Sustainable Quality Model

• Sustainable Quality Model is a formal framework that defines sustainability through explicit attributes, metrics, and evaluation procedures across technical, economic, social, and temporal dimensions.
• It extends traditional models like ISO/IEC 25010 by incorporating energy consumption, resource optimization, and perdurability to assess both short-term operations and long-term system endurance.
• It utilizes quantitative methods such as weighted aggregation, multi-criteria synthesis, and non-compensatory analysis to guide decision-making and lifecycle integration.

Searching arXiv for the supplied papers to ground the article and citations. arxiv_search query: (Calero et al., 2013) A Sustainable Quality Model is a formal representation of sustainability as a quality concern, expressed through explicitly defined attributes, metrics, dependencies, and evaluation procedures. Early software-quality work placed sustainability inside the ISO/IEC 25010 product quality model as a new characteristic composed of Energy Consumption, Resource Optimization, and Perdurability, thereby treating sustainability as “part of the quality of a software product” and as a non-functional concern that can be specified, measured, and evaluated (Calero et al., 2013). Subsequent work generalized this view to software architecture, model-based systems engineering, AI model reporting, manufacturing systems, research software governance, and collaborative platforms, often extending the scope from environmental efficiency alone to technical, economic, social, and time-dependent effects (Lago et al., 2024, Fatima et al., 28 Jan 2025, Ponsard, 28 Feb 2025). Taken together, these works suggest that a Sustainable Quality Model is best understood as a family of rigorous formalisms for preserving beneficial system behavior over time while making sustainability trade-offs measurable and operational across heterogeneous domains.

1. Conceptual foundations

Within software product quality, sustainability was formalized as a distinct characteristic to be added alongside the existing ISO/IEC 25010 characteristics. In that formulation, sustainable software development is defined as “a mode of software development in which resource use aims to meet product software needs while ensuring the sustainability of natural systems and the environment,” while the sustainability of a software product is “the capacity of developing a software product in a sustainable manner.” The same line of work emphasizes that “software sustainability is a way to improve a software product, being part of its quality and being related to non-functional requirements” (Calero et al., 2013).

A second foundational line defines sustainability more broadly as “the preservation of the beneficial use of digital solutions in a context that continuously changes.” In the Sustainability Assessment Framework Toolkit, this preservation-oriented view is organized through four indivisible dimensions—technical, environmental, economic, and social/organizational—and through a time perspective structured around first-order, second-order, and third-order impacts (Lago et al., 2024). A related model-based line makes multidimensionality even more explicit by tagging values, strategies, and patterns with environmental, economic, social, personal, and technical dimensions, and by introducing explicit constructs for Regulation, Assumption, Goal, Obstacle, Activity/Process, Fragment, and Pattern (Ponsard, 28 Feb 2025).

A recurrent misconception is that sustainability is exhausted by energy efficiency. The product-quality extension contradicts this directly by separating short-term operational aspects—energy and resource use while software runs—from long-term endurance captured by Perdurability. The architecture-level and pattern-based approaches widen the scope further by treating sustainability as a cross-dimensional and temporally evolving property rather than as a single operational metric (Calero et al., 2013, Lago et al., 2024, Ponsard, 28 Feb 2025).

2. Structural elements and representations

Despite their heterogeneity, Sustainable Quality Models tend to share a common structural logic: they define sustainability-relevant entities, arrange them into dimensions or characteristics, and connect them to measurable evidence.

Research line	Primary structural unit	Sustainability organization
ISO/IEC 25010 extension	Characteristic and subcharacteristics	Energy Consumption, Resource Optimization, Perdurability
SAF Toolkit	Decision Map, SQ Model, DMatrix, KPI Model	Technical, Environmental, Economic, Social/organizational
Pattern-based MBSE	Value, Goal, Obstacle, Pattern, Fragment	Environmental, Economic, Social, Personal, Technical
USFM	Objects, Processes, States, Links	Goals, KPIs, Data Process, factory information map

In the ISO/IEC 25010 extension, the structure is hierarchical. The characteristic Sustainability comprises Energy Consumption, Resource Optimization, and Perdurability. The first two are short-term operational subcharacteristics. Perdurability is the long-term subcharacteristic and is defined as “the degree to which a software product can be modified, adapted and reused in order to perform specified functions under specified conditions for a long period of time.” Its basis is explicitly drawn from Reusability, Modifiability, and Adaptability, while subcharacteristics from reliability such as Maturity, Availability, Fault tolerance, and Recoverability are examined and excluded because they concern operational reliability rather than long-term endurance (Calero et al., 2013).

