Design Of Experiments Ontology
type: Ontology
abstract: This module imports the Statistics module and extends it with constructs necessary for representing design of experiments, including study design objectives, factor-level combinations, design points, and selected design point types used in screening, optimization, robustness testing, and response-surface studies.
license: http://opensource.org/licenses/MIT
imports: Statistics
imports: Core
version IRI: DesignOfExperiments
copyright: Copyright (c) 2022, 2023, 2024, 2025, 2026 Open Applications Group
maturity: Provisional

axial point
type: Class
subclass of: design point
example: In a two-factor central composite design with factorial settings of pH 6.8 and 7.2 and temperature 35 °C and 37 °C, and center settings of pH 7.0 and temperature 36 °C, the design point specifying pH 6.6 and temperature 36 °C is an axial point; the design point specifying pH 7.4 and temperature 36 °C is its paired axial point.
adapted from: https://wolfson.huji.ac.il/purification/PDF/Others/GE_DOE_in_Protein_Production_and_Purification_Handbook.pdf
explanatory note: Axial points, also called star points, occur in pairs for each factor and support estimation of quadratic effects and fitting of second-order response-surface models. Their distance from the design center is commonly denoted α.
first order logic axiom: AxialPoint(x) → DesignPoint(x)
is primitive: true
natural language definition: design point where one factor is set at an extreme high or low level and all other factors are set at their center levels
primitive rationale: There are insufficient constructs to define a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is an 'axial point' then x is a 'design point'

center point
type: Class
subclass of: design point
example: In a two-factor experiment where pH ranges from 6.8 to 7.2 and temperature from 35 °C to 37 °C, the design point specifying pH 7.0 and temperature 36 °C is a center point.
adapted from: https://wolfson.huji.ac.il/purification/PDF/Others/GE_DOE_in_Protein_Production_and_Purification_Handbook.pdf
explanatory note: Center points are commonly included in factorial and response-surface designs to assess overall curvature and, when replicated, to estimate pure error. A difference between the mean response at the center points and the mean response at the factorial points provides evidence that a first-order model may be inadequate. When replicated center-point runs are distributed through the run order, they may also reveal time-related changes in experimental performance.
first order logic axiom: CenterPoint(x) → DesignPoint(x)
is primitive: true
natural language definition: design point where all factors are set at their middle levels
primitive rationale: There are insufficient constructs to define a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is a 'center point' then x is a 'design point'

control point
type: Class
subclass of: design point
example: In a cell-culture design of experiments evaluating alternative feed formulations, the design point specifying the existing platform feed formulation under the standard process settings is included as a control point; it represents the current baseline condition used to compare the new feed formulations and need not be located at the center of the factor ranges.
adapted from: https://www.itl.nist.gov/div898/handbook/index.htm
explanatory note: A control point is a planned condition included in an experimental design to give the experiment a clear point of comparison. In many cases, this is the current or standard process condition, such as an existing platform recipe or standard process setpoints (baseline). In other cases, it may be another deliberately selected condition that is useful for interpreting the experimental results (reference). A control point is not defined by where it lies in the design region. This distinguishes it from a center point, which is defined by the middle levels of the factors. A control point may also be a center point, but only when the selected comparison condition happens to be located at the middle factor levels. Its main purpose is to help interpret how the tested design points differ from a known or selected comparison condition.
first order logic axiom: ControlPoint(x) → DesignPoint(x)
is primitive: true
natural language definition: design point where the factors are set at levels corresponding to a predefined baseline or reference condition
primitive rationale: There are insufficient constructs to define a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is a 'control point' then x is a 'design point'

corner point
type: Class
subclass of: design point
example: Three-factor factorial design investigates agitation speed (low = 100 rpm, high = 200 rpm), feed rate (low = 2 mL/min, high = 6 mL/min), and temperature (low = 35 °C, high = 37 °C). The eight unique combinations of these levels constitute the factorial corner points
adapted from: https://wolfson.huji.ac.il/purification/PDF/Others/GE_DOE_in_Protein_Production_and_Purification_Handbook.pdf
explanatory note: In a factorial design, corner points are the design points at the vertices of the factorial region. At each corner point, every factor is set at either its low or high factorial level. These points provide the principal contrasts for estimating main effects and interactions and delimit the factorial region represented by the selected low and high levels.
first order logic axiom: CornerPoint(x) → DesignPoint(x)
is primitive: true
natural language definition: design point located at a vertex of the region defined by the studied factor levels
primitive rationale: There are insufficient constructs to define a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is a 'corner point' then x is a 'design point'

