Screening

Screening Designs are a subcategory under Design of Experiments (DoE), focused on identifying the most significant factors that influence a response variable before optimizing. These designs are used when there are many potential factors to consider, and the goal is to quickly determine which ones have a meaningful effect in order to preserve resources and minimize cost. By systematically varying multiple factors at different levels and analyzing their effects, screening designs help prioritize the factors that warrant further investigation in more detailed studies.

Table of contents

1. Plackett Burman
2. Fractional Factorial
3. References
4. Version History

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Plackett Burman

Plackett-Burman designs are an efficient and economical approach within the DoE framework, particularly tailored for screening large numbers of factors in a system, similar to the Fractional Factorial Design. These designs are used to explore the main effects of up to $𝑘 = 𝑁 − 1$ factors in $𝑁$ experimental runs, where $𝑁$ is a multiple of 4 (e.g., 8, 12, 16). Moreover, all factors should have exactly two levels which we call high(+) and low (-). This structure allows researchers to identify which factors have significant main effects while minimizing the number of experimental runs required. This method becomes invaluable in scenarios where a full factorial design would necessitate prohibitively large experiments, consuming excessive time and resources.

Plackett-Burman designs achieve their efficiency by maximizing the number of factors that can be evaluated in a minimal number of runs. Unlike fractional factorial designs, which are crafted to manage both main effects and interactions, Plackett-Burman designs are specifically focused on detecting main effects. They are classified as resolution III designs, meaning that while they are well-suited to identify main effects, they confound these main effects with two-factor interactions. This confounding is a calculated trade-off, as the design assumes that two-factor interactions are either negligible or of less interest in the preliminary stages of experimentation.

For instance, in a Plackett-Burman design with 12 runs, up to 11 factors can be investigated, and any two-factor interactions will be indistinguishable from the main effects. This arrangement is particularly useful when the goal is rapid screening to pinpoint which factors have the most influence on the response variable, rather than an exhaustive analysis of all interactions. When the number of runs is a power of two (e.g., 8 or 16), the Plackett-Burman design is identical to a resolution III fractional factorial design.

Plackett-Burman designs are exceptionally valuable in early-stage experiments where a large number of factors are present, but only a subset is likely to have a substantial impact on the outcome. In these situations, they provide a powerful means to filter out the less impactful factors, allowing researchers to focus subsequent experiments on the most promising candidates. By reducing the number of necessary experiments, Plackett-Burman designs offer a practical balance between resource efficiency and the acquisition of critical data, making them an indispensable tool in experimental research for system optimization and improvement.

Use the Plackett Burman designs by browsing in the top ribbon:

DOE \(\rightarrow\) Screening \(\rightarrow\) Plackett Burman

Input

Numerical values should be specified in the input datasheet. Plackett-Burman design is applied when at least four factors (columns) are specified along with exactly two levels/values (rows).

Configuration

Number of Center Points	Select manually the Number of Center Points to be included in the output list of experiments. There is no minimum requirement or any other limitation.
Number of Blocks	Select manually the Number of Blocks. The lowest value that can get is 1.
Random Standard order	You can tick/select the box if randomness is required in the output list of experiments.
Time-based RNG Seed	If the randomness is selected, then you have the option to also tick/select the box to set the random generated number seed based on time.
RNG Seed	Select manually the random generated number seed if required.
Include/exclude columns	Select manually the columns through the dialog window: Use the buttons to move columns between the Included Columns and Excluded Columns list. Single-arrow buttons will move all selected columns and double-arrow buttons will move all columns.

Output

A list of experiments (combinations) is generated in the output datasheet along with the Block number and the Standard order based on the Plackett-Burman design.

Example

Input

In the input datasheet minimum requirement is to specify three factors (columns) and insert minimum two levels (values) for each factor (column), as shown below.

Configuration

1. Select DOE \(\rightarrow\) Screening \(\rightarrow\) Plackett Burman.
2. Select the Number of Center Points [1] to be generated in the output list of experiments.
3. Select the Number of Blocks [2]. The lowest value that can be set is 1.
4. Select/tick if required the Random Standard order [3] to imply randomness in the output list of experiments.
5. If randomness is selected either select/tick to generate the number seed for randomness based on time [4] or by manually setting a value [5].
6. Select the columns by clicking on the arrow buttons [8] and moving columns between the Excluded Columns [6] and Included Columns [7] lists.
7. Click on the Execute button [9] to perform Plackett-Burman design method.

