Integrating Economic Analysis and Reliability Assessment for Sustainable Management in the Italian Used Car Market

The transition towards a circular economy is reshaping industries globally, with the automotive sector at the forefront of this transformation. In the context of the used car market, circular economy principles promote the reuse, recycling, and life extension of vehicles, significantly reducing environmental impact (G​a​v​a​z​z​a​ ​e​t​ ​a​l​.​,​ ​2​0​1​4). By reintroducing vehicles into the economy through second-hand transactions, the need for new resource extraction is mitigated, and the carbon footprint of the automotive industry is minimised (D​u​ ​e​t​ ​a​l​.​,​ ​2​0​2​5; Monburinon et al., 2018). This aligns with broader sustainability goals aimed at reducing waste and promoting resource efficiency.

The automotive industry has long been recognized as a major contributor to environmental degradation, primarily due to emissions during production and the resource intensity of vehicle manufacturing. The implementation of circular economy strategies, including remanufacturing, recycling, and component reuse, has proven essential for reducing the industry's overall environmental impact (D​e​o​r​e​ ​&​ ​M​a​t​a​i​,​ ​2​0​2​4; W​u​r​s​t​e​r​,​ ​2​0​2​1). The application of closed-loop recycling systems and design-for-reuse frameworks has demonstrated potential in lowering both material waste and emissions (G​h​i​s​e​l​l​i​n​i​ ​e​t​ ​a​l​.​,​ ​2​0​1​6). By extending vehicle lifespans through these practices, the automotive sector can contribute significantly to the reduction of greenhouse gas emissions and resource consumption (P​r​o​c​h​a​t​z​k​i​ ​e​t​ ​a​l​.​,​ ​2​0​2​3; S​u​ ​e​t​ ​a​l​.​,​ ​2​0​1​3).

The used car market is particularly relevant to sustainability due to its ability to prolong the lifespan of vehicles, reducing waste and postponing the need for energy-intensive manufacturing processes. Vehicles that remain in use for longer periods lower the demand for energy-intensive production processes, a significant source of greenhouse gas emissions (Monburinon et al., 2018; P​o​t​t​i​n​g​ ​e​t​ ​a​l​.​,​ ​2​0​1​7). While both aspects contribute to sustainability, the former emphasises reducing waste through reuse, while the latter focuses on minimising resource extraction and energy consumption. Despite these benefits, the market faces challenges, notably in terms of transparency regarding vehicle reliability. Buyers often struggle to assess the remaining lifespan of used vehicles, leading to uncertainty and potential dissatisfaction, which hinders trust in the market (G​e​g​i​c​ ​e​t​ ​a​l​.​,​ ​2​0​1​9).

To address these issues and promote sustainable management within the Italian used car market, this study first presents an economic analysis of the Italian used car market, focusing on how it supports sustainability by reducing waste and extending vehicle life cycles. This economic analysis assesses the market's contribution to resource optimisation and serves as a basic framework for integrating reliability assessment into sustainable management practices. By reducing waste and encouraging extended vehicle use, the analysis highlights how the market can support a circular economy.

The study then presents a reliability-based model for estimating the PRL of used vehicles. This model applies Weibull distribution techniques to failure data (R​ ​e​t​ ​a​l​.​,​ ​2​0​2​2), providing an objective measure of a vehicle's remaining life based on key factors such as mileage and age. The integration of economic analysis with the PRL model provides a comprehensive approach to sustainable management where economic viability and technical reliability are addressed together to improve the overall sustainability of the market. By providing a quantitative assessment of vehicle reliability, the PRL model increases transparency and helps reduce the uncertainty that buyers often face in the used car market.

This study is a novel contribution to the Italian used car market from a technical point of view. It highlights the sector's role in sustainability by extending vehicle life, reducing waste and improving access to transport. The inclusion of over 100,000 vehicle data points in the PRL model ensures robustness and scalability, making it adaptable to different vehicle types and models. In addition, the combination of economic analysis and reliability assessment ensures that sustainable management practices are supported by both market performance assessment and technical reliability metrics. Beyond the used car market, the findings have broader implications, potentially informing sustainable management practices in other industrial sectors. In addition, future integration of machine learning and Internet of Things (IoT) technologies is expected to improve the predictive accuracy of PRL, enabling real-time vehicle health monitoring and further advancing the circular economy (S​a​r​a​n​g​i​ ​e​t​ ​a​l​.​,​ ​2​0​2​1).