design point
type: Class
subclass of: InformationContentEntity
subclass of: Restriction
  on property: BFO_0000110
  some values from: Class
    intersection of: STATO_0000265
    intersection of: Restriction
      on property: IAO_0000136
      some values from: OBI_0000750
subclass of: Restriction
  on property: BFO_0000177
  some values from: OBI_0500000
example: In a two-factor factorial design, temperature is studied at 35 °C and 37 °C and pH at 6.8 and 7.2; the design point with coded levels Temperature = −1 and pH = +1 specifies the planned condition Temperature = 35 °C and pH = 7.2; separate study runs may concretize this same design point when the condition is replicated.
adapted from: https://wolfson.huji.ac.il/purification/PDF/Others/GE_DOE_in_Protein_Production_and_Purification_Handbook.pdf and https://www.fda.gov/media/71535/download
counter example: Randomly adjusting pH between 6.5 and 7.5 without a predefined plan does not create design points, since the conditions are not predetermined by a structured experimental design.
explanatory note: 1) A design point specifies the planned factor levels for the independent variables that define one study condition. In some designs, independent variables may be assigned at different experimental-unit levels, such as whole-plot factors and subplot factors in a split-plot design. Depending on the study design, a design point may also include assignments for blocking variables or other nuisance variables when these are explicitly represented as part of the planned condition. 2) In DoE contexts, design points enable systematic study of main effects, interactions, and, where supported by the design type, curvature in the response surface. Depending on the design, design points may include corner points, center points, axial points, or other structured factor-level combinations. Replicate runs at a design point support estimation of variability and increase confidence in the observed response.
first order logic axiom: DesignPoint(x) → InformationContentEntity(x) ∧ ∃s(StudyDesign(s) ∧ continuantPartOfAtAllTimes(x,s) ∧ ∀v((StudyDesignIndependentVariable(v) ∧ declares(s,v)) → ∃f(FactorLevel(f) ∧ hasContinuantPartAtAllTimes(x,f) ∧ isAbout(f,v) ∧ ∀g((FactorLevel(g) ∧ hasContinuantPartAtAllTimes(x,g) ∧ isAbout(g,v)) → g=f))) ∧ ∀f((FactorLevel(f) ∧ hasContinuantPartAtAllTimes(x,f)) → ∃v(StudyDesignIndependentVariable(v) ∧ declares(s,v) ∧ isAbout(f,v))))
is primitive: true
natural language definition: information content entity that is a combination of planned factor levels, with one factor level specified for each independent variable declared by a study design
primitive rationale: There are insufficient constructs to define a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is a 'design point' then x is an 'information content entity' that is a 'continuant part of at all times' some 'study design', for every 'study design independent variable' declared by that study design x 'has continuant part at all times' exactly one 'factor level' that 'is about' that variable, and every 'factor level' that x 'has continuant part at all times' 'is about' a 'study design independent variable' declared by that same 'study design'

edge point
type: Class
subclass of: design point
example: In a three-factor formulation study with excipient concentration levels of 2 %, 4 %, and 6 %, temperature levels of 20 °C, 25 °C, and 30 °C, and relative-humidity levels of 40 %, 55 %, and 70 %, the design point specifying 4 % excipient concentration, 20 °C, and 70 % relative humidity is an edge point.
adapted from: https://wolfson.huji.ac.il/purification/PDF/Others/GE_DOE_in_Protein_Production_and_Purification_Handbook.pdf
explanatory note: At an edge point, one factor is set at its middle level and the remaining factors are set at high or low levels. In a three-factor Box–Behnken design, the non-center design points are edge points. Edge points can support estimation of interaction and quadratic effects without including the corner points of the studied region.
first order logic axiom: EdgePoint(x) → DesignPoint(x)
is primitive: true
natural language definition: design point where one factor is set at its middle level and all other factors are set at high or low levels
primitive rationale: There are insufficient constructs to define a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is an 'edge point' then x is a 'design point'