Output

A list of experiments (combinations) is generated in the output datasheet along with the Block number based on the Plackett-Burman design method selected. The standard order is provided in Col2.

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Fractional Factorial

Fractional factorial designs represent a refined approach within the framework of DoE that addresses the challenge of studying systems with multiple factors without resorting to the exhaustive method used in full factorial designs. By selectively sampling a fraction of the full factorial design, these designs allow researchers to explore the effects of various factors using a substantially reduced number of experimental runs. This method is particularly valuable when dealing with a large number of factors, where a full factorial design would require an impractically large set of experiments, escalating costs and resource usage.

The efficiency of fractional factorial designs comes from their strategic choice of factor level combinations, capturing essential information about the system while significantly cutting down on the number of required experiments. This efficiency, however, introduces the primary challenge of confounding. Confounding occurs when the effects of some factor combinations become indistinguishable from others. For instance, in a four-factor experimental setup, a typical confounding pattern such as “A - B - C - BC” implies that the effect of the fourth factor is entangled with the combined effects of the second and third factors. This overlap means that while the design is more efficient, it sacrifices some ability to precisely attribute effects to individual factors or their specific combinations.

Despite this trade-off, with meticulous design and a clear understanding of the system under study, fractional factorial designs can yield significant insights. They are particularly adept at identifying the main effects and certain interactions among the factors, which are often sufficient for preliminary analysis or when certain factors or interactions are suspected to be of lesser importance.

Moreover, fractional factorial designs prove exceptionally useful in scenarios where some factors are presumed to have minimal or no effect, or where certain interactions are deemed negligible. In these cases, the designs can provide nearly as comprehensive information as full factorial designs but at a fraction of the operational cost and effort. This makes fractional factorial designs a highly strategic tool in experimental research, balancing resource management with the acquisition of critical data points necessary for effective decision-making in system optimization and improvement.

Isalos uses a term called “Fraction Relationship” to determine the confounding pattern the user wishes to use. The “Fraction Relationship” is a sequence of strings, separated by spaces, where the $k^{th}$ string specifies how the $k^{th}$ factor is confounded. If a factor is not confounded with any other, it is represented by its corresponding single letter. For example, when conducting an experiment with 5 factors which we denote A, B, C, D and E, a valid “Fraction Relationship” would be “A B C AB AC” which determines that D = AB and E=AC.

Resolution measures the extent to which effects—such as main effects and interactions between factors—can be uniquely estimated without confounding. It is determined by the shortest word in the defining relation of the design, which represents the smallest group of factors whose effects are confounded. The minimum acceptable resolution for a design is Resolution III, as resolutions below this result in main effects being confounded with one another, which is undesirable for meaningful analysis.

To assist users in determining the required “Fraction Relationship,” the software provides a comprehensive list of available designs that deliver maximum resolution for each case. These designs serve as a reliable reference, derived from authoritative sources ^{3, 4, 5}.