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The Italian used car market, while distinct in its structure and regulatory framework, shares many characteristics and challenges with global used car markets. As such, insights and practices from the Italian context often hold relevance on an international scale. This sector plays a critical role in providing accessible vehicle options, promoting sustainability goals, and aligning with global trends such as the adoption of circular economy principles.

With increasing environmental regulations and consumer demand for ethical practices, the market is forced to adopt innovative strategies and sustainability principles. The sector promotes Sustainable Development Goals (SDGs) such as promoting responsible consumption (SDG 12) and reducing emissions (SDG 13) by extending vehicle lifecycles, which is in line with circular economy principles. However, the market faces several challenges:

1. Information asymmetry: Consumers often lack reliable information on vehicle history and quality, leading to mistrust. This barrier can be mitigated by improving transparency through digital tools (L​i​a​n​g​,​ ​2​0​2​3);

2. Environmental footprint: The adoption of sustainable vehicles, such as electric and hybrid cars, comes with complexities related to higher upfront costs and limited infrastructure for charging and maintenance (M​i​c​o​n​i​ ​&​ ​D​i​m​i​t​r​i​,​ ​2​0​2​3; P​r​o​c​h​a​t​z​k​i​ ​e​t​ ​a​l​.​,​ ​2​0​2​3).

3. Lack of standardised practices: There is a need for universally accepted methodologies for vehicle evaluation and environmental impact assessment to create market uniformity and consumer confidence (S​h​a​r​m​a​ ​&​ ​P​a​n​d​e​y​,​ ​2​0​2​0).

The absence of standardized practices in vehicle valuation and environmental impact assessments complicates the establishment of market uniformity and consumer trust. To address these challenges, the market is integrating practices that promote sustainability across the vehicle lifecycle. For example, circular economy models that emphasize resource recovery and reuse are becoming more prevalent, supported by tools like the Automotive Sustainability Assessment Model (A-SAM), which aids in quantifying sustainability impacts and balancing cost-efficiency with environmental goals. Furthermore, the adoption of artificial intelligence and machine learning is enhancing market analysis, pricing prediction, and overall transparency, facilitating informed purchasing decisions (M​i​c​o​n​i​ ​&​ ​D​i​m​i​t​r​i​,​ ​2​0​2​3).

Policy-driven initiatives are also taking hold, with non-financial and sustainability reporting mandates pushing companies to integrate sustainable practices, increasing transparency and building consumer trust (S​h​a​r​m​a​ ​&​ ​P​a​n​d​e​y​,​ ​2​0​2​0). Effective end-of-life vehicle (ELV) management offers opportunities for significant sustainability improvements. Recycling materials such as aluminium and iron from ELVs minimises dependence on raw materials and reduces environmental impacts (D​u​ ​e​t​ ​a​l​.​,​ ​2​0​2​5). However, integrating the informal sector into formal recycling processes is essential to improve efficiency and scalability (I​z​z​o​ ​e​t​ ​a​l​.​,​ ​2​0​2​0). Collaborative models involving manufacturers, policy makers and recyclers can create more effective frameworks for the disposal and recycling of end-of-life vehicles.

Market dynamics are further influenced by the preferences of younger consumers, who prioritise corporate social responsibility and environmental stewardship (D​o​b​r​o​w​o​l​s​k​i​ ​e​t​ ​a​l​.​,​ ​2​0​2​2; G​a​z​z​o​l​a​ ​e​t​ ​a​l​.​,​ ​2​0​2​0). This trend urges companies to effectively market their sustainable practices (P​e​n​c​a​r​e​l​l​i​ ​e​t​ ​a​l​.​,​ ​2​0​1​9). To achieve sustainable management, several strategic approaches are recommended:

1. Regulatory support: Providing incentives for the adoption of green technologies and sustainable practices;

2. Stakeholder collaboration: Engaging industry players, policy makers and consumers to address systemic challenges such as information asymmetries and infrastructure gaps;

3. Awareness campaigns: Promoting the long-term economic and environmental benefits of sustainable car ownership to change consumer preferences and drive market transformation.

Accordingly, significant progress has been made in integrating sustainability principles into the Italian used car market, but several gaps remain. Existing tools and models, such as the A-SAM, provide valuable insights into environmental impacts, but often lack precision in estimating the life cycle of individual vehicles. In addition, current market practices and policy-driven initiatives tend to focus on broad systemic improvements, leaving a need for more granular, data-driven methodologies to improve transparency and decision-making for both buyers and sellers.

