Explainer8 min readJuly 15, 2026

Design Space, NOR and PAR: ICH Q8 Explained

Q: Can I derive a design space from historical process data instead of a DoE?

Partly. With 30 historical runs, `covaopt_train_models` reached cross-validated Q-squared 0.80 for yield and 0.72 for purity, and `covaopt_design_space` produced per-factor NORs by Monte Carlo. But historical data is unbalanced and correlated, so the resulting window is often very narrow and the tool flagged the joint 90% yield plus 98% purity criterion as aggressive. Treat it as process understanding that tells you which experiments to run next.

Q: Why did my design space come back as the full factor range?

Usually a wrong key or a missing acceptance criterion. `covadoe_design_space` expects `spec_lower` / `spec_upper`; passing `lower` / `upper` instead makes it return probability 1.0 and the untrimmed range, which looks like a perfect result. Any design space reported as 100% passing over the whole factor space should be treated as a configuration error until proven otherwise.

ICH Q8 design space, NOR and PAR defined precisely, with real CovaDOE and CovaOPT tool output showing what a tighter spec costs you in operating window.

Oliver Kraft

CovaSyn

Design Space, NOR and PAR: ICH Q8 Explained

Most design space sections in a filing are a picture of a contour plot and a sentence that says "the design space is the shaded region". That does not survive a question. A reviewer wants to know which ranges you claim, what acceptance criterion defines them, and what happens at the edges. This article defines design space, NOR and PAR precisely, then shows with real tool output what a tighter specification costs you in operating window.

The three terms, defined

ICH Q8(R2) is short on numbers and long on definitions. Here they are, in the order a practitioner needs them.

Design space

is the multidimensional combination of input variables and process parameters that has been demonstrated to provide assurance of quality. It is multidimensional. It is not a list of per-factor ranges. Working within it is not a change; moving out of it is. The design space is what you propose and what the regulator approves.

PAR (Proven Acceptable Range)

is a characterised range of one parameter, for which operation within that range, *while holding other parameters constant*, will result in a product meeting the relevant quality attribute. That "while holding other parameters constant" clause is the whole point. A collection of PARs is univariate. It is not a design space, and Q8(R2) says so explicitly.

NOR (Normal Operating Range)

is the tighter band you actually run in day to day. It sits inside the PAR and inside the design space, with deliberate headroom so that ordinary process variability does not push you to the edge. NOR is a control-strategy decision, not a science decision.

The nesting is: setpoint sits inside NOR, NOR sits inside PAR, PAR is a univariate slice through the design space.

Where the numbers come from

Two routes to a defensible region. Designed experiment plus response surface: run a structured design, fit an explicit model, interrogate the surface. Best when you can afford the runs and want confidence intervals you can defend. Model over existing process data: fit and cross-validate models on historical runs, derive ranges by Monte Carlo. Best when the runs already happened.

Below, one worked example of each. Every number is a verbatim return from the named tool.

Worked example 1: PAR from a response surface (CovaDOE)

A three-factor catalytic step: temperature, catalyst loading, time, response = yield.

covadoe_create_design built an 18-run central composite design (8 factorial, 6 axial, 4 centre points), rotatable with alpha = 2.236. covadoe_fit_rsm fitted the quadratic model: R-squared 0.9988, adjusted 0.9974, every term significant at p < 1e-4.

covadoe_find_optimum and covadoe_predict located the optimum at 91.2 C, 3.76 mol% catalyst, 9.7 h, predicting 93.5% yield with a 95% confidence interval of 93.16-93.76% and a prediction interval of 92.73-94.20%. Note the gap between the two intervals: the CI is about the mean response, the PI is about the next single batch. Quote the PI when someone asks what one run will do.

Then covadoe_design_space sampled 10,000 Monte Carlo points across the factor space at two different acceptance criteria.

Acceptance criterion	Temperature	Catalyst	Time	Fraction of space passing
Yield >= 90%	69.9-112.1 C	1.4-6.0 mol%	4.6-14.5 h	10.6%
Yield >= 92%	80.5-101.2 C	2.55-5.01 mol%	7.1-12.0 h	3.05%

Two percentage points of extra yield specification cut the acceptable temperature window from 42.2 C wide to 20.7 C wide, the catalyst window from 4.6 to 2.46 mol%, and the passing fraction of the sampled space from 10.6% to 3.05%, a 3.5-fold reduction. Nothing about the chemistry changed. Only the line you drew changed. That is the number to put in front of whoever is proposing the tighter internal limit: a spec is a purchase, and the currency is operating window.

Two practitioner notes. covadoe_residual_diagnostics ran Shapiro-Wilk (p 0.036) and Cook's distance on the same fit and flagged run 9 (Cook's D 0.277) as a leverage point - run the diagnostics before you quote ranges from a model with an unexamined influential point. And covadoe_design_space expects the keys spec_lower / spec_upper; pass lower / upper by mistake and it silently returns probability 1.0 and the full range, which looks like a wonderful result and is not one.