In the SAF Toolkit, the main representational instruments are the Decision Map, the Sustainability-Quality Model, the Interdimensional Dependency Matrix, and the planned KPI Model. The Decision Map records sustainability-relevant design concerns, features, effect types, and first-/second-/third-order impacts. The SQ Model collects quality attributes grouped by sustainability dimension and associates them with internal, external, and quality-in-use metrics. The DMatrix makes dependencies across dimensions explicit, initially including technical–social, technical–economic, and technical–environmental matrices. The KPI Model links strategic sustainability goals, critical success factors, metrics, measures, and KPI fitness functions, thereby closing the design–measurement loop (Lago et al., 2024).

The pattern-based MBSE approach uses a meta-model in which Value is the central construct, complemented by Regulation and Assumption for contextual constraints, and by Goal and Obstacle for robustness reasoning. Fragments serve as modular encapsulation units, and Patterns are reusable solutions anchored into models through “bubbles.” The associated pattern template consists of Summary, Category, Dimensions, Applicability, Content, Archetype, Example, Discussion, and Related Patterns, with Category and Dimensions added explicitly to support sustainability structuring and traceability (Ponsard, 28 Feb 2025).

Manufacturing-oriented work provides another structural variant. The Unified Smart Factory Model integrates Manufacturing Process and System, the Data Process, and KPI Selection and Assessment inside an Object-Process Methodology representation. It models Objects, Processes, States, and procedural or structural Links, so that sustainability KPIs can be mapped to precise data requirements, process states, and material or energy flows (Kaushal et al., 11 Dec 2025).

3. Measurement, aggregation, and trade-off analysis

Measurement frameworks for Sustainable Quality Models range from direct metering to weighted multi-criteria synthesis. In the software product formulation, the paper itself leaves measures and indicators as future work, but the accompanying synthesis specifies a consistent operational scheme. For energy, the core quantity is runtime energy over a scenario,

$E=\int_{t_0}^{t_1} P(t)\,dt,$

with the approximation $E=P_{avg}\cdot \Delta t$, and a scenario-level sustainability index can be aggregated as

$$S = w_E \cdot S_{energy} + w_R \cdot S_{res} + w_P \cdot S_{perd},$$

with $w_E+w_R+w_P=1$. In this scheme, Energy Consumption is measured through hardware power meters, on-chip counters such as Intel RAPL, OS-level telemetry, and scenario instrumentation; Resource Optimization uses CPU, memory, disk, and network metrics normalized against sustainability requirements; and Perdurability is assessed through indicators for Reusability, Modifiability, and Adaptability (Calero et al., 2013).

Other Sustainable Quality Models are explicitly multi-criteria. The campus bike-sharing site evaluation model combines an improved Delphi method, AHP, entropy weighting, and fuzzy comprehensive evaluation. The improved Delphi applies thresholds of mean greater than 3.5, percentage of maximum score greater than 0.5, and coefficient of variation less than 0.25. AHP produces subjective weights via pairwise comparison matrices with the Saaty 1–9 scale and requires $\mathrm{CR}<0.10$. Entropy weights are computed from

$$p_{ij} = \frac{x_{ij}}{\sum_i x_{ij}}, \qquad e_j = -k \sum_i p_{ij}\ln p_{ij}, \qquad w_j = \frac{d_j}{\sum_j d_j},$$

and are fused with AHP as

$$\bar{w}_j = \alpha \cdot w^{\text{AHP}}_j + (1-\alpha)\cdot w^{\text{entropy}}_j,$$

with $\alpha=0.5$. The final fuzzy synthesis uses

$\mathbf{B} = \mathbf{W}\cdot \mathbf{R},$

followed by the maximum membership principle (Qi et al., 2023).

