Optimization in QBD

Optimization Techniques in Pharmaceutical Sciences.

1. OPTIMIZATION TECHNIQUES Suraj C. AACP

2. 2 PPT. Package Concept Of Optimization Optimization Parameters Classical Optimization Statistical Design Simulation & Search

3. 3 INTRODUCTION OPTIMIZATION

4. 4 INTRODUCTION

5. 5 In development projects , one generally experiments by : a series of logical steps, carefully controlling the variables & changing one at a time, until a satisfactory system is obtained It is not a screening technique. IDEA !

6. 6 OPTIMIZATION TECHNIQUES Parametric Non-Parametric Factorial Central Composite Mixture Lagrangian Multiple Regression Fractional Factorial Plackett-Burman Evolutionary methods EVOP REVOP

7. CLASSICAL OPTIMIZATION 7 Involves application of calculus to basic problem for maximum/minimum function. One factor at a time (OFAT). Restrict attention to one factor at a time. Not more than 2 variables.

8. CLASSICAL OPTIMIZATION 8 Using calculus the graph obtained can be solved. Y = f (x) When the relation for the response y is given as the function of two independent variables,X1 & X2 Y = f(X1 , X2) The above function is represented by contour plots on which the axes represents the independent variables X1& X2 Contd …..

9. CLASSICAL OPTIMIZATION 9 Response Variable Independent Variable Contd …..

10. CLASSICAL OPTIMIZATION 10 Independent Variable - X2 Independent Variable - X1 Contd …..

11. OFAT vs DOE 11 Properties OFAT DOE Type Classical- Sequenctial one factor method Scientific – simultaneous with multiple factor method No. of experiments High – Decided by experimenter Limited – Selected by design Conclusion Inconclusive – Interaction unknown Comprehensive – Interactions studied too. Precision & Efficiency Poor – sometimes misleading result with errors (4 exp.) High – Errors are shared evenly (2 exp.) Consequences One exp. Wrong… all goes wrong -Inconclusive Orthogoanl design – Predictable & conclusive Information gained Less per experiment High per experiment

12. STATISTICAL DESIGN 12 Techniques used divided in to two types: Experimentation continues as optimization proceeds Experimentation is completed before optimization takes place.

13. STATISTICAL DESIGN 13 Experimentation is completed before optimization takes place. Theoretical approach Empirical or experimental approach Contd …..

14. STATISTICAL TERMS 14 R elationship with single independent variable - Simple regression analysis or Least squares method . Relationship with more than one important variable - Statistical design of experiment & Multi linear regression analysis . Most widely used experimental plan is Factorial design.

15. STATISTICAL DESIGN 15 Optimization : helpful in shortening the experimenting time. DOE : is a structured , organized method used to determine the relationship between – the factors affecting a process & the output of that process. Statistical DOE : planning process + appropriate data collected + analysed statistically. Contd …..

16. MATHEMATICAL MODELS 16 Permits the interpretation of RESPONSES more economically & becomes less ambiguous . First Order : 2 Levels of the factor – Linear relationship LCL (Lower control limit) - {- ve or -1} UCL (Upper control limit) - {+ ve or +1} 2. Second Order : 3 Levels (Mid-level) – coded as “0” – Curvature effect

17. FIRST ORDER 17 X 1 Response LOW HIGH Predictable Response at X 1

18. SECOND ORDER 18 X 1 Response LOW HIGH True Response

19. SIMULATION & SEARCH METHODS 19 Search method does not requires CONTINUITY or DIFFERENTIALITY function. Search methods also known as - “Sequential optimization”. NOTE: Simulation involves the computability of a response.

20. SIMULATION & SEARCH METHODS 20 A simple inspection of experimental results is sufficient to choose the desired product. If the independent variable is Qualitative – Visual observation is enough. Computer aid not required , but if it there then added advantage. Even 5 variables can be handled at once. Contd …..

21. SIMULATION & SEARCH (types) 21 Steepest Ascent Method Response Surface Methodology (RSM) Contour Plots

22. Steepest Ascent Method 22 Procedure for moving sequentially along the path (or direction) in order to obtain max. ↑ i n response. Applied to analyze the responses obtained from: Factorial Designs Fractional Factorial Designs NOTE : Initial estimates of DOE are far from actual, so this method chosen for optimum value.

23. Response Surface Methodology (RSM) 23 A 3-D geometric representation that establishes an empirical relationship between responses & independent variables. For: Determining changes in response surface Determining optimal set of experimental conditions NOTE : Overlap of plots for complete info is possible.

24. Contour Plots 24 Are 2-D (X 1 & X 2 ) graphs in which some variables are held at one desired level & specific response noted. Both axes are in experimental units. Sometimes both the contour & RSM plots are drawn together for better optimum values.

25. Contour Plots 25 RSM & Contour Combined

26. 26 Thank you