This study addresses these gaps by introducing the PRL model, a novel and reliable approach specifically tailored to the Italian used car market. Unlike previous models, the PRL model directly incorporates real-world data from over 100,000 vehicles and uses Weibull distribution techniques and regression analysis to estimate vehicle reliability. This data-driven framework provides a more accurate estimate of vehicle longevity and addresses information asymmetries by providing clear, quantifiable metrics for decision making. The PRL model complements existing frameworks such as A-SAM by providing individualised assessments that increase transparency and sustainability at the vehicle level.

By focusing on key factors such as mileage and age, the PRL model significantly increases transparency in the used car market, enabling buyers and sellers to make more informed decisions. Reliable PRL estimates encourage the continued use of vehicles in good condition, reducing the need for premature scrapping. From a sustainability perspective, the PRL model promotes the efficient use of resources and the reduction of waste. In addition, the economic factors driving Italian consumers towards older vehicles are in line with the principles of the circular economy, while the PRL model ensures that vehicles are used for their maximum reliable lifetime (Z​i​r​p​o​l​i​ ​&​ ​C​a​b​i​g​i​o​s​u​,​ ​2​0​1​8).

This section aims to provide a comprehensive overview of the Italian automotive market, focusing in particular on the structural and economic factors that influence the dynamics of the used car market. By examining trends in vehicle production, sales, technological changes and market composition, this section lays the foundations for understanding how the Italian used car market contributes to broader sustainability objectives. It also highlights the increasing age of the circulating vehicle fleet and the importance of the used car market in promoting resource efficiency and extending vehicle life cycles. This contextual analysis is essential to establish a coherent link between the economic analysis and the reliability-based PRL model presented in the following sections.

The Italian automotive market is undergoing a profound transformation, driven by a series of systemic disruptions reshaping the production, sale, and lifecycle management of vehicles and their components. This transformation affects the production and sale of both new and used vehicles - including cars, trucks, buses, trailers and semi-trailers - and their components, such as engines, electrical and mechanical parts, rubber elements, sheet metal and glass. These components are also widely used in related industries, including the two-wheeler, rail, marine and agricultural sectors. The changes are inevitable, far-reaching and mutually reinforcing. Specifically, several systemic disruptions can be identified:

1. The product technology, from analog to digital and from thermal to electric/hydrogen and further towards autonomous and interconnected driving and the IoT;
2. The process technology, where automation, flexibility and the size of production plants and distribution and repair sites proceed at forced stages towards new goals;
3. The use of new materials, from aluminium alloys to carbon fibres to high-strength steels, to glass fibre-reinforced plastics, to titanium, to ceramics in the name of lightness, efficiency, safety and ecology;
4. Customer needs and values in terms of function of use, increasing mobility, ecological sensitivity, transition from ownership to possession of the vehicle;
5. Competitive context logics oriented towards the concentration of players, collaboration and competition at the same time, a more efficient and less risky reorganization of the supply chain;
6. New infrastructural needs, from charging stations for electric cars to the production of electricity, from the closure of historic centres to cars;
7. The geopolitics of car manufacturers increasingly favour the territory of Asian producers and, in particular, Chinese ones;
8. The criticality of many raw materials, in terms of availability, concentration (China holds 90 percent of the 17 fundamental chemical materials, the so-called rare earths from lithium downwards) and price volatility;
9. The ongoing deglobalization triggered by geopolitical tensions, by the crisis on microchips, the engine of artificial intelligence, and by the acquired awareness of the risks associated with the lack of a production structure and the related technical skills;
10. The increase in the selling prices of new cars and the record profits achieved in 2023 by car manufacturers;
11. The increasing age of the circulating fleet, reflecting a slowing renewal rate due to the rising cost of new cars and economic constraints. This trend has significant implications for sustainability, as older vehicles tend to be less efficient and more polluting. However, it also highlights the importance of the used car market as a viable way to promote circular economy principles by extending the life cycle of vehicles.

The increasing age of the circulating car fleet, highlighted by the average age rising from 10.5 years in 2014 to 12.4 years in 2023 (+19.4%), indicates an urgent need for sustainable management practices. By improving the reliability and lifetime of existing vehicles through the used car market, it is possible to reduce the negative environmental impact associated with the production of new cars (D​u​ ​e​t​ ​a​l​.​,​ ​2​0​2​5).

Before continuing into the detailed analysis of the used car sector, a brief mention of the Italian macroeconomic context is considered appropriate (Table 1) and of the Italian registrations and circulating fleet, for the period 2014-2023. In particular (I​S​T​A​T​,​ ​2​0​2​4):

1. The gross domestic product shows a substantially flat start and finish interspersed with the significant negativity of -9.0% in 2020, due to the COVID-19 pandemic, and a relative rebound in the two-year period 2021-2022;
2. The inflation rate is substantially very close to zero until the two-year period 2022-2023 where it records an increase of +8.2% and +5.6%, respectively;
3. The unemployment rate progressively decreases by -5.2 percentage points, from 12.8% in 2014 to 7.6% in 2023.