A conceptually different choice is made in the Strong Sustainability Paradigm based Analytical Hierarchy Process for healthcare systems. Here the key issue is non-exchangeability: good performance on one criterion cannot compensate for poor performance on another. The model reduces compensation by penalizing dispersion from the cohort mean. With normalized values $r_{ij}$, mean $E=P_{avg}\cdot \Delta t$0, and sustainability coefficient $E=P_{avg}\cdot \Delta t$1, the penalized value is

$E=P_{avg}\cdot \Delta t$2

and the composite score is

$E=P_{avg}\cdot \Delta t$3

This preserves an additive form, but only after introducing a strong-sustainability penalty that constrains compensability (Wątróbski et al., 2023).

At the software architecture level, the Sustainability Impact Score quantifies cross-dimensional effects among quality attributes. For any pair of dimensions,

$E=P_{avg}\cdot \Delta t$4

where $E=P_{avg}\cdot \Delta t$5. Priorities are derived from risk and importance using

$E=P_{avg}\cdot \Delta t$6

normalized into $E=P_{avg}\cdot \Delta t$7, and the SIS can be further normalized against a theoretical optimal matrix for relative comparison across dimension pairs (Fatima et al., 28 Jan 2025).

These measurement traditions expose a central methodological divide. Some models are compensatory and use weighted sums or fuzzy synthesis; others, such as SSP-AHP, are explicitly designed to block or reduce compensation. This divide is not ancillary. It reflects a substantive disagreement about whether sustainability deficits in one dimension may be offset by gains in another.

4. Domain-specific instantiations

Sustainable Quality Models have been instantiated in markedly different domains, but the domain-specific forms remain recognizable as variations on the same core problem: how to represent sustainability-relevant quality concerns so that alternatives can be compared and governed.

In healthcare, the SSP-AHP framework defines five major areas—equity, quality, responsiveness, financial coverage, and adaptability—with 25 indicators $E=P_{avg}\cdot \Delta t$8–$E=P_{avg}\cdot \Delta t$9. Its emphasis is explicitly social sustainability-oriented, and its benchmark application over 16 countries ranks Norway, Sweden, Germany, the Netherlands, Iceland, Belgium, and France above Hungary, Latvia, the Slovak Republic, and Poland under expert AHP weights with $$S = w_E \cdot S_{energy} + w_R \cdot S_{res} + w_P \cdot S_{perd},$$0 (Wątróbski et al., 2023).

In campus mobility, the sustainable development-oriented site evaluation model defines four dimensions—User’s characteristics, The implementation and use characteristics of the parking spots, Environmental sustainability, and Social sustainability—and fourteen indicators $$S = w_E \cdot S_{energy} + w_R \cdot S_{res} + w_P \cdot S_{perd},$$1–$$S = w_E \cdot S_{energy} + w_R \cdot S_{res} + w_P \cdot S_{perd},$$2. For the South Campus of Henan Polytechnic University, the fused weight vector over the four dimensions is $$S = w_E \cdot S_{energy} + w_R \cdot S_{res} + w_P \cdot S_{perd},$$3, the final fuzzy output is $$S = w_E \cdot S_{energy} + w_R \cdot S_{res} + w_P \cdot S_{perd},$$4, and the final grade is “Good” (Qi et al., 2023).

In manufacturing, the Unified Smart Factory Model translates high-level sustainability goals into factory-level KPIs through a ten-step framework and an OPM-based information map. In the PCB assembly case, the foreground system is the PCB assembly line, the functional unit is 1 kg of PCB assembled, average energy per PCB is reported as approximately $$S = w_E \cdot S_{energy} + w_R \cdot S_{res} + w_P \cdot S_{perd},$$5–$$S = w_E \cdot S_{energy} + w_R \cdot S_{res} + w_P \cdot S_{perd},$$6 kWh/PCB, the reflow oven accounts for about 90% of total energy, and the cradle-to-gate global warming impact is approximately $$S = w_E \cdot S_{energy} + w_R \cdot S_{res} + w_P \cdot S_{perd},$$7 kg CO2 eq per 1 kg of assembled PCBs (Kaushal et al., 11 Dec 2025).

