Placket Burman Design PPT (Design of Experiments)

Design of Experiments

1. Plackett - Burman design NANDHINI LAXMAN NAIK PAMB2147 DEPARTMENT OF AS, AM & CS.

2. contents Some basic concepts. Introduction to PBD. Methodology. Merits and Demerits. Applications. Case studies. Conclusion and Summary. References. 2

3. Some basic concepts Factorial design: To evaluate the combined effect of two or more factors when they are used simultaneously. = K factors, Z levels 3factors, 2 levels = 2factors, 3 levels Factorial design is divided into two types: F ull factorial design (FD) F ractional factorial design(FFD)   3

4. C ontd …  Full factorial design(FD): It consists of all possible factor combinations in an experiment and factors vary simultaneously rather than one factor at given time. Number of runs (N)= Where, Z = number of levels, = number of factors E.g. - 3 factors, 2 levels each, N = = 8 runs.   4

5. Contd… Fractional factorial design(FFD): In f ull f actorial design as a number of factor or level increases, the number of experiment required exceeds to unmanageable levels . In such cases, the number of experiments can be reduced systemically and resulting design is called as fractional factorial design. Applied when number of factors are > . In general, design is a fraction of a design using runs. For example: design is a design using = =8 runs.   5

6. Plackett Burman design In a classic 1946 published research paper in the journal of Biometrika , the Plackett and Burman showed how to construct 2-level orthogonal designs when the number of runs ‘N’ is a multiple of ( 4,8,12,16,20,24, and so on). If the run size is a power of 2(for example, 8,16,32, ...), these designs are identical to the fractional factorial designs. As per the literature, this is called as popular screening design. These designs are very efficient screening designs when only the main effects are of interest to evaluate in complex way.   Johannes and Arthur( )   6

7. Contd... These are useful for detecting large main effects economically, assuming all interactions are negligible when compared with important main effects. These are two-level fractional factorial designs for studying k =n - 1 variables or factors in n runs, where n is a multiple of 4 (n = 4,8,12,16,20,24, and so on). It is a two-level design, each variables represented in two levels i.e., High(+) and Low (-). Ea ch horizontal row represents a trial or runs and each vertical column represents the either of 2 levels (High or Low level). 7 Johannes and Arthur( )  

8. Contd... Any factors are not assigned to variable can be designated as a dummy variable alternatively, factors known to not have any effect may be included and designated as dummy variables. The effect of dummy variables into an experiment makes it possible to estimate the variance of an particular effect in the driven experimental material (experimental error). 8 Stanbury et.al. (𝟐𝟎𝟏𝟑)

9. Table 1: COMPARISON Full Factorial Designs Fractional factorial Designs Plackett -Burman Design Considers all possible combinations of levels for each factor. Considers only a fraction of all possible combinations, reducing the number of runs. Suitable for screening experiments when the number of factors is large. Requires a large number of runs. Requires a less number of runs compared with the factorial design. Requires very few runs for a large number of variables. Represented as where k is the number of factors . Represented as where p is the fraction of the full factorial design. Multiples of Full Factorial Designs Fractional factorial Designs Plackett -Burman Design Considers all possible combinations of levels for each factor. Considers only a fraction of all possible combinations, reducing the number of runs. Suitable for screening experiments when the number of factors is large. Requires a large number of runs. Requires a less number of runs compared with the factorial design. Requires very few runs for a large number of variables. 9

10. Contd... Full Factorial Designs Fractional factorial Designs Plackett -Burman Design Used when a comprehensive understanding of all factors and interactions is required. Mainly used for screening experiments when the number of factors is large. Primarily used for screening experiments, especially when resources are limited. Inefficient for large numbers of factors would be exponentially distributed . More efficient than a full factorial design, allowing for a reduction in the number of runs. Efficient for screening a large number of factors with a minimal number of runs 10