In summary, in the period 2014-2023, an economic system with a very modest growth rate and an inflation rate much higher than the ECB's monetary policy equilibrium target of 2 % and a comforting reduction in the unemployment rate are evident.

On the other hand, in relation to the circulating fleet and car registrations on the Italian market, the analysis shows a constant increase in the former, +10.3% in the period 2014-2023, and a recovery in the latter compared to the minimum period of 2020, although still in decline, -18.28%, compared to the peak of 2019 (I​S​T​A​T​,​ ​2​0​2​4). The 2024 ratio between the circulating fleet and registrations is equal to 26.1, which would imply, with the same annual registrations and constant circulating fleet, a renewal of the circulating fleet achievable in approximately 26.1 years.

In relation to the size of the used car market, the number of transfers of ownership in Italy of cars and off-road vehicles, net of mini transfers (the sale of a vehicle to a used vehicle dealer/reseller), highlights (A​C​I​,​ ​2​0​2​4):

1. In 2023 a result equal to 2,865,332 units, i.e., an increase of +12.8% compared to 2014 and +7.4% compared to 2022;
2. The clear prevalence of the Fiat brand with 23.1% of transactions in 2023, 26.9% in 2014, followed by Volkswagen with 7.5%, 8.5% in 2014, and Ford with 5.0%, 6.8% in 2014;
3. A particularly significant increase and decline, respectively, for the Jeep brand, +399.4% from 2014 to 2023, and for the Smart and Lancia brands, -20.1% and -20.0% from 2014 to 2023;
4. Coverage by the top 15 brands of 82.2% in 2023, down from 93.6% in 2014 due to the entry of many new brands, especially Asian ones;
5. coverage by other brands increasing from 6.4% in 2014 to 17.8% in 2023;
6. the relationship between ownership transfers and registrations, equal to 1.83 in 2023 and substantially stable compared to 2014 with 1.87 (U​N​R​A​E​,​ ​2​0​2​4).

Table 2 shows the volume of ownership transfers on a regional basis and the relationship with registrations, which is recalled being equal to 1.83 in Italy, highlights (A​C​I​,​ ​2​0​2​4):

1. The leadership in absolute value of Lombardy with 15.5 % of ownership transfers of market share in 2023, slightly down from 16.0% in 2014; the first 5 regions, compared to the 20 total, recorded a market share of 50.7% in 2023, compared to 51.6% in 2014;
2. The highest ratio of ownership transfers to registrations by the regions of southern Italy: Puglia with a value of 5.0 compared to 4.3 in 2014, Sicily 4.3 in both 2023 and 2014, Campania 4.2 in 2023 and 4.5 in 2014, Calabria 4.0 in 2023 and 3.7 in 2014;
3. The extremely low ratios of Valle d’Aosta, 0.2 in 2023, and Trentino Alto Adige, 0.4 in 2023, are caused by the presence of long-term rental companies that register their vehicles in these regions.

One of the reasons underlying the limited number of car registrations in the period 2014-2023, and the consequent increasing age of the circulating car fleet and the significant sale of used cars is to be attributed to the significant increase in the price of new cars. Table 3 highlights (U​N​R​A​E​,​ ​2​0​2​4):

1. An increase in the average price of new cars between 2014 and 2023 equal to +54.7%, from €19,312 to €29,872 with particular intensity in the two-year period 2022/2023 with high inflation certainly as a contributing factor;

2. The segments with the greatest increases in the sales price in the period 2023-2014 were sports cars, +91.3%, Multi-Purpose Vehicles, +76.0%, and E/F Sedans, +63.0%;

3. The segments with the smallest increases in the sales price were the B-SUV, +28.6%, D-Sedan, +35.2%, and A, +37.6%.

The aforementioned increase in the selling price of new cars, on the one hand, slows down the requalification of the vehicle fleet, with very significant costs in terms of road safety and environmental impact, and, on the other hand, increases the value of used cars and favours the development of aftermarket components.

The analysis of transfers of ownership of cars and off-road vehicles, net of mini transfers, in relation to the type of contractor, shows the clear prevalence of transactions from private company to private company, equal to 56.7% of market share and decreasing from 59.1% in 2015, and from operator to private company, 39.1%, increasing compared to 37.0% in 2015 (U​N​R​A​E​,​ ​2​0​2​4).

