Q 577.  How does a Plackett-Burman design differ from a regular 2-level design? What are the benefits and limitations of Plackett-Burman designs? Provide some real-world examples of Plackett-Burman designs.

 

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Plackett Burman Design is an experimental design used in DoE to sort out or screen out the number of factors to minimize the number of experimental runs. In this design some critical factors to be identified from large number of factors available.

 

In 2 level design, Full factorial design or Fractional Factorial Design is used, and it required large number of experimental runs. Which is not a cost effective and efficient way.

 

Benefits of Plackett Burman Design:

• Plackett Burman Design is comparatively simple and easy to create and apply. It required only binary coding (-1 and +1) making it easy to implement.
• Plackett Burman Design can be used to efficient sorting of large number of factors.
• Plackett Burman Design is robust design against variability in the experiments.
• Plackett Burman Design identify the most significant factors and thus effectively identify the main effects of the factors.

Limitations of Plackett Burman Design

• Plackett Burman Design cannot estimate interactions between factors in high resolution design.
• Plackett Burman Design uses binary coding (-1 and +1), which is not suitable for factors with more than 2 levels.

 

Plackett Burman Design is useful in manufacturing in quality control process to identify significant factors that may affect the efficiency of equipment, defects in product etc. These factors may be product parameters, manufacturing process parameters, Equipment settings etc.

 

Plackett Burman Design is useful in Food product manufacturing to identify significant factors like moisture content, feed rate, raw material composition, color composition, etc. Which may affect the texture, shelf life and taste of food product.

A Placket-Burman design exhibits the following differences when compared to a regular 2-level design:

 

Plackett-Burman Designs	Regular 2 -Level Designs
1.  These are highly fractional resolution III designs where the main effects are confounded with the 2-way interactions.	1.  These could be either full factorial designs or fractional factorial resolution IV or V designs where there is no confounding of main effects with 2-way or other higher order interactions.
2.  Only used to screen main factors from a long list of potential factors.	2.  These are used to screen as well as to optimize the main factors.
3.  The number of experimental runs in these designs are in multiples of 4 starting from 4 to 128 and the number of factors has to be one less than the number of runs.  For e.g., A design with 32 runs can screen main effects of up to 31 factors.	3.  The number of experimental runs in these designs is expressed as 2k (full factorial) and 2k-n (fractional factorial) where k denotes number of factors and n could be 1, 2 or 3 for 1/2 factorial, 1/4 factorial or 1/8 factorial designs.
4. 7 factors with 2 levels would warrant just 12 runs in a PB design as show below:     Design Summary: Factors:    7    Replicates:    1 Base runs:    12    Total runs:    12 Base blocks:    1    Total blocks:    1	4. 7 factors with 2 levels would require 128 runs for a full factorial and 64 runs in a fractional factorial as shown below: Design Summary - Full factorial Factors:    7    Base Design:    7, 128 Runs:    128    Replicates:    1 Blocks:    1    Center pts (total):    0 Design Summary - Fractional factorial Factors:    7    Base Design:    7, 64   Resolution:    VII Runs:    64    Replicates:  1    Fraction:  1/2 Blocks:    1    Center pts (total):    0

 

Benefits of Plackett-Burman Designs:

 

·         Plackett-Burman designs are usually helpful when we have a significantly large number of factors, and it is not economically feasible to conduct even 1/4 or 1/8 factorial designs.

·         Not only does it saves time and money but provides us with vital few from trivial many which can then be optimized further via full factorial or resolution IV or V fractional factorial designs.

 

Limitations of Plackett-Burman Designs:

 

·         These are only helpful early on in a study when we have limited knowledge about the overall study and there are large number of factors to choose from.

·         Due to them being highly fractional, it is not advisable to use them for studying interaction effects.

·         Recommended to be used only when there are negligible 2-way interactions.  The results of these designs to identify main effects are not reliable when two-way or other higher order interactions are present.

 

Examples of Plackett-Burman Designs:

 

·         Clinical Research – There are several potential factors that are at a play at the initial stages of a drug development against a diesease and PB designs come to its rescue by weeding out the insignificant factors. Once the main interactions are identified, the drug resistance is measured against those by deploying a full factorial or a fractional factorial design.