11. Design Resolution Plackett -Burman designs are Resolution III Resolution III designs: Designs in which no main effects are aliased (chain) with any other main effects. Main effects are aliased with at least two-factors interactions. Some two-factor interactions may be aliased with each other. 11 Douglas C. Montgomery (2012)

12. Generator of rows for Constructing PBD =Factors =Runs Factor levels 8-11 12 + + - + + + - - - + - 16-19 20 + + - - + + + + - + - + - - - - + + - 20-23 24 + + + + + - + - + + - - + + - - + - + - - - - 32-35 36 - + - + + + - - - + + + + + - + + + - - + - - - - + - + - + + - - + - Factor levels 8-11 12 + + - + + + - - - + - 16-19 20 + + - - + + + + - + - + - - - - + + - 20-23 24 + + + + + - + - + + - - + + - - + - + - - - - 32-35 36 - + - + + + - - - + + + + + - + + + - - + - - - - + - + - + + - - + - 12 Douglas C. Montgomery (2012) Table 2 : Plus and Minus Signs for the Plackett–Burman Designs

13. Table 3: PBD for up to factors in N =12 Runs   George et.al. (2005) FACTORS Runs A B C D E F G H I J K 1 + - + - - - + + + - + 2 + + - + - - - + + + - 3 - + + - + - - - + + + 4 + - + + - + - - - + + 5 + + - + + - + - - - + 6 + + + - + + - + - - - 7 - + + + - + + - + - - 8 - - + + + - + + - + - 9 - - - + + + - + + - + 10 + - - - + + + - + + - 11 - + - - - + + + - + + 12 - - - - - - - - - - -

14. Methodology Construction of design .Using F- values. .Using alias chain. .Analytically -Using R- programme.   14

15. using F- values . . Determine the difference between the + (high) and - (low) responses for each independent and dummy variable. Difference= - . Determine effect of each variables Effect of Factors = Where, = number of runs.   15 Stanbury et.al. (2013)

16. Contd… . Estimate the mean square of each variable (the variance of effect). Factor Mean square = . The experimental error can be calculated by averaging the mean squares of the dummy effects. EMS =   16 Stanbury et.al. (2013)

17. Contd … . The final stage is to identify the factors which are showing large effects and this was done using an F-test. F= . Larger F-ratios and smaller p- values suggest more significant effects .   17 Stanbury et.al. (2013)

18. Table 4: Anova Source of Variation Df SS MSS F-ratio p-value Model (Factors) SSF SSF/k MSF/MSE XXX Residual (Error) - - 1 SSE SSE/(N-k-1) - - Total - 1 SST - - - Source of Variation Df SS MSS F-ratio p-value Model (Factors) SSF SSF/k MSF/MSE XXX Residual (Error) SSE SSE/(N-k-1) - - Total SST - - - 18 =Number of factors. = Total n umber of runs.   The ANOVA table can guide decisions on which factors are likely to have a substantial impact. A low p-value for a factor indicates that the factor has a significant effect on the response variable.

19. Using alias chain Example: A human performance analyst is conducting an experiment to study eye focus time and has built an apparatus in which several factors can be controlled during the test. Seven factors are A= Sharpness of vision B= distance from target to eye C= target shape D = illumination level E = target size F = target density G = subject Douglas C. Montgomery (2012) 19

20. Contd… Table 5 : Design for the eye focuse time experiment( =8, =7)   Douglas C. Montgomery (2012) 20 Factors Runs A B C D=AB E=AC F=BC G=ABC Time 1 - - - + + + - 85.5 2 + - - - - + + 75.1 3 - + - - + - + 93.2 4 + + - + - - - 145.4 5 - - + + - - + 83.7 6 + - + - + - - 77.6 7 - + + - - + - 95.0 8 + + + + + + + 141.8