A further relevant question to answer is whether current registrations, for example, in the period 2014-2023, will be able to improve, with the introduction of new technologies and hybrid and electric engines, the level of CO₂ emissions of used cars in the coming years (Table 4) (U​N​R​A​E​,​ ​2​0​2​4):

1. CO₂ emissions from registered cars increased from 2014 to 2023 by 1.7%, from 117.5 to 119.5, with the interruption of the reduction trend starting from 2020 (to limit global temperature rise to around 1.5℃, the safest threshold recommended by science and the 2015 Paris Agreement to avoid the worst effects of climate change, net greenhouse gas emissions would need to fall by 43% by 2030, compared to 2010 levels);

2. The segments with the largest reductions in CO₂ emissions in the period 2023-2014 were D-Sedan, -50.0%, A-SUV, -36.0%, D.SUV, -30.4%, and E-Sedan, -26.6%;

3. The segments that worsened CO₂ emissions the most were C-Sedan, +5.0%, B-SUV, +2.6%, Station Wagon, +2.4%, and B-Sedan, +1.9%, unfortunately those with the highest sales volumes.

The aforementioned increase in CO₂ emissions with reference to registrations is confirmed by the persistence of thermal, petrol and diesel engines, which represent, respectively, 39.0% and 47.6% of ownership transfers in 2023, while the hybrid electric world represents 6.5% (5.4% of phev+rex and 1.1% of bev) (U​N​R​A​E​,​ ​2​0​2​4).

A final analysis relating to ownership transfers concerns, from a safety perspective, the dynamics of the number of road accidents involving cars. In this case, the result is comforting (I​S​T​A​T​,​ ​2​0​2​4):

1. The number of road accidents involving private and public cars decreased, in the period 2023-2014 by -8.3%, both the isolated road accidents by -7.3%, and the road accidents involving vehicles by -8.7%;

2. The incidence of road accidents involving private and public cars compared to the total number of road accidents decreased from 73.72% in 2014 to 71.84% in 2023;

3. The incidence of road accidents involving private and public cars compared to the total number of road accidents in circulation decreased from 0.35% in 2014 to 0.29% in 2023.

In summary, the used car market in Italy (net of mini transfers) records a number of transactions almost double compared to the number of new cars sold, in particular in the southern regions, consisting of 99.9% cars with internal combustion engines and with substantially constant CO₂ emissions. With the aim of improving the level of safety of cars, reducing the environmental impact, promoting sustainable practices through reuse and resource optimization, incentivizing the circular economy and enhancing the aftermarket components supply chain, the authors believe that a renewal of the circulating fleet is absolutely necessary and this direction can be encouraged by favouring, also using the tax leverage and reducing the costs of transfers, the commercial transactions of used cars and, in particular, those of more recent construction (M​u​r​a​ ​e​t​ ​a​l​.​,​ ​2​0​2​0).

The used car market represents an important segment of the automotive industry at the intersection of sustainability and economic efficiency. This market plays an important role in the circular economy by extending the life cycle of vehicles (A​g​u​i​l​a​r​ ​E​s​t​e​v​a​ ​e​t​ ​a​l​.​,​ ​2​0​2​1). However, the reliability of used vehicles remains a critical concern for buyers and sellers, as it significantly impacts purchase decisions and market dynamics. To address this issue, this study proposes a reliability-based model for estimating the PRL of used vehicles. The proposed model integrates statistical methods and failure data to quantify the remaining life of a vehicle, thereby promoting informed decision-making and increasing transparency and confidence in the used car market.

The PRL model is rooted in reliability theory and conceptualises a vehicle as a complex system comprising multiple subsystems and components, each contributing to the overall reliability. It uses the concept of system reliability, where the failure of a critical component can significantly affect the overall reliability of the vehicle. This approach is particularly relevant for used vehicles, where component wear and maintenance history are key determinants of remaining life. Similar methodologies have been successfully applied in other domains, such as aviation and industrial machinery, to predict system performance and optimise preventive maintenance schedules (G​h​a​s​e​m​i​ ​e​t​ ​a​l​.​,​ ​2​0​1​0; W​a​n​g​ ​e​t​ ​a​l​.​,​ ​2​0​1​5). These precedents demonstrate the robustness and versatility of reliability-based models for complex systems, including used vehicles.

The Weibull distribution is particularly suitable for modelling component reliability in the context of used vehicles due to its flexibility in capturing different failure behaviours. Unlike other distributions, the Weibull distribution can model increasing, decreasing or constant failure rates depending on the value of its shape parameter (k) (M​o​n​t​g​o​m​e​r​y​ ​e​t​ ​a​l​.​,​ ​2​0​1​0). Specifically:

• When k < 1, the failure rate decreases over time, which is typical for components that fail early in life (infant mortality).