 

·         FMCGs – PB designs are used in the initial stages of a product development for screening significant factors from a list of potential factors that can be further studied and optimized with an eye towards enhanced customer experience and increased market share.

 

·         Agriculture:  Plant fertilizer industry always strives to enhance the effectiveness of their plant foods by investing a considerable time and effort on optimizing the factors that are crtitical to the crop yield and quality. PB designs helps them to narrow down to these vita few from trivial many.

 

 

Design of Experiments is a method to determine the relationship between impacted input factors (Controllable and uncontrollable) and output of the process. The controllable input factors can be modified for output optimization. DOE delivers an equation that quantifies the relationship between factors and outputs and explains which all factors have big and less impact on the outputs. DOE understands the influence of the experimental parameters on the outcome and to find an optimal solution for the process.

 

Design Type vs features	Plackett-Burman Design	2 Level Factorial Design
Definition	Plackett-Burman Design helps to identify the factors that are important in the experiment. This design can be applied for experiments that are multiples of 4.. A minimum of 4n (n>1) experiments are needed for identifying main effects for 4n-1 factors.	2 level Factorial designs are carried to determine whether certain factors or interactions between two or more factors have an effect on the responses. The number of experiments are based on the number of factors which is 2^n where n is >= 1
Pros	Plackett Burman design can provide data with less experimental runs which saves cost and time. Two way interactions is aliased with the main effect factors.	Highlighting the relationships between variables, it also allows the effects of manipulating a single variable to be isolated and analyzed singly.  No aliasing and confounding as all possible combinations are studied.
Cons	Cannot verify if the effect of one factor depends on other factor in the experiment due to less data points collected/few experimental runs. Not feasible to run all the 2^n factorial experiments.	There is a difficulty of experimenting with more than two factors or many levels. All combinations to be considered irrespective of the factor importance that results in experimental waste.
Factors Vs Runs	4 to 7 factors leads to 8 experimental runs 8 to 11 factors leads to 12 experimental runs 12 to 15 factors leads to 16 experimental runs	2 factors leads to 4 experimental runs 4 factors leads to 16 experimental runs 7 factors leads to 128 experimental runs

 

Benefits of Plackett-Burman Design:

1.       With few experimental runs large number of factors can be analyzed ,this makes easy to identify the vital factors and eliminate the effects that are insignificant.

2.       Time and cost is optimized as fewer experimental runs are considered.

3.       Variance of the dependencies is minimized using a limited number of experiments.

 

Limitation of PB Design:

1.       Interactions are partially confounding with the main effects of different factors and cannot be evaluated individually. Interpreting the results is risky and difficult due to less experimental runs.