21. Contd… Seven main effects and their aliases may be estimated from these data, the effects and their aliases are [A]=20.63 A+BD+CE+FG [B]=38.38 B+AD+CF+EG [C]=-0.28 C+AE+BF+DG [D]=28.88 D+AB+CG+EF [E]=-0.28 E+AC+BG+DF [F]=0.63 F+BC+AG+DE [G]=-2.43 G+CD+BE+AF Douglas C. Montgomery (2012) 21

22. Using R PROGRAMME John Lawson developed the code by using the data of Hunter et.al. (1982) of the fatigue life of weld-repaired castings. #The R package BsMD contains the data frame PB12Des, which is the equivalent to a 12-run Plackett -Burman design library(BsMD) data( PB12Des, package = "BsMD" ) #assign the factors names colnames(PB12Des) <- c("c11", "c10", "c9", "c8", "G", "F", "E","D", "C", "B", "A") 22 John Lawson (2015)

23. Contd… #use PB12Des to create PB12 design matrix castf <- PB12Des[c(11,10,9,8,7,6,5,4,3,2,1)] #assign the response values y <- c(4.733, 4.625, 5.899, 7.0, 5.752, 5.682, 6.607, 5.818, 5.917, 5.863, 6.058, 4.809) #combind the response values and factors castf1 <- cbind ( castf , y ) #the lm function was used to estimate the coefficients for each of the 11 columns modpb <- lm ( y ~ (.), data = castf1 ) 23 John Lawson (2015)

24. Contd… # package daewr was used to create the half-normal plot of effects. library( daewr ) cfs <- coef ( modpb )[2:12] names<-names(cfs) halfnorm(cfs, names, alpha = .35, refline=FALSE) Fig.1 John Lawson (2015) 24

25. MERITS This design helps us to explore which factor is found to be highly important in an Agricultural field trial, multi centric drug trial experimentation, DNA sequencing analysis. To reduce experimental runs with different experiment block. This design acts as navigation tool for enabling a quick reduction in the number of potential factors whichever the factor researcher affixed. This design screens out less scope factors from design. 25

26. DEMERITS Ignore higher order interaction. The selection of factors is very crucial, and if key factors are omitted from the design, the results may be incomplete. The researcher will allow c areful consideration and research domain knowledge are required during selection of factors on predominant basis. It requires prior knowledge 26

27. Applications . Pharmaceutical industry: Screening drug formulations in different age groups when the drug is effective or ineffective. Optimizing manufacturing processes. To identify the critical factors affecting the product quality. . Chemical manufacturing: Different concentrations were screened to know factors influencing yield, purity, reaction kinetics and chemical structure of substances. . Food and beverage industry: Assessing factors attributed taste at different persons with different time intervals , texture, and shelf life.   27

28. Contd… . Biotechnology: Identifying the key variables in the bioprocess optimization. For Example: Vaccination effect. Screening factors influencing cell culture, cell biology, fermentation, and product yield. . Agricultural research: Assessing factors influencing crop yield and quality, meteorological parameters .   28

29. Case study 1

30. This study focus on Screening of process components and their effects on production of lactase by newly isolated Bacillus sp . VUVD101 strain from dairy effluent by using PBD. Objectives: Lactase production increases. Screening the factors affecting of the production process. Isolated bacterium increase more profit. Karlapudi et.al. (2018) 30

31. Contd… The Plackett- Burman statistical design is very frequently used to study the effects of broth components on lactase production. It is a two factorial (i.e. -1 and +1 ) design that locates significant variables for the production by “n” variables. factors( Table 6) chosen in the present investigation were tested at these two levels, based on the Plackett- Burman matrix design. The main effect was calculated basically as a difference between the average measurements of each variable made at a high level(+) and low level(-).   Karlapudi et.al. (2018) 31

32. Contd… This design screened variables based on a first-order model : = + ∑ . Where, represents the response( Lactase activity ) β is the Model intercept , β i is the Variable estimates , is the level of the independent variable. The regression equation was obtained using the P lackett -Burman design, which predicted the factors that a ff ected the response In this study, the variables were screened using MINITAB 17.0 software.   Karlapudi et.al. (2018) 32

