Factorial design ,full factorial design, fractional factorial design

factorial design,introduction, types, applications,full factorial design, fractional factorial design

1. Contents INTRODUCTION TYPES OF FACTORIAL DESIGN (FD) APPLICATION SUMMARY

2. INTRODUCTION Factorial experiment is an experiment whose design consist of two or more factor each with different possible values or “levels”. FD technique introduced by “Fisher” in 1926. Factorial design applied in optimization techniques. Effect of disintegrant & lubricant conc . on tablet dissolution . It is based on theory of probability and test of significance

3. It identifies the chance variation ( present in the process due to accident) and the assignable variations ( which are due to specific cause.) Factorial design are helpful to deduce IVIVC. IVIVC are helpful to serve a surrogate measure of rate and extent of oral absorption. BCS classification is based on solubility and permeability issue of drugs, which are predictive of IVIVC. Sound IVIVC omits the need of bioequivalence study. IVIVC is predicted at three levels: Level A- point to point relationship of in vitro dissolution and in vivo performance. Level B- mean in vitro and mean in vivo dissolution is compared and co related. Level C- correlation between amount of drug dissolved at one time and one pharmacokinetic parameter is deduced.

4. BCS classification and its expected outcome on IVIVC for Immediate release formulation BCS Class Solubility Permeability IVIVC I High High Correlation( if dissolution is rate limiting II Low High IVIVC is expected III High Low Little or no IVIVC IV Low Low Little or no IVIVC

5. TYPES OF FACTORIAL DESIGN (FD) Full F actorial Design(FD) Two Levels Full FD Three level Full FD 2. Fractional Factorial Design Homogenous fractional Mixed level fractional Box-Hunter Plackett - Burman Taguchi Latin square

6. Full Factorial Design A design in which every setting of every factor appears with setting of every other factor is full factorial design If there is k factor , each at Z level , a Full FD has z k (Levels) factor  z k

7. Factorial Design : 2 2 2 3 3 2 3 3 2 2 FD = 2 Factors , 2 Levels = 4 runs 2 3 FD = 3 Factors , 2 Levels = 8 runs 3 2 FD = 2 Factors , 3 Levels = 9 runs 3 3 FD = 3 factors , 3 Levels = 27 runs TWO Levels Full FD : 2 factors : X1 and X2 (Independent variables) 2 levels : Low and High + - Coding : (-1) LOW , (+1) HIGH + - - ++ +- -+ --

8. Three level Full FD : In three level factorial design , three levels are use , 1) low (-1) 2) intermediate (0) 3) high (+1) It is written as 3 k factorial design. It means that k factors are considered each at 3 levels . These are usually referred to as low, intermediate & high values . These values are usually expressed as 0, 1 & 2 The third level for a continuous factor facilitates investigation of a quadratic relationship between the response and each of the factors

9. Factorial design These are the designs of choice for simultaneous determination of the effects of several factors & their interactions. Used in experiments where the effects of different factors or conditions on experimental results are to be elucidated . FRACTIONAL FACTORIAL DESIGNS It is used to examine multiple factors efficiently with fewer runs than corresponding full factorial design Type of fractional factorial designs Homogenous fractional Mixed level Box-Hunter Plackett - Burman Taguchi Latin squares

10. Homogenous fractional Useful when large number of factors must be screened Mixed level fractional Useful when variety of factors needed to be evaluated for main effects and higher level interactions can be assumed to be negligible. Ex-objective is to generate a design for one variable, A, at 2 levels and another, X, at three levels , mixed &evaluated. Box-hunter Fractional designs with factors of more than two levels can be specified as homogenous fractional or mixed level fractional

11. Plackett-Burman It is a popular class of screening design. These designs are very efficient screening designs when only the main effects are of interest. These are useful for detecting large main effects economically ,assuming all interactions are negligible when compared with important main effects Used to investigate n-1 variables in n experiments proposing experimental designs for more than seven factors.

12. Taguchi It is similar to PBDs. It allows estimation of main effects while minimizing variance. Taguchi Method treats optimization problems in two categories, STATIC PROBLEMS :Generally, a process to be optimized has several control factors which directly decide the target or desired value of the output. DYNAMIC PROBLEMS :If the product to be optimized has a signal input that directly decides the output

13. APPLICATIONS: Formulation and processing Clinical Chemistry Medicinal chemistry HPLC Analysis Formulation of culture medium in virological studies Study of pharmacokinetic parameters