• When k = 1, the failure rate is constant, representing random failures independent of age or mileage.

• When k > 1, the failure rate increases over time, which is common for components that deteriorate due to wear and age.

This flexibility makes the Weibull distribution highly suitable for modelling a wide range of components within used vehicles, which may exhibit different failure patterns due to different usage histories and maintenance conditions (D​e​v​o​r​e​,​ ​2​0​1​1). In addition, regional and market-specific analyses reveal significant variability in vehicle lifetime and survival rates, highlighting the need for accurate lifetime modelling to better understand market dynamics (H​e​l​d​ ​e​t​ ​a​l​.​,​ ​2​0​2​1).

The PRL model is grounded in reliability theory, treating a vehicle as a complex system composed of various subsystems and components, each contributing to the overall reliability. The model employs the concept of system reliability, where the failure of any critical component can significantly impact the vehicle's overall reliability. This approach is particularly relevant in the context of used vehicles, where component wear and historical maintenance play crucial roles in determining the remaining lifespan.

The reliability $R_{C_i}(T)$ of a generic component $C_i$ is defined as the probability that the component will perform its intended function without failure for $t>T$. Mathematically, it is expressed as:

where, f(t) is the probability density function and T is the considered time point. For a system S composed of N independent components $\left(S=\left\{C_1, C_2, \ldots, C_N\right\}\right)$, the system reliability $R_{C_i}(T)$ is the product of the reliabilities of its components:

The PRL is thus a function of the reliabilities of all critical components, adjusted for the vehicle’s age and mileage.

To estimate the reliability of each component, the model employs the Weibull distribution, which is widely used in reliability analysis due to its flexibility in modelling various types of failure rates. The probability density function of the Weibull distribution is given by (Bertsche, 2008):

where, λ is the scale parameter and k is the shape parameter. The parameters λ and k were estimated using Maximum Likelihood Estimation (MLE) techniques (M​o​n​t​g​o​m​e​r​y​ ​e​t​ ​a​l​.​,​ ​2​0​1​0), applied to the historical failure data for each component. The goodness-of-fit for the Weibull distribution was verified using appropriate “goodness-of-fit” tests (D​e​v​o​r​e​,​ ​2​0​1​1; M​o​n​t​g​o​m​e​r​y​ ​e​t​ ​a​l​.​,​ ​2​0​1​0). The data, subjected to fitting concerning the variables "mileage" and "age," were treated as censored, given that the warranty coverage (and thus the information reported in the analysed database) typically relates to a limited time period of 12/24 months. As an example, Figure 1 shows a Quantile-Quantile (QQ) plot for the distribution of alternator failures concerning the mileage at failure.

The observed values for these failure data align along the dotted line, supporting the hypothesis that the data distribution follows a Weibull distribution.

Thus, the two parameters λ (scale parameter) and k (shape parameter) of the Weibull distribution for each component were calculated, along with their respective confidence intervals at a significance level of 𝛼 = 10%.

For each component reliability , where T represents the mileage or age, the confidence interval with a 10% significance level (α=10%) was calculated. This interval provides a range within which the true reliability is expected to fall with a high degree of confidence:

This approach allows the uncertainty inherent in reliability estimates to be captured, especially for components with limited failure data.

For components where the database lacked sufficient failure data to perform a reliable fitting (e.g., vehicles under warranty with incomplete failure histories), reliability was estimated by interpolating the values from other components with similar characteristics. This interpolation ensures that all critical components are accounted for in the PRL calculation.

Accordingly, to account for uncertainties in the input data and improve the robustness of the PRL estimates, the model incorporates confidence intervals for the reliability calculation of each component. Specifically, the 10% significance level (𝛼 = 10%) is used to construct a confidence interval, which provides a range within which the true reliability is expected to fall with a high degree of confidence. By using the lower bound of this interval in PRL calculations, the model takes a conservative approach that accounts for data limitations and measurement error, thereby increasing the reliability of the estimated PRL for each component:

This conservative approach minimizes the risk of overestimating the remaining life of the vehicle, providing a more cautious estimate that enhances buyer confidence and aligns with the goal of sustainability by potentially extending the useful life of vehicles.