Number of Factors	Fraction	Number of Runs	Design Generators	Fraction Relationship	Resolution
3	“1/2”	4	c=ab	a b ab	III
4	“1/2”	8	d=abc	a b c abc	IV
5	“1/2”	16	e=abcd	a b c d abcd	V
	“1/4”	8	d=ab, e=ac	a b c ab ac	III
6	“1/2”	32	f=abcde	a b c d e abcde	VI
	“1/4”	16	e=abc, f=bcd	a b c d abc bcd	IV
	“1/8”	8	d=ab, e=ac, f=bc	a b c ab ac bc	III
7	“1/2”	64	g=abcdef	a b c d e f abcdef	VII
	“1/4”	32	f=abcd, g=abde	a b c d e abcd abde	IV
	“1/8”	16	e=abc, f=bcd, g=acd	a b c d abc bcd acd	IV
	“1/16”	8	d=ab, e=ac, f=bc, g=abc	a b c ab ac bc abc	III
8	“1/2”	128	h=abcdefg	a b c d e f g abcdefg	VIII
	“1/4”	64	g=abcd, h=abef	a b c d e f abcd abef	V
	“1/8”	32	f=abc, g=abd, h=bcde	a b c d e abc abd bcde	IV
	“1/16”	16	e=bcd, f=acd, g=abc, h=abd	a b c d bcd acd abc abd	IV
9	“1/2”	256	i=abcdefgh	a b c d e f g h abcdefgh	IX
	“1/4”	128	h=acdfg, i=bcefg	a b c d e f g acdfg bcefg	VI
	“1/8”	64	g=abcd, h=acef, i=cdef	a b c d e f abcd acef cdef	IV
	“1/16”	32	f=bcde, g=acde, h=abde, i=abce	a b c d e bcde acde abde abce	IV
	“1/32”	16	e=abc, f=bcd, g=acd, h=abd, i=abcd	a b c d abc bcd acd abd abcd	III
10	“1/2”	512	j=abcdefghi	a b c d e f g h i abcdefghi	X
	“1/8”	128	h=abcg, i=bcde, j=acdf	a b c d e f g abcg bcde acdf	V
	“1/16”	64	g=bcdf, h=acdf, i=abde, j=abce	a b c d e f bcdf acdf abde abce	IV
	“1/32”	32	f=abcd, g=abce, h=abde, i=acde, j=bcde	a b c d e abcd abce abde acde bcde	IV
	“1/64”	16	e=abc, f=bcd, g=acd, h=abd, i=abcd, j=ab	a b c d abc bcd acd abd abcd ab	III
11	“1/2”	1024	k=abcdefghij	a b c d e f g h i j abcdefghij	XI
	“1/16”	128	h=abcg, i=bcde, j=acdf, k=abcdefg	a b c d e f g abcg bcde acdf abcdefg	V
	“1/32”	64	g=cde, h=abcd, i=abf, j=bdef, k=adef	a b c d e f cde abcd abf bdef adef	IV
	“1/64”	32	f=abc, g=bcd, h=cde, i=acd, j=ade, k=bde	a b c d e abc bcd cde acd ade bde	IV
	“1/128”	16	e=abc, f=bcd, g=acd, h=abd, i=abcd, j=ab, k=ac	a b c d abc bcd acd abd abcd ab ac	III
12	“1/2”	2048	l=abccdefghijk	a b c d e f g h i j k abccdefghijk	XII
	“1/32”	128	h=acdg, i=abcd, j=bcfg, k=abcdefg, l=cdef	a b c d e f g acdg abcd bcfg abcdefg cdef	IV
	“1/64”	64	g=def, h=abc, i=bcde, j=bcdf, k=abef, l=acef	a b c d e f def abc bcde bcdf abef acef	IV
	“1/128”	32	f=ace, g=acd, h=abd, i=abe, j=cde, k=abcde, l=ade	a b c d e ace acd abd abe cde abcde ade	IV
	“1/256”	16	e=abc, f=abd, g=acd, h=bcd, i=abcd, j=ab, k=ac, l=ad	a b c d abc abd acd bcd abcd ab ac ad	III
13	“1/2”	4096	m=abcdefghijkl	a b c d e f g h i j k l abcdefghijkl	XIII
	“1/64”	128	h=defg, i=bceg, j=bcdfg, k=abdef, l=acef, m=abc	a b c d e f g defg bceg bcdfg abdef acef abc	IV
	“1/128”	64	g=abc, h=def, i=bcdf, j=bcde, k=abef, l=acef, m=bcef	a b c d e f abc def bcdf bcde abef acef bcef	IV
	“1/256”	32	f=ace, g=bce, h=abc, i=cde, j=abcde, k=abe, l=acd, m=ade	a b c d e ace bce abc cde abcde abe acd ade	IV
	“1/512”	16	e=abc, f=abd, g=acd, h=bcd, i=abcd, j=ab, k=ac, l=ad, m=bc	a b c d abc abd acd bcd abcd ab ac ad bc	III
14	“1/2”	8192	n=abcdefghijklm	a b c d e f g h i j k l m abcdefghijklm	XIV
	“1/128”	128	h=efg, i=bcfg, j=bceg, k=abef, l=acef, m=bcdef, n=abc	a b c d e f g efg bcdg bceg abef acef bcdef abc	IV
	“1/256”	64	g=bef, h=bcf, i=def, j=cef, k=bce, l=cdf, m=acde, n=bcdef	a b c d e f bef bcf def cef bce cdf acde bcdef	IV
	“1/512”	32	f=abc, g=abd, h=abe, i=acd, j=ace, k=ade, l=bcd, m=bce, n=bde	a b c d e abc abd abe acd ace ade bcd bce bde	IV
	“1/1024”	16	e=abc, f=abd, g=acd, h=bcd, i=abcd, j=ab, k=ac, l=ad, m=bc, n=bd	a b c d abc abd acd bcd abcd ab ac ad bc bd	III
15	“1/2”	16384	o=abcdefghijklmn	a b c d e f g h i j k l m n abcdefghijklmn	XV
	“1/256”	128	h=abfg, i=acdef, j=bef, k=abcdeg, l=cdfg, m=acdeg, n=efg, o=abdefg	a b c d e f g abfg acdef bef abcdeg cdfg acdeg efg abdefg	IV
	“1/512”	64	g=abc, h=abd, i=abe, j=bcde, k=acf, l=adf, m=aef, n=cdef, o=abcdef	a b c d e f abc abd abe bcde acf adf aef cdef abcdef	IV
	“1/1024”	32	f=abc, g=abd, h=abe, i=acd, j=ace, k=ade, l=bcd, m=bce, n=bde, o=cde	a b c d e abc abd abe acd ace ade bcd bce bde cde	IV
	“1/2048”	16	e=abc, f=abd, g=acd, h=bcd, i=abcd, j=ab, k=ac, l=ad, m=bc, n=bd, o=cd	a b c d abc abd acd bcd abcd ab ac ad bc bd cd	III

