# Accelerated stability models compared — Arrhenius, ASAP, AccelStab & probabilistic decisioning

> Equations and assumptions of the four model families — classic Arrhenius/MKT, ASAP's humidity-corrected Arrhenius, the Šesták–Berggren AccelStab R package, and Synlogica's probabilistic Arrhenius + Monte-Carlo — compared side by side, and when each answers a development shelf-life question vs an operational release decision.

- Type: White paper · v1.0 · Jun 2026 · 12 pages · 16 min read
- Author: Adam Karpiński, Synlogica
- Canonical: https://synlogica.ai/resources/stability-models-compared/

## 1. Executive summary

Four families of model dominate accelerated and predictive stability work in pharma: the **classic Arrhenius** equation, the ** humidity-corrected Arrhenius** used by the ** Accelerated Stability Assessment Program (ASAP)**, the **Šesták–Berggren** kinetic approach implemented in the open-source ** AccelStab** R package, and the ** probabilistic Arrhenius + Monte-Carlo** approach Synlogica Terminus Quality uses for excursion decisioning.

They are often discussed as competitors. They are not. Three of them (Arrhenius, ASAP, AccelStab) answer a *development* question — *"what shelf-life can I claim from a short, stressed study?"* — while Synlogica answers an *operational* question — *"given this product's already-characterised kinetics and this actual logger trace, is this batch releasable, and with what confidence?"* This paper states each model's equations and assumptions plainly, compares them, and shows where each belongs.

**Bottom line** Every method here rests on Arrhenius. They differ in (a) whether they model humidity, (b) how they describe the degradation curve, (c) how they quantify uncertainty, and (d) whether their job is shelf-life prediction or release decisioning. Pick by the question you are answering, not by which is "newest".

## 2. The shared foundation — Arrhenius

All four approaches inherit the Arrhenius temperature dependence of the degradation rate constant *k*:

**k(T)** = A · exp(−** Ea** / (R · T))

**A** = pre-exponential factor · ** Ea** = activation energy (≈60–120 kJ/mol for small molecules)

**R** = 8.314 J/(mol·K) · ** T** = absolute temperature (K)

What they add on top of this base equation — a humidity term, a non-linear degradation form, an uncertainty model — is exactly what distinguishes them.

## 3. Classic Arrhenius & MKT

The traditional approach fits *k* at several elevated temperatures, extrapolates to the storage condition, and reports a single shelf-life. For non-isothermal exposure (e.g. a distribution excursion) it is often collapsed to **Mean Kinetic Temperature (MKT)**:

**TK** = (Ea/R) / −ln( ( Σ e^−Ea/RTi ) / n )

**Assumptions:** one dominant, rate-limiting degradation reaction; Ea constant across the whole temperature range; simple (zero- or first-order) kinetics; humidity either irrelevant or held constant; the sensor temperature equals the product temperature.

**Limits:** produces a point estimate that hides uncertainty in Ea, in sensor calibration and in spatial inhomogeneity; MKT discards the shape of the excursion; no humidity term; breaks down when the degradation mechanism changes with temperature.

## 4. ASAP — humidity-corrected Arrhenius

The **Accelerated Stability Assessment Program** (Waterman et al.) extends Arrhenius with an explicit, log-linear humidity term and uses an *isoconversional* design: hold products at several temperature/relative-humidity combinations for days to weeks, measure time-to-a-fixed-degradation-level, and fit:

ln **k** = ln A − ** Ea**/(R·T) + ** B** · RH

**RH** = relative humidity (%) · ** B** = humidity sensitivity coefficient

Shelf-life and its confidence interval are then propagated by Monte-Carlo simulation over the fitted parameters. ASAP underpins commercial Accelerated Predictive Stability (APS) tools and is widely used in QbD submissions.

**Assumptions:** a single isoconversional degradation endpoint; log-linear humidity dependence; moisture equilibration with the (open or defined) package; Arrhenius behaviour across the stressed range; a known specification limit defining "failure".

**Limits:** needs a humidity-controlled study design; the log-linear RH term is an empirical approximation; isoconversional framing assumes the degradation pathway does not switch across conditions.

## 5. AccelStab — Šesták–Berggren kinetics

**AccelStab** is an open-source R package (CRAN; AccelStab on GitHub) that pairs the Arrhenius temperature term with the **Šesták–Berggren** reaction-model function, giving a flexible, closed-form non-linear fit to the whole degradation curve rather than a single isoconversional point:

dα/dt = **k(T)** · f(α), with f(α) = α^m · (1 − α)^n

α = fraction degraded · m, n = empirical reaction-model exponents

It extrapolates degradation in both *time and temperature*, and quantifies uncertainty with a **parametric bootstrap** (kinetic parameters drawn from a multivariate *t*-distribution) and/or the analytical **delta method** — yielding confidence and prediction intervals on the predicted curve.

**Assumptions:** the Šesták–Berggren form captures the true degradation shape; Arrhenius temperature dependence; parameter estimates are approximately multivariate-*t*; a humidity-modified Arrhenius term can be added where humidity matters.