The PRL model was implemented in a software tool developed in Matlab®, designed to process the input data (vehicle brand, model, mileage, age) and output the PRL value along with a detailed reliability report. The tool operates in two phases:

1. Fitting phase: This phase updates the parameters of the Weibull distributions based on the latest available data. The process is computationally intensive and is performed periodically to incorporate new failure data. A flowchart of this phase is represented in subgraph (a) of Figure 2;

2. Evaluation phase: This phase calculates the PRL for a specific vehicle, using the precomputed distribution parameters. The process is optimized for rapid execution, allowing the tool to be used in real-time assessments by car dealers and consumers. A flowchart of this phase is represented in subgraph (b) of Figure 2.

The PRL model was developed using an extensive and anonymized dataset comprising records from over 100,000 used vehicles. This dataset included detailed information on vehicle maintenance, repair history, mileage, and age, sourced from multiple data repositories. To protect the confidentiality of the data provider, the specific Italian company supplying the data is not disclosed. This large and diverse dataset provided valuable insights into the performance and failure rates of vehicle components, which were essential for fitting the distributions and building the reliability model.

Figure 3 illustrates the application of the Weibull distribution to key vehicle components, including transmission kinematics, the turbo compressor, and the EGR valve, and their failure data, enabling to model reliability as a function of mileage and vehicle age. These key components were chosen as representative due to their critical role in vehicle functionality and their prevalence in the failure data. The fitting was performed on datasets where the number of failure events was greater than 30, ensuring robust reliability estimates. The graphs show a strong correlation between the empirical data and the fitted Weibull distribution, indicating a good fit for all components. In each case, the probability of failure increases with distance travelled, following a typical S-shaped cumulative failure curve. In particular, reliability decreases sharply beyond certain mileage thresholds: around 150,000 km for the transmission kinematics and EGR valve, and around 200,000 km for the turbocharger. This pattern confirms the relevance of mileage as a primary factor influencing component degradation.

As illustrated, the reliability (the complement of failure probability) decreases sharply with increasing mileage, reflecting the wear and tear experienced by these components over time. A similar trend is observed when vehicle age is considered as the independent variable. This result aligns with expectations, as components are more likely to fail after prolonged usage or aging.

The PRL value was computed for several vehicle models, taking both mileage and age into account as key factors in assessing the remaining lifespan of each vehicle. The model employs a weighted average approach to combine the information from these two variables, with mileage weighted at 65% and age at 35%. These weights were determined through regression analysis performed on the dataset, which showed that mileage had a stronger correlation with failure rates and reliability estimates than age. This result is in line with previous studies which indicate that accumulated mileage is generally a more direct indicator of component wear and degradation (G​h​a​s​e​m​i​ ​e​t​ ​a​l​.​,​ ​2​0​1​0; W​a​n​g​ ​e​t​ ​a​l​.​,​ ​2​0​1​5). However, the age of the vehicle also has a substantial influence on component degradation, independent of mileage.

To ensure an accurate representation of the vehicle's overall condition, the model also incorporates a corrective coefficient. This coefficient is applied when there is a significant discrepancy between the PRL calculated from age and the PRL calculated from mileage. Specifically, the corrective factor ensures that when one measure (e.g., PRL based on age) is notably lower than the other (e.g., PRL based on mileage), the lower value is given more weight in the final PRL calculation. This conservative approach is designed to provide a cautious and reliable estimate of the vehicle's remaining life, prioritizing the worst-case scenario to avoid overestimating reliability.

The corrective coefficient $r$ is defined as the ratio of PRL based on age to PRL based on mileage $\left(r=\frac{P R L_{a g e}}{P R L_{k m}}\right)$. If $r \leq 1$, it means that the PRL based on age is lower than or equal to the PRL based on mileage, the model applies a factor that adjusts the final PRL downward. Conversely, if $r>1$, indicating that the PRL based on mileage is lower, a different corrective formula is used to avoid overcompensating in the other direction.

In practical terms, this approach provides a balanced and cautious assessment of vehicle reliability. By incorporating this corrective mechanism, the model avoids potential bias that could result from relying too heavily on either mileage or age alone, thus offering a more holistic and trustworthy estimate of a vehicle’s residual life.

A more detailed analysis of the PRL results shows that different vehicle models show different patterns in their PRL values (Table 5). This variability reflects differences in build quality, maintenance history, usage patterns and inherent reliability of the models. For example, the Fiat Panda, which has a relatively low mileage of 66,299 km and was registered in 2016, has a high PRL of 83.8%. This suggests that the vehicle is still in good condition and has a significant amount of life remaining, making it an attractive option for consumers looking for reliable and affordable transport. On the other hand, the Audi Q5 with 200,000 km registered in 2013 has a significantly lower PRL of 30.8%, indicating a more limited remaining useful life despite being a premium car.