In research software governance, the Sustainable Research Software Institute model operationalizes sustainability through a Community Services Arm and a Sustainability Funding Arm. Its scorecard-oriented view tracks dimensions such as reproducibility, maintainability, test coverage, documentation quality, usability, performance, portability, community health, user support/responsiveness, and archiving/preservation, and it organizes maturity through levels ranging from L0 Incubating to L4 Platinum (Graduated) (Watson et al., 2023).

These instantiations show that the object under evaluation can vary from a national health system to a bike-sharing stop, a factory line, or a research software project. What remains stable is the attempt to connect sustainability goals to explicit indicators, structured aggregation, and decision consequences.

5. AI, reputation systems, and dynamic collaborative ecosystems

AI-oriented work pushes Sustainable Quality Models toward tighter formalization of operational metrics. In GreenAuto, the quality model centers on Energy per inference $$S = w_E \cdot S_{energy} + w_R \cdot S_{res} + w_P \cdot S_{perd},$$8, Accuracy $$S = w_E \cdot S_{energy} + w_R \cdot S_{res} + w_P \cdot S_{perd},$$9, Latency $w_E+w_R+w_P=1$0, Power $w_E+w_R+w_P=1$1, and Carbon footprint $w_E+w_R+w_P=1$2 for the search or training process. The search space expands NAS-Bench-201 to 959,417 valid models, uses kernel-level energy predictors and NASWOT scores inside a Pareto-front search guided by Multiple Gradient Descent, and applies stopping constraints $w_E+w_R+w_P=1$3 mJ and $w_E+w_R+w_P=1$4. On the reported smartphone setup, GreenAuto’s energy-focused best model achieves $w_E+w_R+w_P=1$5 at $w_E+w_R+w_P=1$6 mJ, the accuracy-focused best achieves $w_E+w_R+w_P=1$7 at $w_E+w_R+w_P=1$8 mJ, and the reported search emissions are about $w_E+w_R+w_P=1$9 kgCO2/model compared with $\mathrm{CR}<0.10$0 kgCO2/model for NASNet-A (Tu et al., 25 Jan 2025).

A complementary line formalizes sustainability reporting itself. The Sustainability Model Card DSL defines a machine-processable structure with MetaData, Training, Inference, Platform, EnergySource, EnergyMix, and CarbonOffsetCredit, and directly stores energy consumption, carbon emissions, water consumption, hardware, provider, region, energy-source carbon intensity, and timestamps. Its purpose is to make sustainability descriptions formal enough for automatic analysis, comparison, selection, and future certification processes while remaining compatible with Model Cards (Jouneaux et al., 25 Jul 2025).

Digital-market and collaboration settings broaden the meaning of sustainable quality from resource efficiency to the durability of trustworthy signals and durable high-quality outcomes. The integrity-driven rating model for blockchain-based reputation systems defines sustainability through budget-balanced and bounded credit-point updates, stake-based incentives, sybil resistance, and convergence toward high-integrity equilibria. Its stake-weighted alignment metric

$\mathrm{CR}<0.10$1

makes integrity a measurable quality property of the reputation process itself (Wen et al., 2023).

In Wikipedia, sustainable quality is defined temporally. An article is labeled unsustainable if it was promoted to Featured Article or Good Article and later demoted:

$\mathrm{CR}<0.10$2

Using over 40K articles and 326 pre-promotion features, the best-performing model achieves AU-ROC $\mathrm{CR}<0.10$3 for FA and $\mathrm{CR}<0.10$4 for GA under bootstrap, with approximately 0.88 AU-ROC on average across the two tasks. The analysis reports that longer time-to-promotion and higher user experience are associated with sustained success, while fast promotion, high edit velocity, many discussers, and negative discussion signals are associated with unsustainability (Israeli et al., 2024).