Use the Fractional Factorial function by browsing in the top ribbon:

DOE \(\rightarrow\) Screening \(\rightarrow\) Fractional Factorial

Input

Numerical values should be specified in the input datasheet. Fractional factorial design is applied when at least three factors (columns) are specified along with minimum two levels/values (rows).

Configuration

Number of Center Points	Select manually the Number of Center Points to be included in the output list of experiments. There is no minimum requirement or any other limitation.
Number of Blocks	Select manually the Number of Blocks. The lowest value that can get is 1.
Random Standard order	You can tick/select the box if randomness is required in the output list of experiments.
Time-based RNG Seed	If in the randomness is selected, then you have the option to also tick/select the box to set the random generated number seed based on time
RNG Seed	Select manually the random generated number seed if required.
Fraction Relationship	Insert manually the Fraction Relationship to define the desired Fractional Factorial design. The $k^{th}$ independent factor (column) corresponds to the $k^{th}$ letter of the alphabet (The letter “I” is not a special character and should be used for the $9^{th}$ if that exists). Only alphabetical characters, spaces, “+” and “-“ are allowed.
Include/exclude columns	Select manually the columns through the dialog window: Use the buttons to move columns between the Included Columns and Excluded Columns list. Single-arrow buttons will move all selected columns and double-arrow buttons will move all columns.

Output

A list of experiments (combinations) is generated in the output datasheet along with the Block number and the Standard order based on the Fractional Factorial design method selected.

Example

Input

In the input datasheet minimum requirement is to specify three factors (columns) and insert minimum two levels (values) for each factor (column), as shown below.

Configuration

1. Select DOE \(\rightarrow\) Screening \(\rightarrow\) Fractional Factorial.
2. Select the Number of Center Points [1] to be generated in the output list of experiments.
3. Select the Number of Blocks [2]. The lowest value that can be set is 1.
4. Select/tick if required the Random Standard order [3] to imply randomness in the output list of experiments.
5. If randomness is selected either select/tick to generate the number seed for randomness based on time [4] or by manually setting a value [5].
6. Insert the Fraction Relationship [6].
7. Select the columns by clicking on the arrow buttons [9] and moving columns between the Excluded Columns [7] and Included Columns [8] lists.
8. Click on the Execute button [10] to perform Fractional Factorial design method.

Output

A list of experiments (combinations) is generated in the output datasheet along with the Block number based on the Fractional Factorial design method selected. The standard order is provided in Col2.

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References

1. Box, G.E. and Behnken, D.W., Some new three level designs for the study of quantitative variables. Technometrics, 1960. 2(4): p. 455-475. doi.org/10.1080/00401706.1960.10489912.

2. Box, G.E. and Wilson, K.B., On the experimental attainment of optimum conditions, in Breakthroughs in statistics: methodology and distribution. 1992, Springer. p. 270-310. doi.org/10.1007/978-1-4612-4380-9_23.

3. Montgomery, Douglas C. Design and analysis of experiments. John wiley & sons, 2017.

4. Speed, Terry. Statistics for Experimenters: Design, Innovation, and Discovery. 2006.

5. Wu, CF Jeff, and Michael S. Hamada. Experiments: planning, analysis, and optimization. John Wiley & Sons, 2011.

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Version History

Introduced in Isalos Analytics Platform v0.2.4

Instructions last updated on January 2025