33. 33 Table 6: The variables and levels used in statistical design for screening medium components affecting lactase production. Karlapudi et.al. (2018) Variable Code Variable Name Minimum Value Maximum Value A Incubation time 10 40 B Temperature 25 40 C pH 6 10 D RPM 100 200 E DO 1 3 F Inoculum size 0.25 1 G Inoculum age 24 72 H MgSO 4 0.5 1 J L-Cysteine 0.1 1 K KH 2 PO 4 0.01 0.05 L CaCl 2 0.001 0.005 M K 2 PHO 4 0.01 0.05 N Corn steep liquor 0.5 1 O Lactose 0.5 2 Contd...

34. Karlapudi et.al. (2018) 32 Table 7: Effect of variables on lactase production by bacillus sp. VUVD101 using Plackett-Burman design . Runs A B C D E F G H J K L M N O Lactase activity (U/ml) 1 40 40 10 100 3 0.25 24 0.5 0.1 0.05 0.001 0.05 0.5 2 0.82 2 10 40 10 100 3 1 72 0.5 0.1 0.05 0.005 0.01 1 2 1.85 3 40 40 6 100 3 1 24 1 1 0.01 0.001 0.01 0.5 2 6.1 4 10 40 10 200 3 0.25 24 1 1 0.01 0.005 0.05 0.5 0.5 5.06 5 10 25 6 200 3 0.25 72 1 1 0.05 0.001 0.01 1 2 15.85 6 10 40 6 200 1 0.25 24 1 0.1 0.05 0.001 0.05 1 2 6.82 7 40 40 6 100 1 0.25 72 0.5 1 0.01 0.005 0.05 1 2 2 8 10 25 10 100 1 1 24 1 1 0.05 0.005 0.01 0.5 2 5.75 9 40 40 6 200 1 1 72 0.5 1 0.05 0.001 0.01 0.5 0.5 4.28 10 10 25 10 200 1 1 72 0.5 0.1 0.01 0.001 0.05 0.5 2 8.6

35. Contd… 11 40 40 10 200 1 0.25 72 1 0.1 0.05 0.005 0.01 0.5 0.5 2.01 12 40 25 6 100 1 1 24 1 0.1 0.05 0.005 0.05 1 0.5 5.35 13 40 25 10 200 1 0.25 24 0.5 1 0.01 0.005 0.01 1 2 5.18 14 40 25 10 100 3 0.25 72 1 0.1 0.01 0.001 0.01 1 0.5 2.5 15 10 25 6 100 3 0.25 72 0.5 1 0.05 0.005 0.05 0.5 0.5 9.1 16 40 25 10 200 3 1 24 0.5 1 0.05 0.001 0.05 1 0.5 2 17 10 25 6 100 1 0.25 24 0.5 0.1 0.01 0.001 0.01 0.5 0.5 7.92 18 10 25 6 200 3 1 72 1 0.1 0.01 0.005 0.05 0.5 2 16.25 19 10 40 6 200 3 1 24 0.5 0.1 0.01 0.005 0.01 1 0.5 2.99 20 10 40 10 100 1 1 72 1 1 0.01 0.001 0.05 1 0.5 1.02 Karlapudi et.al. (2018) 33

36. 36 Karlapudi et.al. (2018) Source DF Adj SS Adj MS F-Value P-Value Model 14 347.14 24.796 8.60 0.013 Incubation time 1 16.85 16.85 5.84 0.06 Temperature 1 103.345 103.345 35.83 0.002 pH 1 87.196 87.196 30.23 0.003 RPM 1 35.725 35.725 12.39 0.017 DO 1 9.09 9.09 3.15 0.136 Inoculum size 1 0.443 0.443 0.15 0.711 Inoculum age 1 11.833 11.833 4.10 0.099 MgSO 4 1 24.358 24.358 8.44 0.034 L-Cysteine 1 0.064 0.064 0.02 0.887 KH 2 PO 4 1 0.753 0.753 0.26 0.631 CaCl 2 1 0.010 0.010 0.00 0.954 K 2 PHO 4 1 0.3130 0.3130 0.11 0.755 Corn steep liquor 1 20.462 20.462 7.09 0.045 Lactose 1 36.697 36.697 12.72 0.016 Error 5 14.422 2.884  -  - Total 19 361.562  -  -  - Table 8: ANOVA Results and discussion Level of significance =0.05

