplified model for the fatigue growth analysis of surface cracks in round bars under mode I

The fatigue growth of an edge flaw in a round bar under cyclic tension or bending loading is examined, using a two-parameter numerical model. First, it is shown that the crack front evolution is defined by a very small number of parameters, which varies during crack growth. Approximated solutions for both the crack propagation path and the stress intensity factor are derived, and the fatigue predictions using this simple analytical method are finally compared with the numerical results.     

On the relationship of the cumulative jump model for random fatigue to empirical data

The cumulative jump model, consisting of a random sum of random increments, has previously been proposed, in a general format, to model the fatigue crack growth process. In this paper the cumulative jump process for random fatigue is used to model the constant-load amplitude Virkler fatigue crack growth data. It is shown, through the proper choice of the intensity function of the underlying birth process, that the mean crack growth behavior of the model may be specified to match any desired functional form. This assures reasonable agreement with experiments. For fatigue crack growth the intensity function is characterized by a constant and a random variable (this makes the underlying birth process a so-called doubly stochastic counting process). For the case of the ‘simplified' jump model (constant elementary crack increments), the constant and the random variable characterizing the intensity function may be estimated by matching approximate formulae for the mean and the variance of the model with the data. Simulations of the jump model show trajectories which behave qualitatively like the data and yield distribution functions for the crack length which match well the data.     

A general model for the economic-statistical design of adaptive control charts for processes subject to multiple assignable causes

Fully adaptive control charts are efficient statistical process control means to monitor a quality characteristic affecting the outcome of a manufacturing process. Usually, the performance of these adaptive charts is investigated in processes characterised by the possibility of the occurrence of a single assignable cause. However, this assumption is frequently far from reality, because a process shift to the out-of-control condition can be the consequence of several assignable causes, which can occur at the same time or independently. In this paper, we investigate the economic-statistical design of a variable-parameter (Vp) Shewhart control chart monitoring the process mean in the presence of multiple assignable causes. We develop a Markov chain that models the occurrence of several assignable causes leading to progressive process deterioration and calling for different corrective actions. A benchmark of examples has been generated to compare the performance of the Vp control chart with other adaptive control charts and the fixed-parameter control chart. The obtained results reveal the economic superiority of the Vp control chart.     

A mathematical model and a heuristic approach for design of the hybrid manufacturing systems to facilitate one-piece flow

One-piece flow is a design rule that entails production in manufacturing cells on a ‘make one, check one, and move-on one’ basis (Black, J.T., 2007. Design rules for implementing Toyota Production System. International Journal of Production Research, 45 (16), 3639–3664), which reduces manufacturing lead time significantly. This paper proposes a sequential methodology comprised of a mathematical model and a heuristic approach (HA) for the design of a hybrid cellular manufacturing system (HMS), to facilitate one-piece flow practice. The mathematical model is employed in the cases of small- and medium-sized problems, and it attempts to minimise the total number of exceptional operations, while considering machine capacities and alternative machines. The machine-part matrix achieved by the mathematical model is input into the flow line design stage of the HA, where backflow within the cells is eliminated. However, for industrial problems, the proposed HA is utilised. After the formation of the cells by clustering, the HA attempts to eliminate exceptional operations of a given cellular configuration together with a functional structure by employing alternative machines, based on the decision rules developed. Later, unidirectional flow within the cells is achieved and the capacity and budget constraints are satisfied. A medium-sized problem is solved by using both of the approaches, namely, the model integrated with the flow-line design stage of the HA and the complete HA. The results are discussed and the limitations are explained.     

How to search the experimental conditions that improve a Partial Least Squares calibration model: Application to a flow system with electrochemical detection for the determination of sulfonamides in milk

This paper deals with the selection of experimental conditions and how the signals obtained in these conditions influence the fitted Partial Least Squares calibration model. The multivariate signals come from a flow analysis system with amperometric detection when determining sulfadiazine, sulfamerazine and sulfamethazine in milk.The solution (carrier plus analyte) was pumped through the system to provide a continuous supply of analyte to the cell. The detector was programmed for a scan mode operation being the multivariate signal the hydrodynamic voltammogram. To obtain an analytical signal of enough analytical quality, the Net Analyte Signal and its standard deviation have been optimised by using an experimental design. The conflicting behaviour of the two responses has been solved by estimating the Pareto-optimal front.The multivariate signals recorded in the optimal conditions found have been calibrated by Partial Least Squares regression and their figures of merit validated according to the criteria established in European Decision 2002/657/EC.In relation to the permitted limit, 100 µg l^− 1 in milk, for the total content of sulfonamides established in the Commission Regulation EC no. 281/96 the proposed method has a decision limit of 109.1 µg l^− 1 and the capability of detection is 117.9 µg l^− 1 for both probability of false non-compliance and of false compliance equal to 5%. A recovery of 86.5% ± 2.4% (n = 5) has been obtained.