2.       Not feasible to run all the 2^n factorial experiments.

Difference between Plackett-Burman design and Regular 2-level design
Plackett Burman Design	Regular 2-level design
Plackett-Burman (PB) design is used to identify the most important factor in the experiment. It helps to develop an efficient screening method to identify the active factors using as few runs as possible. PB design used in manipulating seven-two level factors require 8 experimental runs vs 2^7 runs as required by full factorial deign (1 – (8/128) = 93.75% economy achieved)	Regular 2-level designs typically referred to as 2^k designs -k factors where k denotes the number of factors investigated in the experiment. They are factorial experiments in which each factor is investigated at only 2 levels. For example, a two-level experiment with three factors will require 8 runs. The number of experiments increases rapidly, it is satisfactory for up to 5 factors.
These designs are used to identify and screen main effects when it can be assumed that the 2-way interactions are negligible. It is most important to find out contributing and non-contributing factors.	All effects are clear, there is no confounding by interactions. Regular 2-level design is useful for estimating main effects and interactions by varying the factors together.
PBD is the starting point for screening where there is desire to identify few main factors affecting the outcomes. It greatly reduces the amount of data you have to collect.	Once the significant factors are available and their interactions are required, it will be better to go with full factorial design.
Experimental runs are in the multiple of 4.	Experimental runs are in power of 2 i.e. 2^k where k is the number of factors in study.
Plackett-Burman design is used when neglecting higher order interactions is possible, when there are more than 5 factors making it more economical and appropriate to run.	Regular 2-level design works best up to 5 factors else the number of runs increases exponentially making it too expensive to run.
It is helpful when complete knowledge about the system is unavailable or in case of screening with higher number of factors.	Regular 2-level designs are appropriate once few significant factors from a list of many potential ones are identified.
The greater number of dummy factors results in better estimate of measurement error, so it is common for experimenters to use large PB designs than is strictly necessary	Random errors (noted differences in data are statistically significant) can be reduced by repeating experimental runs.
Plackett-Burman Design (Pros and Cons)
Pros	Cons
These designs are very useful for economically detecting large main effect, assuming all interactions are negligible when compared to few main effects	It does not verify if the effect of one factor depends on another factor.
Very efficient screening designs when only the main effects are of interest	Main effects may be aliased by two-way interactions.
Used to investigate (n-1) variables in n experiments proposing experimental designs for more than 7 factors and especially for n*4 experiments.	Theory shows that in a PB design the main factors are not confounded, but there is strong confounding between the main factors and any two factor interactions that may arise (difficult to distinguishes between the main effect and their interactions). So, if there are significant interactions, PB design can give misleading results.
Real life examples of PB designs
PB designs are extensively used in chemical and biochemical studies, spectroscopy, electrochemistry, chromatography, etc. There have been many studies made to improve yield in farming. Used in determining best composition present in the fermentation media so as to get the maximum yield, screen out factors affecting the production process Biopharmaceutical industry uses PB designs to develop high performing processes to meet increasing customer demand and reduce manufacturing cost. Clinical studies having many factors included as part of study like determining influence of protein and carbohydrate contents on cell density

Plackett –Burrman design is used to find out which factors are important in an experiment /DOE.

There by ,we can avoid collecting large amounts of data on unimportant factors.

 

It can only be used for experiments that are multiples of 4,with 8 as starting point(N=8,12,16,20,24,28,32,26).

So 4,5,6 or 7 factors would require 8 experimental runs & 8,9,10 or 11 factors ,would require 12 runs.

 

For example, If we 16 factors in a design – just around 20 runs may be sufficient in a Placket Burman. However full factorial would require more than 100 . working with such few data points we can neither predict effects , so it shall be used only as starting point for further experiments. After identifying those important factors , later full factorial can be done. Hence this Plackett- Burman design would save lot of time and resources in R&D applications and in Pharma research formula combinations.

 

This design identifies most important factors early in experimentation phase. Resolution 3, two level designs with main effects heavily confounded with 2 factor .

 

Advantages of Plackett – Burrman Design:

1>More number of factors can be studied with limited number of runs.99 factors can be studied with just 100 runs

2>Main effects have complicated relationships with 2 factor interactions.

3>This allows screening of main factors for more number of Process variables – thus avoiding time and resources.

 

Disadvantages of Plackett – Burrman Design:

1>Each main effect is partially aliased with every 2 – way interaction not involving that main effect.

2>This degrades to accurately estimate true underlying active main effects or 2 way interctions.

3> This design does not allow to analyse and interpret if no replication exists in the design.

 

Example:

The decision for combination formula for a fibre reinforced composite to be used in space applications .

Screening of the material level for the materials selection(rough combinations), can take place using Plackett- Burrman , while detailed % composition of each material can be decided by a full - factorial design.

Difference:

2-Level Design	Planket Burman Design
Small Number of factors	Large number of factors
More experimental runs	Fewer experimental runs
Includes all possible factors	Does not consider all possible factors

 

Benefits:

1. Since it enables large factors through lesser number of experiments, there is a lot of cost and effort reduction possible.

2. Helps in identifying and narrowing down a list of significant factors.

Limitations:

1. Cannot separate main effects from interactions.

2. Does not provide estimates of interaction effects between factors.

Real-world examples:

FMCG and Pharma Industry can use the design to screen a large number of factors like contents, packaging, etc to enhance their products.

While all published answers are noteworthy, Pradeep Kandpal's answer is selected as the best answer, mainly due to the citation of relevant examples.