Historical design and optimization techniques MCQs With Answer

Introduction: Understanding historical design and optimization techniques is essential for B. Pharm students involved in pharmaceutical formulation and process development. This overview links classical experimental design, factorial and fractional factorial designs, Taguchi methods, response surface methodology (RSM), central composite and Box–Behnken designs, and modern Design of Experiments (DOE) applied within Quality by Design (QbD). Focus areas include statistical analysis, screening versus optimization, interaction effects, model fitting, ANOVA, robustness, and scale-up considerations. Practical contexts cover dissolution optimization, tablet hardness, particle size control, and process parameter tuning. These MCQs focus on theoretical principles and practical applications. Now let’s test your knowledge with 30 MCQs on this topic.

Q1. Which design is most appropriate for initial screening of many factors to identify the important ones?

• Full factorial design
• Central composite design
• Plackett–Burman design
• Box–Behnken design

Correct Answer: Plackett–Burman design

Q2. In a 2-level full factorial design, what does a significant interaction between two factors indicate?

• Both factors have no main effects
• The combined effect differs from the sum of individual effects
• The response is independent of factor levels
• Replication is insufficient

Correct Answer: The combined effect differs from the sum of individual effects

Q3. Which method is specifically developed to improve robustness against noise factors using orthogonal arrays?

• Response surface methodology (RSM)
• Taguchi methods
• Central composite design
• Mixture design

Correct Answer: Taguchi methods

Q4. What is the main objective of response surface methodology (RSM) in formulation development?

• Screening a large number of factors
• Finding the relationship between factors and response and locating optimum settings
• Confirming stability of a final product over time
• Replacing analytical method validation

Correct Answer: Finding the relationship between factors and response and locating optimum settings

Q5. Which design includes axial (star) points to estimate curvature in the response surface?

• Plackett–Burman design
• Central composite design (CCD)
• Taguchi L9 design
• Fractional factorial design

Correct Answer: Central composite design (CCD)

Q6. What does the term “aliasing” refer to in fractional factorial designs?

• Random error in repeated runs
• Confounding of effects so that they cannot be separated
• Optimal selection of factor levels
• Transformation of the response variable

Correct Answer: Confounding of effects so that they cannot be separated

Q7. Which statistical test in ANOVA assesses whether model terms explain significant variation in the response?

• T-test for means
• Chi-square test
• F-test
• Kruskal–Wallis test

Correct Answer: F-test

Q8. In RSM, what is the primary purpose of a contour plot?

• Display factor aliasing
• Show experimental randomization order
• Visualize response levels across two factors to locate optima
• Report residual diagnostics

Correct Answer: Visualize response levels across two factors to locate optima

Q9. Which design is efficient for fitting quadratic models with fewer runs than a full three-level factorial?

• Box–Behnken design
• Plackett–Burman design
• Simplex-lattice design
• One-factor-at-a-time (OFAT)

Correct Answer: Box–Behnken design

Q10. What does “resolution” describe in fractional factorial designs?

• The number of replicate runs
• The degree to which main effects and interactions are confounded
• The steepness of the response surface
• The size of experimental error

Correct Answer: The degree to which main effects and interactions are confounded

Q11. Which approach combines multiple responses into a single objective for optimization in DOE?

• ANOVA decomposition
• Desirability function
• Principal component analysis (PCA)
• Kaplan–Meier estimation

Correct Answer: Desirability function

Q12. When is transformation of the response (e.g., logarithm) commonly applied during modeling?

• To increase aliasing between factors
• To stabilize variance and improve normality of residuals
• To reduce the number of required runs
• To convert categorical factors to numerical

Correct Answer: To stabilize variance and improve normality of residuals

Q13. Which DOE principle helps to protect experiments from systematic bias due to uncontrolled variables?

• Blocking and randomization
• Increasing factor levels
• Using only center points
• Eliminating replication

Correct Answer: Blocking and randomization

Q14. In pharmaceutical formulation, which response is commonly optimized using DOE to meet release criteria?

• Tablet color only
• Dissolution profile
• Supplier lead time
• Invoice processing time

Correct Answer: Dissolution profile

Q15. What is the advantage of using factorial design over one-factor-at-a-time (OFAT)?