37. Main effect of variables on production by Bacillus sp . VUVD101 a . Normal plot of standardized effects (Fig.2). b . Pareto chart of standardized effects (Fig. 3). 37 Karlapudi et.al. (2018) Fig.2 Fig. 3

38. Conclusion This study had led to the isolation of bacterium, Bacillus sp. VUVD101 strain with high activity for lactose hydrolysis. The components namely temperature, pH, RPM, MgSo 4 , Corn steep liquor and lactose were found to be highly significant to achieve the maximum production of lactose (18.31U/ml). These results revealed that the isolated bacterium could be used as a good source for industrial production of lactase. 38 Karlapudi et.al. (2018)

39. Case study 2

40. This study focus on application of Plackett-Burman Design for screening the media components for tannase production from red gram husk using submerged fermentation. Objective: To identify which ingredients of medium have significant effect on tannase enzyme production. Mohan et.al. (2013) 40

41. Contd… Placket-Burman design used in screening experiment as the number of experiment run required are very few, leading to saving of time, chemicals and man power. Placket-Burman design was used for screening the media components to enhance tannase enzyme production . This design does not consider the interaction effects between the variables and is used to screen the important variables affecting tannase production. It can be represented by first-order polynomial Equation : = + ∑ . Where, represents the response, β is the model coefficient, β i is the linear coefficient, is the level of the independent variable.   Mohan et.al. (2013) 41  

42. Contd… The statistical software package ‘ Design expert ’, was used for analyzing the experimental data. The variables( Table 9) and inducer tannic acid were screened in experimental trials. The low level (–1) and high level (+1) of each factor are listed in (Table 9). The effect of variables namely concentrations of eleven nutrients and tannic acid as inducer on tannase enzyme production by submerged fermentation by A. Foetidus were analysed . Table 9 shows the Plackett–Burman experimental design and the results obtained from the experiments which are generated by the MINITAB software .   Mohan et.al. (2013) 42

43. Mohan et.al . (2013) 43   Run No. A B C D E F G H I J K L Tannase Activity (U/ml) Experimental Predicted 1 1 1 1 1 -1 -1 1 1 -1 1 1 -1 44.35 33.35 2 -1 1 -1 1 -1 1 1 1 1 -1 -1 1 89.09 86.97 3 -1 -1 1 -1 1 -1 1 1 1 1 -1 -1 87.98 85.79 4 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 48.49 56.01 5 1 -1 1 -1 1 1 1 1 -1 -1 1 1 78.74 88.91 6 1 -1 -1 -1 -1 1 -1 1 -1 1 1 1 88.11 80.05 7 -1 -1 -1 1 -1 1 -1 1 1 1 1 -1 70.53 77.26 8 1 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 49.96 55.37 9 -1 1 1 -1 1 1 -1 -1 -1 -1 1 -1 120.40 108.95 10 1 1 -1 -1 1 1 -1 1 1 -1 -1 -1 105.80 103.64 Table 9 : The effect of Variables on Tannase Enzyme Production by A. foetidus using Plackett-Burman Experimental Design .