one factor at a time design
type: Class
subclass of: OBI_0500000
subclass of: Restriction
  on property: BFO_0000110
  some values from: STATO_0000005
example: A cell-culture study in which separate series of runs are performed to vary pH, temperature, and agitation rate individually; all other parameters remain fixed at the same baseline condition; A cell-culture study that first varies pH while keeping temperature and agitation constant; after selecting the optimal pH, temperature is varied in a subsequent series of runs
abbreviation: OFAT design
adapted from: http://purl.obolibrary.org/obo/PROCO_0000275 and https://www.6sigma.us/six-sigma-in-focus/ofat-one-factor-at-a-time/ and https://www.itl.nist.gov/div898/handbook/pri/section2/pri212.htm
counter example: A screening experiment where pH and feed rate are both changed in each run according to a fractional factorial design matrix; A time-course experiment in which pH, temperature, and agitation are adjusted dynamically within a single run
explanatory note: 1) The principle of an OFAT design is to vary one controlled factor through a sequence of levels while maintaining all other controlled factors at fixed baseline settings. That is, each experimental run corresponds to one experimental configuration that differs from the baseline only in the value assigned to the varied factor. 2) An OFAT design permits observation of response changes associated with one-factor changes at specified baseline settings, but it does not estimate interactions and the observed factor effect may depend on the baseline levels of the other factors. 3) OFAT designs may be used for simple process tuning, range finding, or troubleshooting when interaction effects are not a study objective. They are generally less informative than multivariable designs for screening or optimization. 4) Sequential OFAT approaches may update the baseline after identifying a favorable level for one factor and then proceed to vary another factor; the defining characteristic remains that only one factor changes per experimental sequence. 5) In an OFAT design, the dependent variable or response is declared at the level of the overall study design, while each single factor design represents a separate experimental sequence varying one selected independent variable. This allows the sequences to be interpreted as coordinated parts of one study, rather than unrelated single factor studies.
first order logic axiom: OneFactorAtATimeDesign(x) → StudyDesign(x) ∧ ∃s (SingleFactorDesign(s) ∧ continuantPartOfAtAllTimes(s, x))
is primitive: true
natural language definition: study design composed of single factor designs, each of which investigates a different selected factor while other relevant factors are held fixed
primitive rationale: There are insufficient constructs present to create a set of necessary and sufficient conditions
semi formal natural language axiom: if x is a 'one factor at a time design' then x is a 'study design' and x 'has continuant part at all times' some 'single factor design'

study design objective
type: Class
subclass of: ObjectiveSpecification
subclass of: Restriction
  on property: BFO_0000177
  some values from: OBI_0500000
example: objective to determine which process parameters significantly influence product yield
explanatory note: A study design objective defines what the study is intended to accomplish, such as identifying influential factors, determining optimal conditions, or verifying process robustness. It provides the rationale for selecting the design type, factors, ranges, and responses, ensuring that the experimental structure aligns with the intended analytical or process-development goal.
first order logic axiom: StudyDesignObjective(x) → ObjectiveSpecification(x) ∧ ∃y(continuantPartOfAtAllTimes(x, y) ∧ StudyDesign(y))
is primitive: true
natural language definition: objective specification that prescribes the purpose of a study design in relation to its declared variables
primitive rationale: There are insufficient constructs to determine a set of necessary and sufficient conditions
semi formal natural language axiom: if x is a 'study design objective' then x is an 'objective specification' and x is a 'continuant part of at all times' some 'study design'

study design optimization objective
type: Class
subclass of: study design objective
example: Determining the load density, residence time, and wash pH that maximize step yield while maintaining predefined host-cell-protein clearance in a protein A capture step
adapted from: https://wolfson.huji.ac.il/purification/PDF/Others/GE_DOE_in_Protein_Production_and_Purification_Handbook.pdf
explanatory note: Optimization objectives are used to estimate and model the quantitative relationships between selected independent variables and dependent variables. The goal is to find the factor settings that maximize or minimize the desired responses within the studied region. When multiple dependent variables are optimized simultaneously, trade-offs may be required. The predicted optimum is typically verified through confirmatory runs.
first order logic axiom: StudyDesignOptimizationObjective(x) → StudyDesignObjective(x)
is primitive: true
natural language definition: study design objective that prescribes determining the combination of independent variable values under which the values of one or more dependent variables are optimal according to specified criteria
primitive rationale: There are insufficient constructs to determine a set of necessary and sufficient conditions
semi formal natural language axiom: if x is a 'study design optimization objective' then x is a 'study design objective'

study design resolution
type: Class
subclass of: InformationContentEntity
subclass of: Restriction
  on property: describes
  some values from: OBI_0500000
example: Study design resolution with the value IV describes a fractional factorial design in which main effects can be estimated separately from two-factor interactions but not all two-factor interactions can be distinguished from each other.
adapted from: https://wolfson.huji.ac.il/purification/PDF/Others/GE_DOE_in_Protein_Production_and_Purification_Handbook.pdf
explanatory note: 1) Study design resolution summarizes the aliasing structure of a regular fractional factorial design. Higher resolution indicates that lower-order effects are aliased only with higher-order effects, but usually requires more runs. 2) Resolution is commonly written as a Roman numeral. In a resolution III design, main effects are aliased with two-factor interactions. In a resolution IV design, main effects are not aliased with two-factor interactions, although two-factor interactions may be aliased with one another. In a resolution V design, no main effect or two-factor interaction is aliased with another main effect or two-factor interaction, although two-factor interactions may be aliased with three-factor interactions.
first order logic axiom: StudyDesignResolution(x) → InformationContentEntity(x) ∧ ∃y (describes(x, y) ∧ StudyDesign(y))
is primitive: true
natural language definition: information content entity that describes the degree to which a study design distinguishes different factor effects and interaction effects based on its confounding structure
primitive rationale: There are insufficient constructs to define a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is a 'study design resolution' then x is an 'information content entity' and x 'describes' some 'study design'