**Limits:** more parameters (m, n) need more/cleaner data to identify; still a development-study tool, not a per-shipment decision engine; open-source — the validated state is the user's responsibility.

## 6. Synlogica Terminus Quality — probabilistic excursion decisioning

Terminus Quality does not try to *establish* a shelf-life from a stressed study. It takes the product's *already-characterised* Arrhenius kinetics (Ea, A, and their uncertainty, from the ICH Q1A development study) and applies them to the **actual, non-isothermal logger trace** of a real distribution event to answer a release question:

Δ(shelf-life) = ∫ **k** (T(t)) dt over the logged profile

with Ea, A, sensor error and spatial variation propagated by **Monte-Carlo**

→ a **distribution** of remaining shelf-life, not a point estimate

Where the degradation is non-linear, Terminus fits the same **Šesták–Berggren** reaction model used by AccelStab (dα/dt = k·f(α)) by non-linear least squares, and reports confidence and prediction intervals by ** parametric bootstrap** (kinetic parameters drawn from a multivariate-*t* distribution) and the **delta method** — in addition to Monte-Carlo propagation of Ea, A, sensor-calibration and spatial uncertainty. The engine therefore spans both the simple integrated-Arrhenius case and the full Šesták–Berggren kinetic case, choosing per product.

The output is a probability-weighted recommendation — **RELEASE / CONDITIONAL / HOLD** with a stated confidence interval — packaged with every input, model version and assumption for audit. The human (QA / QP) makes the binding call.

**Assumptions:** the development-stage Arrhenius parameters are valid and version-pinned; the logger trace, after calibration and gap screening, represents the product within stated spatial bounds; cumulative exposure (the integral) is the relevant quantity. Humidity is included where the product's stability data support a humidity term.

**What it is not:** it is not a replacement for ASAP/AccelStab in development, and it is advisory by design — it does not sign the batch disposition.

## 7. Side-by-side comparison

| Dimension | Classic Arrhenius / MKT | ASAP | AccelStab | Synlogica Terminus Quality | |

| **Question answered** | Shelf-life claim | Shelf-life claim (fast) | Degradation curve + shelf-life | Is *this batch* releasable? | |

| **Temperature model** | Arrhenius | Arrhenius | Arrhenius | Arrhenius | |

| **Humidity** | No | Yes (log-linear, B·RH) | Optional | Optional (if characterised) | |

| **Degradation form** | Zero/first-order | Isoconversional point | Šesták–Berggren f(α) | Integrated profile + Šesták–Berggren | |

| **Uncertainty** | Usually none | Monte-Carlo | Bootstrap (mv-t) / delta | Monte-Carlo + bootstrap (mv-t) / delta | |

| **Input data** | Multi-temp study | Stressed T×RH study | Stressed study | Product kinetics + real logger trace | |

| **Stage** | Development | Development | Development | Distribution / release | |

| **Output** | Point shelf-life | Shelf-life + CI | Curve + CI/PI | RELEASE/CONDITIONAL/HOLD + CI + decision package | |

## 8. Assumptions & failure modes they share

Every model here will mislead if its assumptions are violated. The common failure modes:

- **Mechanism switching** — if the rate-limiting degradation pathway changes between stressed and storage conditions, Arrhenius extrapolation (and everything built on it) is invalid.

- **Ea uncertainty ignored** — a ±15% error in activation energy can move a shelf-life estimate by months; point estimates hide this.

- **Sensor ≠ product** — logger calibration error and spatial inhomogeneity inside a shipment mean the measured profile is not exactly the product's profile.

- **Humidity neglected** for moisture-sensitive products — classic Arrhenius and a humidity-blind integration both overstate confidence.

## 9. Which model, when

- **Setting a registered shelf-life fast, humidity matters:** ASAP / APS.

- **Modelling the full degradation curve, open and reproducible:** AccelStab (Šesták–Berggren).

- **Quick internal sanity check:** classic Arrhenius / MKT — knowing its blind spots.

- **Deciding release on a specific shipment after an excursion:** Synlogica Terminus Quality — it consumes the development model and the real trace and returns an auditable, probability-weighted recommendation.

## 10. References

- Waterman K.C. et al. — *The Application of the Accelerated Stability Assessment Program (ASAP) to Quality by Design (QbD) for Drug Product Stability.* AAPS PharmSciTech (PMC3167263).

- *Humidity-corrected Arrhenius equation: the reference condition approach.* Int. J. Pharmaceutics, 2016 (S0378517316300473).

- *AccelStab: Accelerated Stability Kinetic Modelling* — CRAN package & vignette; source at github.com/AccelStab/AccelStab (Šesták–Berggren + Arrhenius; parametric bootstrap / delta-method intervals).

- ICH Q1A(R2) Stability Testing; ICH Q1E Evaluation of Stability Data.

## 11. Takeaways

- All four methods share an Arrhenius core; they differ in humidity handling, degradation form, uncertainty method, and purpose.

- ASAP and AccelStab are **development** tools for shelf-life; Synlogica is an ** operational** tool for per-batch release decisioning — they are complementary.

- Whatever the model, the defensible output is a **distribution with stated assumptions**, not a single number — and, for release, an auditable decision package with the human as the decision authority.