A still broader ecosystem model is the five-state dynamical system for human–AI collective knowledge, with archive size $\mathrm{CR}<0.10$5, archive quality $\mathrm{CR}<0.10$6, model skill $\mathrm{CR}<0.10$7, aggregate human skill $\mathrm{CR}<0.10$8, and query volume $\mathrm{CR}<0.10$9. It identifies regimes such as healthy growth, inverted flow, inverted learning, and oscillations, and calibrates Wikipedia separately for pre-ChatGPT and post-ChatGPT eras. The reported calibration finds a rise in LLM additions with a concurrent decline in human inflow, consistent with a regime identified by the model (Nettasinghe et al., 27 Jan 2026).

These AI and platform-oriented models show that sustainable quality need not denote only a property of a static artifact. It can also denote the persistence of trustworthy evaluation signals, the long-term maintenance of recognized quality, or the dynamical stability of a human–AI knowledge ecosystem.

6. Lifecycle integration, governance, limitations, and open problems

Operationally, Sustainable Quality Models are increasingly embedded in lifecycle processes rather than used only as post hoc assessment devices. In the software-product view, sustainability requirements can be integrated into Requirements, Architecture and design, Implementation, Testing, and Deployment/Operation, with roles distributed across product owners, architects, developers, QA, and operations. The SAF Toolkit extends this lifecycle logic through Green Lab measurements, KPI models, dashboard integration, and planned ISO/IEC/IEEE 42010 traceability from design concerns and decisions to architecture elements (Calero et al., 2013, Lago et al., 2024). In research software, SRSI aligns scorecards, community services, and foundation funding so that governance, infrastructure, and incentive allocation all act on measured sustainability practices (Watson et al., 2023).

Several limitations recur across the literature. The ISO/IEC 25010 sustainability extension is explicitly a conceptual model without empirical validation or standardized measures, and the definition of indicators is stated as future work (Calero et al., 2013). The model-based catalogue approach addresses fairness and circularity through separate catalogues, but it reports no statistical validation protocol and no formal composition semantics or OCL constraints (Ponsard, 28 Feb 2025). The architecture-level SIS depends on correctly eliciting all relevant quality attributes and interdependencies, while its effect magnitudes are restricted to $$p_{ij} = \frac{x_{ij}}{\sum_i x_{ij}}, \qquad e_j = -k \sum_i p_{ij}\ln p_{ij}, \qquad w_j = \frac{d_j}{\sum_j d_j},$$0 (Fatima et al., 28 Jan 2025). The sustainability model card line formalizes energy, carbon, water, and platform descriptors, but does not yet integrate latency, throughput, or accuracy inside the DSL itself (Jouneaux et al., 25 Jul 2025). GreenAuto demonstrates strong results on one smartphone configuration, but the paper notes hardware heterogeneity, predictor fidelity, and coverage limits beyond the current search space (Tu et al., 25 Jan 2025). Wikipedia-based sustainable success is sensitive to right-censoring and domain-specific governance processes (Israeli et al., 2024). The human–AI dynamical model is intentionally minimal and mean-field, so parameter identifiability from aggregate data remains limited (Nettasinghe et al., 27 Jan 2026).

There is also a substantive methodological controversy concerning aggregation. Compensatory models such as AHP–entropy fusion, fuzzy evaluation, and additive weighted sums allow trade-offs among dimensions or indicators; strong-sustainability models seek to reduce or block such trade-offs; dependency-based models such as SIS avoid direct dimensional summation until directional effects have been modeled. A plausible implication is that future work will continue to diverge unless communities standardize not only metrics but also the admissible semantics of compensation, thresholding, and theoretical optima.

The main research trajectory is nevertheless clear. Sustainable Quality Models are moving from conceptual taxonomies toward instrumented, traceable, and machine-processable systems: runtime profiling and KPI dashboards in software architecture, OPM-linked data pipelines in manufacturing, DSL-based sustainability reporting for AI models, scorecards tied to funding decisions in research software, and predictive or dynamical models for long-term collaborative quality. This suggests that the field is converging on a common ambition: to make sustainability a first-class quality property that can be specified as a requirement, represented structurally, measured empirically, aggregated with explicit value assumptions, and acted upon throughout the system lifecycle.