study design robustness testing objective
type: Class
subclass of: study design objective
example: Testing whether small adjustments in buffer pH and flow rate (independent variables) meaningfully affect product yield (dependent variable).
adapted from: https://wolfson.huji.ac.il/purification/PDF/Others/GE_DOE_in_Protein_Production_and_Purification_Handbook.pdf
explanatory note: Robustness testing evaluates whether specified small variations in process or analytical-procedure parameters materially affect performance. Robustness is supported when the relevant responses continue to meet predefined performance or acceptance criteria across the studied variations.
first order logic axiom: StudyDesignRobustnessTestingObjective(x) → StudyDesignObjective(x)
is primitive: true
natural language definition: study design objective that prescribes assessing the sensitivity of one or more dependent variables to specified small variations in independent variables
primitive rationale: There are insufficient constructs to determine a set of necessary and sufficient conditions
semi formal natural language axiom: if x is a 'study design robustness testing objective' then x is a 'study design objective'

study design run
type: Class
subclass of: PlannedProcess
equivalent class: Class
  intersection of: PlannedProcess
  intersection of: Restriction
    on property: BFO_0000059
    some values from: design point
  intersection of: Restriction
    on property: BFO_0000132
    some values from: OBI_0000471
example: In a cell-culture DoE used to study pH, temperature, and feed concentration, each bioreactor culture performed at one planned combination of those factor levels is a study run; In a media optimization study, each shake-flask culture prepared with one planned medium formulation is a study run; In a single factor pH study, each culture performed at one planned pH level while temperature, inoculum density, and feed conditions are held fixed is a study run; In a chromatography optimization study, each column operation performed at one planned combination of load density, flow rate, and buffer pH is a study run;
explanatory note: 1) Saying that the factor levels are applied means that the run is set up or operated using those planned levels, for example by setting pH, temperature, feed concentration, agitation rate, buffer pH, resin load, or medium composition to the levels specified by the design point. Multiple study runs may apply the same design point when the study includes replicates. 2) In a split-plot design, each study design run is the process performed on an experimental unit under the complete combination of whole-plot and subplot factor levels specified by its design point. A containing whole-plot process may establish a factor level shared by several nested study design runs without itself being a study design run unless it applies one complete design point.
first order logic definition: StudyDesignRun(x) ↔ PlannedProcess(x) ∧ ∃e∃s∃d(StudyDesignExecution(e) ∧ StudyDesign(s) ∧ DesignPoint(d) ∧ occurrentPartOf(x,e) ∧ prescribedBy(e,s) ∧ continuantPartOfAtAllTimes(d,s) ∧ concretizesAtSomeTime(x,d) ∧ ∀d1((DesignPoint(d1) ∧ concretizesAtSomeTime(x,d1)) → d1=d))
natural language definition: planned process that is an occurrent part of a study design execution and in which the factor levels of a single design point are applied
semi formal natural language definition: every instance of 'study design run' is defined as exactly an instance of 'planned process' that is an 'occurrent part of' some 'study design execution' prescribed by a 'study design' and 'concretizes at some time' exactly one 'design point' that is a 'continuant part of at all times' that same 'study design'

study design screening objective
type: Class
subclass of: study design objective
example: Identifying which buffer components significantly affect product purity in an affinity chromatography step.
adapted from: https://wolfson.huji.ac.il/purification/PDF/Others/GE_DOE_in_Protein_Production_and_Purification_Handbook.pdf
explanatory note: Screening objectives are used to reduce a larger set of candidate factors to those warranting further study based on estimated effects, uncertainty, and scientific or practical relevance. Screening results commonly inform a subsequent characterization or optimization study and do not by themselves establish causality or criticality.
first order logic axiom: StudyDesignScreeningObjective(x) → StudyDesignObjective(x)
is primitive: true
natural language definition: study design objective that prescribes identifying which independent variables impact one or more dependent variables
primitive rationale: There are insufficient constructs to determine a set of necessary and sufficient conditions
semi formal natural language axiom: if x is a 'study design screening objective' then x is a 'study design objective'