44. Contd… 11 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 100.43 103.92 12 -1 1 1 1 1 -1 -1 1 1 -1 1 1 64.70 64.94 13 -1 -1 1 1 -1 1 1 -1 -1 -1 -1 1 87.40 81.16 14 -1 -1 -1 -1 1 -1 1 -1 1 1 1 1 99.65 98.06 15 1 -1 1 1 1 1 -1 -1 1 1 -1 1 47.56 38.96 16 -1 1 -1 1 1 1 1 -1 -1 1 1 -1 77.65 85.43 17 1 1 1 -1 -1 1 1 -1 1 1 -1 -1 53.20 55.71 18 1 1 -1 -1 -1 -1 1 -1 1 -1 1 1 89.60 91.38 19 1 -1 -1 1 1 -1 1 1 -1 -1 -1 -1 69.34 70.24 20 1 1 -1 1 1 -1 -1 -1 -1 1 -1 1 36.76 43.67 Mohan et.al. (2013) 44

45. Contd… From the table 9 , it was observed that the variation in tannase activity was 36.76–120.40 U/ml. I n run no.9, the maximum tannase activity was obtained with the medium. In run no.20 , t he minimum tannase activity was obtained with the medium. Mohan et.al. (2013) 45  

46. Nutrient Code Nutrient Minimum Value Maximum Value t-value p-value A Tannic acid 1 5 3.40 0.011 B Yeast extract 0.1 1 1.19 0.273 C Magnesium sulphate 0.1 1 3.31 0.013 D Ferrous sulphate 0.1 1 3.85 0.006 E Ammonium nitrate 0.1 1 0.47 0.655 F Ammonium chloride 0.1 1 1.89 0.101 G Urea 0.1 1 1.08 0.317 H Potassium chloride 0.1 1 0.88 0.407 I Sodium nitrate 0.1 1 0.43 0.678 J Potassium di-hydrogen phosphate 0.1 1 3.96 0.005 K Ammonium sulphate 0.1 1 1.75 0.124 L Peptone 0.1 1 0.11 0.918 Mohan et.al. (2013) 46 Table 10 : Statistical analysis of medium optimization using Plackett-Burman design for tannase production using A. foetidus . Results and discussion Level of significance =0.05

47. Contd… On analysis of regression coefficient (t -value) of 12 medium components in ( T able 10 ), Ammonium sulphate , ammonium nitrate, ammonium chloride, urea, showed positive effect on tannase production, Whereas the remaining components showed negative effect on tannase production. The variables namely concentration of tannic acid, potassium di-hydrogen phosphate, magnesium sulphate and ferrous sulphate were found to be the most significant for tannase enzyme production as indicated by p-value < 0.05. Mohan et.al. (2013) 47

48. Contd… Mohan et.al. (2013) 48 The Pareto chart as shown in ( Fig.4 ) offers a convenient way to view the results obtained by PBD and the order of significance of the variable affecting tannase production. Fig. 4 Pareto plot for Plackett-Burman Design of experiments for tannase production using A. foetidus.

49. conclusion The plackett-burman design was effectively applied for screening of nutrients for the production of tannase from aspergillus foetidus (MTCC3557) using redgram husk as a substrate in submerged fermentation. From standard plackett-burman data analysis it was conformed that, concentration of tannic acid, concentration of potassium di-hydrogen phosphate, concentration of magnesium sulphate and concentration of ferrous sulphate were found to be the most significant for tannase enzyme production. Mohan et.al. (2013) 49

50. Case study 3 PBD associated with Response Surface design . Basavarajaiah and Narasimha Murthy (2020)

51. The researcher conducted the experimentation at in vitro condition to know the plasma concentration level of newly administered drug significance, he has included the geographical areas with the following factors. He wishes to determine the experimental reliability in PB design.   Basavarajaiah and Narasimha Murthy (2020) 51 : SGOT: X 6 Gender: SGPT: X 7 BMI: X 3 Blood urea : X 8 PPBS:X 4 TC: X 9 WBC :X 5 - SGOT: X 6 SGPT: X 7 BMI: X 3 Blood urea : X 8 PPBS:X 4 TC: X 9 WBC :X 5 -