• Detects interaction effects between factors
• Requires no statistical analysis
• Always needs fewer runs than OFAT
• Prevents the need for randomization

Correct Answer: Detects interaction effects between factors

Q16. Which diagnostic plot is essential to check model adequacy by assessing residuals?

• Contour plot of factors
• Normal probability plot of residuals
• Box plot of factors
• Pie chart of responses

Correct Answer: Normal probability plot of residuals

Q17. For scale-up studies, which DOE consideration is most critical to ensure transferability of optimized conditions?

• Ignoring interactions at small scale
• Including scale as a factor and testing robustness
• Using only Plackett–Burman designs
• Running experiments in uncontrolled environmental conditions

Correct Answer: Including scale as a factor and testing robustness

Q18. What does a significant lack-of-fit in ANOVA imply about the fitted model?

• The model perfectly describes the data
• The chosen model form is inadequate to describe the data
• There is no experimental error
• The residuals follow a normal distribution

Correct Answer: The chosen model form is inadequate to describe the data

Q19. Which of the following best describes a “center point” in RSM experiments?

• A run with all factors at their lowest levels
• A run with factors set to mid-levels to detect curvature and estimate pure error
• A replication of the axial point only
• A method to randomize run order

Correct Answer: A run with factors set to mid-levels to detect curvature and estimate pure error

Q20. In a two-level fractional factorial design of resolution IV, which is true?

• Main effects are aliased with two-factor interactions
• Main effects are aliased with three-factor interactions only
• No aliasing exists between any effects
• All interactions are fully estimable

Correct Answer: Main effects are aliased with two-factor interactions

Q21. Which technique is particularly useful when the experimental region is constrained by formulation composition (components sum to 100%)?

• Mixture design
• Plackett–Burman design
• Central composite design
• Simple random sampling

Correct Answer: Mixture design

Q22. What is the primary role of replication in designed experiments?

• To increase aliasing between factors
• To estimate experimental error and improve precision
• To change factor levels systematically
• To remove the need for ANOVA

Correct Answer: To estimate experimental error and improve precision

Q23. Which term describes the predicted response at untested factor combinations within the design space?

• Extrapolation error
• Predicted value or model response
• Aliased interaction
• Blocking factor

Correct Answer: Predicted value or model response

Q24. How does Taguchi’s signal-to-noise (S/N) ratio guide optimization?

• By maximizing variability of the response
• By summarizing mean and variability to improve robustness
• By eliminating the need for replication
• By optimizing only categorical factors

Correct Answer: By summarizing mean and variability to improve robustness

Q25. Which outcome indicates a good predictive model when validating DOE results?

• High R-squared but large prediction error on new data
• Low R-squared on training data
• Similar performance metrics on training and validation datasets
• No need to test on validation data

Correct Answer: Similar performance metrics on training and validation datasets

Q26. In DOE for stability-indicating method development, which factor type is commonly studied?

• Analytical method parameters like pH and mobile phase composition
• Packaging design only
• Market demand forecasts
• Supplier invoicing frequency

Correct Answer: Analytical method parameters like pH and mobile phase composition

Q27. What is the benefit of using software (e.g., Design-Expert, Minitab) for DOE in pharmaceutical research?

• It eliminates the need to understand statistics
• It automates design selection, analysis, model fitting, and optimization
• It guarantees successful scale-up without experiments
• It replaces laboratory experimentation entirely

Correct Answer: It automates design selection, analysis, model fitting, and optimization

Q28. Which factor should be controlled as a blocking variable to reduce variability between experimental runs?

• Uncontrolled ambient temperature changes between days
• Random noise within a run
• Analyst’s preference for color
• Number of response variables

Correct Answer: Uncontrolled ambient temperature changes between days

Q29. During DOE optimization, what does a steep gradient in the response surface indicate?

• Little to no effect of factors on response
• A sensitive region where small factor changes produce large response changes
• Model inadequacy due to lack of curvature
• No interactions are present

Correct Answer: A sensitive region where small factor changes produce large response changes

Q30. Which practice aligns DOE with regulatory expectations under Quality by Design (QbD) for pharmaceuticals?

• Documenting design space, control strategy, and risk assessment
• Avoiding statistical analysis to simplify reports
• Using only OFAT approaches for validation
• Implementing changes without experimental evidence

Correct Answer: Documenting design space, control strategy, and risk assessment

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