Worked example 2: NOR from process data (CovaOPT)

Different situation: 30 runs of a Pd-catalysed coupling already exist (temperature, catalyst loading, base equivalents, time, giving yield and purity). No new experiments budgeted.

covaopt_validate_data scored data quality 75/100 ("good"), 0 missing, 0 duplicates. covaopt_train_models returned cross-validated Q-squared 0.80 for yield (ridge poly-2) and 0.72 for purity (random forest), both passing Breusch-Pagan heteroscedasticity checks at p 0.28 and 0.21.

covaopt_optimize returned a setpoint of 83.8 C, 1.29 mol% Pd, 2.14 eq base, 11.8 h, predicting 91.0% yield at 98.0% purity, desirability 0.68, feasibility probability 0.96, with the hard purity >= 98 constraint satisfied (violation 0.0).

covaopt_design_space then derived the NOR per factor by Monte Carlo against the joint criterion yield >= 90% *and* purity >= 98%:

catalyst 1.21-1.32 mol%
base 2.01-2.15 eq
time 11.5-12.2 h
temperature effectively pinned at the setpoint

Catalyst is plus or minus about 0.055 mol% around the setpoint. The tool flagged the joint 90/98 target as aggressive, and that flag is the useful output: this process, as understood from these 30 runs, has almost no simultaneous headroom on yield and purity. The correct response is more experiments in the right place, or a renegotiated joint spec - not a NOR of 1.21-1.32 mol% in a batch record. Same Monte Carlo machinery as example 1, but a joint two-response criterion collapses the window far harder than either spec alone. Joint specifications multiply, they do not average.

A joint yield and purity criterion collapses the window far harder than either spec alone. Catalyst at plus or minus 0.055 mol% is a signal to run more experiments, not a NOR for a batch record. Source: Setpoint from covaopt_optimize, ranges from covaopt_design_space, on a representative 30-run Pd-coupling dataset modelled by covaopt_train_models at cross-validated Q-squared 0.80 for yield and 0.72 for purity. Representative data, not a customer batch record; the tool itself flagged the joint 90/98 criterion as aggressive.

How to actually set NOR inside PAR

A workable sequence:

1. Establish the acceptance criterion first, in writing, before you look at any ranges. Yield >= 90% and yield >= 92% are different projects. 2. Derive the PAR from the fitted model at that criterion (example 1). 3. Measure your real process variability - covaopt_process_capability returned I-MR control limits of 72.3-98.9% with 0 of 8 Nelson rules tripped and zero out-of-spec on the coupling dataset above. That spread is what your NOR has to absorb. 4. Set the NOR so that normal variability stays inside the PAR with margin, then confirm the edges experimentally. 5. Only then propose the design space, and propose it as a region, not as a stack of independent ranges.

Step 3 is where "in control" and "capable" separate. That same process had a mean yield of 85.6% against a 90% target: perfectly stable, and 4.4 points short. Stability tells you nothing about whether the NOR you drew is achievable.

Honest limits

What this does not tell you:

A Monte Carlo design space is a model prediction, not evidence. The 10,000-sample pass rates above describe the fitted surface. The edges of a claimed region still need confirmation runs. Q8 wants demonstrated assurance of quality.
Simulated responses in example 1. The 18-run CCD is a real design and every output (R-squared, optimum, intervals, ranges, diagnostics) is a genuine tool computation - but the per-run yields were simulated from a quadratic surface with noise to stand in for lab measurements. The example demonstrates the method, not a specific chemistry.
The CovaOPT dataset is representative, not a customer batch. 30 rows of a Pd-coupling surface. Q-squared 0.80 is a decent model on 30 runs; it is not a validated one.
No Cpk claim. In that deployment covaopt_process_capability received null spec limits and emitted no numeric Cpk. It reported statistical control only.
Per-factor ranges hide correlation. PARs are univariate by definition. If your factors interact - and in example 1 they do - the true acceptable region is not the box formed by the individual ranges.
This is decision support. It tells you where to run the confirmation experiments and what a spec change costs. It does not replace validated wet-lab work, and it is not a filing.

Frequently asked questions

What is the difference between NOR and PAR?

A PAR (Proven Acceptable Range) is the characterised range of one parameter over which product quality is still met, holding other parameters constant. A NOR (Normal Operating Range) is the narrower band you actually operate in day to day, set inside the PAR with deliberate headroom so routine process variability does not reach the edge. PAR comes from experimental and model evidence; NOR is a control-strategy choice.

Is a set of proven acceptable ranges a design space?

No. ICH Q8(R2) is explicit that a combination of PARs is not a design space, because each PAR is established with the other parameters held constant. A design space is multidimensional and accounts for interactions. If your factors interact, the true acceptable region is not the rectangular box formed by stacking individual PARs, and a reviewer can ask you to show that.

How much operating window does a tighter specification cost?

It can cost far more than the spec change suggests. In a CovaDOE example, covadoe_design_space over 10,000 Monte Carlo samples returned a temperature PAR of 69.9-112.1 C at yield >= 90%, shrinking to 80.5-101.2 C at yield >= 92%. The fraction of the sampled space passing fell from 10.6% to 3.05%, a 3.5-fold reduction, for two percentage points of yield.

How many experiments do I need to define a design space?

For three factors, an 18-run central composite design (8 factorial, 6 axial, 4 centre) was enough to fit a quadratic model at R-squared 0.9988 in the CovaDOE example above. Centre-point replication is what gives you the pure-error estimate and therefore the confidence intervals. Fewer runs is possible with a definitive screening design, but you trade curvature resolution for run count.

Can I derive a design space from historical process data instead of a DoE?

Partly. With 30 historical runs, covaopt_train_models reached cross-validated Q-squared 0.80 for yield and 0.72 for purity, and covaopt_design_space produced per-factor NORs by Monte Carlo. But historical data is unbalanced and correlated, so the resulting window is often very narrow and the tool flagged the joint 90% yield plus 98% purity criterion as aggressive. Treat it as process understanding that tells you which experiments to run next.

Why did my design space come back as the full factor range?

Usually a wrong key or a missing acceptance criterion. covadoe_design_space expects spec_lower / spec_upper; passing lower / upper instead makes it return probability 1.0 and the untrimmed range, which looks like a perfect result. Any design space reported as 100% passing over the whole factor space should be treated as a configuration error until proven otherwise.