Proven acceptable range (PAR) and normal
operating range (NOR)
how to estimate and define in a complex
multidimensional context
IFPAC 2016
Anna Persson
Conny Vikström
Change a little. Grow a lot.
Presentation Overview
Background
Terminology
Nature of Design Space
Models, Predictions and Sources of Uncertainty
– 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.
Background
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.
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 - Design Space – PAR/NOR
Knowledge Space = Region
investigated using an experimental
design.
Design Space = Smaller space
within the Knowledge Space.
– 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
Y2
Y=f(X)+e
Y = b0 + b1X1 + b2X2 + b12X1X2 + b11X12 + b22X22 + e
The model complexity that can be used is given by the selected DESIGN.
x1 = Salt
x2 = EtOH
Y/Quality Attribute = Yield
Model Predictions Quality Attributes in Combination
Example:
– Plots three responses in overlay.
– In green region all responses are
within specification.
– No assessment of risk.
Models and Prediction Error
Salt (210) = Yield (62.3) +/- 4.5
Salt (210, +/- 10) = Yield (62.3) +/- 8.2
Sources of Uncertainty
Noise in Y
Coefficients
Incorrect model
Measurement noise
Non measured influences
Model error
Factors
Precision in settings
Normal probability
4 SD
-4 SD
y = β0 + β1x1 + β2x2 + β12x1x2 + β11x12 + β22x22 + ε
Average Prediction versus
Probability Prediction
The probability estimation:
– Presents low risk region in a Sweet Spot type plot.
– The probability acceptance region = a good estimation of Design Space.
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
Models of Probability – Uncertainty Estimates
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
Level (90%, 95%, 99%).
Prediction distribution
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).
Interval distributions
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
using Confidence Interval versus Prediction Interval
%
Design Space - Tutorial decoaded (MLR)
Probability of failure (%) for Y1, Y2 and Y3 - Optimizer Setpoint (R)
%
Design Space - Tutorial decoaded prediction (MLR)
Probability of failure (%) for Y1, Y2 and Y3 - Optimizer Setpoint (R)
0
0
5
-1
0.5 2
-2
10
Confidence
Interval
50
-1
5
10
10
-2
Prediction
Interval
50
10
2
1
50
-3
50
0.5
5
5
-3
-4
2
-4
1
-5
2
1
-5
6
7
8
9
10
X2
No distribution on factors. Interval=Confidence Limit = 1%.
11
12
0.5
X1 = 252
1
6
7
8
9
10
X2
No distribution on factors. Interval=Prediction Limit = 1%.
11
12
0.5
X1 = 251
“…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
Prerequisites for PAR
Design Space:
Proper description of the Design
Space.
Robust Setpoint:
From all Design Space boundaries
in combination.
Robust
Setpoint
The Design Space Regular Hypercube
Communication of PAR
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.
Approach I
Approach II
Approach III – Setpoint Analysis
Alternative Setpoints
Conclusion
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.
– 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!
Thank you for your time!
Change a little. Grow a lot.