52. Basavarajaiah and Narasimha Murthy (2020) 52   Effect Coefficient t-test p-value count: X 1 – 25.52 339.96 0.000 Gender : X 2 0.492 0.27 3.27 0.047 BMI: X 3 6.311 3.15 41.95 0.000 PPBS:X 4 −4.85 −2.4 32.28 0.000 WBC :X 5 −5.27 −2.65 35.03 0.000 SGOT: X 6 0.82 0.410 5.45 0.012 SGPT: X 7 1.01 0.507 6.75 0.000 Blood urea: X 8 1.84 0.921 12.24 0.000 TC: X 9 0.75 0.372 5.01 0.015   Effect Coefficient t-test p-value – 25.52 339.96 0.000 Gender : X 2 0.492 0.27 3.27 0.047 BMI: X 3 6.311 3.15 41.95 0.000 PPBS:X 4 −4.85 −2.4 32.28 0.000 WBC :X 5 −5.27 −2.65 35.03 0.000 SGOT: X 6 0.82 0.410 5.45 0.012 SGPT: X 7 1.01 0.507 6.75 0.000 Blood urea: X 8 1.84 0.921 12.24 0.000 TC: X 9 0.75 0.372 5.01 0.015 Results and discussion Table 11 : Statistical analysis of plasma concentration level of factors using Plackett -Burman design. Level of significance =0.05

53. Conclusion The data was analyzed by PBD, further he has tested the variables by using response surface design(in which variables are highly significant in response to the treatment) The PBD is well suited for massive data sets of life threatening diseases(HIV, Cancer, other neurological disorders) if the patient repeatedly undervent treatment with periodically change of hematological parameters and biochemical parameters. 53 Basavarajaiah and Narasimha Murthy (2020)

54. summary Plackett-Burman design is a statistical technique used to identify important factors that affect a process. It is a type of screening design that allows researchers to efficiently explore a large number of factors with a small number of experimental runs. This seminar provides valuable insights into PBD and their construction, methodologies and emphasizing their significance in screening most important factors. 54

55. Contd… Additionally, three case studies are presented: one focuses on screening of process components and their effects on production of lactase , while second case study involves screening the media components for tannase production from red gram husk and third case study presence the plasma concentration level of newly administered drug significance. It is a great tool for optimizing processes and reducing costs in various fields, including manufacturing and agriculture. 55

56. References ABRAHAM, P. KARLAPUDI, KRUPANIDHI, S., ERVA, R., M. INDIRA, MD. N. BOBBY, AND VEKATESWARULU, T.C., 2018, Plackett-Burman design for screening of process components and their effects on production of lactase by newly isolated Bacillus sp . VUVD101 strain from Dairy effluent. Beni-Suef univ. j. basic appl. Sci., 7 :543-546. Basavarajaiah, D.  M. And Bhamidipati Narasimha Murthy , 2020 Design of experiments and advanced statistical techniques in clinical research. Elsevier , pp.117-120.   56

57. Contd… George, E. p. Box, j. stuart hunter and William, g. hunter, 2015, Statistics for experimenters design, innovation and discovery John Wiley & Sons,Inc ., Hoboken, New Jersey, pp.281-282. John Lawson, 2015 , Design and analysis of experiments with R. Taylor & Francis Group, New York,pp.231-232. Johannes ledolter and arthur j. Swersey, 2007, Testing 1–2–3 experimental design with applications in marketing and service operations. Stanford University Press, Stanford, California, pp.150. 57

58. Contd… 58 MONTGOMERY, D.C., 2012, Design and analysis of experiments . John Wiley & Sons,Inc., Hoboken, New Jersey, pp.351-357. Mohan, S. K., Viruthagiri, T. AND ArunkumaR, C., 2013, Application of plackett-burman design for screening the media components for tannase production from redgram husk using submerged fermentation. Int. J. Pharma res . Rev., 2 (9):24-29. PETER F. STANBURY, Allan Whitaker, and Stephen J. Hall , 2013, Principles of fermentation technology . Elsevier , pp.110-112.