Proven acceptable range (PAR) and normal operating · PDF fileProven acceptable range (PAR)...

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Background
Terminology
Nature of Design Space
Models, Predictions and Sources of Uncertainty
Effect on Design Space.
Presentation Overview
Effect on Design Space.
Components of the Robust Analysis.
Models of Probability
Interval types.
Effect of interval type on Design Space.
How to define Proven Acceptable Ranges (PAR)
Prerequisites.
Three approaches of communication.

The concept of Design Space has been defined in ICH Q8 (R2).
it is expected that operation within the design space will result in a product meeting the defined quality attributes.
A closely related idea to the Design Space concept is the notion of Proven
Acceptable Ranges (PAR) for a set of process variables.
Background
Acceptable Ranges (PAR) for a set of process variables.
ICH Q8 defines PAR as a characterized range of a process parameter for
which operation within this range, while keeping other parameters constant,
will result in producing a material meeting relevant quality criteria.
A definition of preferred PAR may be derived from a robust Design Space
description.
Various factor choices will affect the Design Space description and PAR.

Knowledge Space = Region investigated using an experimental design.
Design Space = Smaller space within the Knowledge Space. Defined by our model y=f(x).
Knowledge Space - Design Space PAR/NOR
Defined by our model y=f(x).
Area/volume where y is according to specifications.
Includes estimates of uncertainties.
Normal Operating Space (NOR) = Smaller space within the Design Space.

Nature of Design Space

MODELS, PREDICTIONS AND SOURCES OF UNCERTAINTY

Model Predictions Y1
Y2Y=f(X)+e
Y = b0 + b1X1 + b2X2 + b12X1X2 + b11X12 + b22X2
2 + e
The model complexity that can be used is given by the selected DESIGN.
x1 = Salt
x2 = EtOH
Y/Quality Attribute = Yield

Example: Plots three responses in overlay.
In green region all responses are within specification.
No assessment of risk.
Model Predictions -
Quality Attributes in Combination

Models and Prediction Error
Salt (210) = Yield (62.3) +/- 4.5Salt (210, +/- 10) = Yield (62.3) +/- 8.2

Coefficients
Incorrect model
Sources of Uncertainty
y = + x + x + x x + x 2 + x 2 +
Noise in Y
Measurement noise
Non measured influences
Model error
y = 0 + 1x1 + 2x2 + 12x1x2 + 11x12 + 22x2
2 +
Factors
Precision in settings
-4 SD
4 SD
Norm
al probability

The probability estimation: Presents low risk region in a Sweet Spot type plot.
The probability acceptance region = a good estimation of Design Space.
Average Prediction versus
Probability Prediction

Components of the Robust Analysis
Process variability, e.g. reproducibility of actual process.
Uncertainties/variability in measurement systems (both X and Y).
Variation in the X parameters around their targets.
Variation in X parameters due to adaptive control strategies (if applied).

MODELS OF PROBABILITY

Confidence interval Average prediction interval. Encloses the average of the sample population. Requires an acceptance level (~probability), usually expressed as the Confidence
Level (90%, 95%, 99%). Mainly used to illustrate the variance of the model coefficients.
Prediction interval Next observation interval. Encloses a region within which we are confident that the next observation will fall. Requires an acceptance level (~probability), usually expressed as the Confidence
Models of Probability Uncertainty Estimates
Prediction distribution
Interval distributions
Requires an acceptance level (~probability), usually expressed as the Confidence Level (90%, 95%, 99%).
Tolerance interval Next population interval. Encloses a region within which we are confident that some proportion of future
samples will fall. Requires an acceptance level (~probability), usually expressed as the Confidence
Level (90%, 95%, 99%). Requires a Tolerance Proportion (fraction of future samples that will fall within the
interval).
The default setting in MODDE Pro 11 for evaluation of model parameters is a 95 % Confidence Level on the Confidence Interval. The default setting for Design Space is a 99% Confidence Level on the Prediction Interval.
Size of design space
decreases!

Design Space - Tutorial decoaded (MLR)
Probability of failure (%) for Y1, Y2 and Y3 - Optimizer Setpoint (R)
5-1
0
%
50
Design Space
using Confidence Interval versus Prediction Interval
Design Space - Tutorial decoaded prediction (MLR)
Probability of failure (%) for Y1, Y2 and Y3 - Optimizer Setpoint (R)
5 10
-1
0
%
50Confidence
Interval
Prediction
Interval0.5
1
210
50
-5
-4
-3
-2
6 7 8 9 10 11 12
X2No distribution on factors. Interval=Confidence Limit = 1%.
0.5
1
2
5
10
X1 = 252
0.5
1
2
5 10
50
-5
-4
-3
-2
6 7 8 9 10 11 12
X2No distribution on factors. Interval=Prediction Limit = 1%.
0.5
1
2
5
10
X1 = 251
Interval Interval

a characterized range of a process
parameter for which operation within this
range, while keeping other parameters
constant, will result in producing a material
meeting relevant quality criteria (ICH Q8,
definition of PAR)
HOW TO DEFINE PAR

Design Space:Proper description of the Design
Space.
Prerequisites for PAR
Robust Setpoint: From all Design Space boundaries
in combination. Robust Setpoint

The Design Space Regular Hypercube

Approach I Based on the robust setpoint.
Approach II Based on the hypercube inside the design space.
Approach III Based on a distribution around a setpoint.
Communication of PAR

Approach I

Approach II

Approach III Setpoint Analysis

Alternative Setpoints

Design Space - usually a highly irregular multidimensional region.
With the use of Monte Carlo simulations, MODDE can estimate an irregular multidimensional design space.
The size and shape of a Design Space will vary considerably based on how it has been estimated. This will have a direct effect on NOR and/or PAR estimation. Consideration of sources of uncertainty.
Conclusion
Type of uncertainty interval used.
New functionality in MODDE facilitate Design Space definition and communication of PAR. Perturbations can be considered in the Design Space estimate. Uncertainties in the models, process factors and interval type. Three approaches of PAR communication.
Easy to manage and communicate yielding powerful
conclusions using the Umetrics Suite MODDE PRO Software!

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