These results suggest that the PRL model can effectively differentiate between vehicles based on their usage history and condition. Such information is particularly valuable to consumers who need to make purchase decisions based on reliability and expected longevity. It also highlights the potential of the PRL model to support sustainable practices by encouraging the sale and use of vehicles with significant remaining useful life, thereby reducing the demand for new vehicles and contributing to resource conservation.

In addition, the PRL model can be used by used car dealers to more accurately assess the quality of their stock. Vehicles with high PRL values can be promoted as reliable options, potentially commanding higher resale prices. Conversely, vehicles with low PRL scores can be targeted for refurbishment or repair, improving their reliability and extending their life.

Subgraph (a) of Figure 4 presents a 3D surface of the PRL index based on vehicle age and mileage. The contour lines represented in subgraph (b) of Figure 4 help visualize how PRL values evolve with increasing mileage and age. The model demonstrates saturation effects at higher distances and vehicle ages, where the PRL value flattens, indicating that further use or aging results in only marginal decreases in reliability.

The implications for consumer decision-making are clear: by providing an objective and quantifiable measure of vehicle reliability, the PRL model enables buyers to make more informed purchasing decisions. This transparency promotes confidence in the used car market and is consistent with sustainability goals by encouraging the purchase of vehicles with significant residual value. In addition, the model could support the development of extended warranties or maintenance plans tailored to vehicles with lower PRL values, thereby increasing their usability and lifetime.

This study successfully developed a reliability-based model (PRL model) to provide accurate estimates of the remaining life of used vehicles based on key factors such as mileage and age. The model demonstrated robustness in differentiating between vehicles with different usage histories, providing objective measures that can improve decision making and promote transparency in the Italian used car market. The analysis also highlighted the sector's contribution to sustainability by promoting resource efficiency and extending the life of vehicles.

The global automotive industry is undergoing significant changes, driven by the shift towards more sustainable practices and the increasing emphasis on the circular economy. In this context, the Italian used car market plays a key role in reducing resource consumption and extending vehicle lifespans. By facilitating the reuse and re-sale of vehicles, the Italian market helps decrease the demand for new car production, which is often associated with high energy consumption and environmental impacts. The rising importance of older vehicles in ownership transfers highlights the growing relevance of sustainability in this market. As more consumers in Italy turn to used cars, assessing their reliability and residual lifespan accurately becomes essential to promote consumer trust and efficient resource use.

This study examines the Italian used car market from a technical perspective. The analysis highlights the sector's contribution to sustainability by extending the life of vehicles, minimising waste and improving access to transport. With a growing share of vehicles over 10 years old in Italy, the market shows its potential to support sustainability efforts through the resale and prolonged use of durable vehicles.

On the technical side, the PRL model introduces a reliable and data-driven method for estimating a vehicle's remaining lifespan. By focusing on key factors such as mileage and vehicle age, the model enhances transparency in the used car market, helping buyers and sellers make more informed decisions. This contributes not only to economic efficiency but also to resource conservation, as reliable PRL estimates encourage the continued use of vehicles that are still in good condition, reducing the need for premature scrapping.

From an economic and social perspective, the PRL model has the potential to positively influence market dynamics. By providing reliable and accessible information on the expected lifetime of a vehicle, it promotes fairer pricing mechanisms and consumer confidence in the used car market. In addition, widespread adoption of the PRL model could encourage longer vehicle use, contributing to social equity by making affordable and reliable vehicles more accessible to low-income consumers. This is in line with the principles of the circular economy, as extending the lifetime of existing vehicles helps to reduce the environmental impact associated with the production of new vehicles.

Nevertheless, despite this progress, there are several areas that need to be further developed. This analysis is limited to the Italian used car market; future research should extend to a global market analysis for a more comprehensive understanding of the sector. In addition, the model's focus on mileage and age as the primary variables is a limitation that may affect the accuracy of PRL estimates. Factors such as maintenance history, driving conditions and environmental influences are not currently included in the model, which could lead to under- or overestimates of vehicle reliability, particularly for vehicles with atypical usage patterns or poor maintenance records. Addressing these limitations by including additional variables would improve the robustness and reliability of the model.

Future research should also explore the integration of advanced technologies, such as machine learning and IoT systems, to improve the predictive accuracy of the PRL model. Machine learning algorithms, particularly deep learning models, can be trained on large datasets to identify complex patterns and relationships between variables that may not be captured by traditional statistical methods. In addition, the application of IoT technologies could enable real-time monitoring of vehicle health, providing continuous updates on key metrics such as temperature, vibration, pressure and engine performance. This real-time data could be integrated into the PRL model to provide dynamic, continuously updated predictions of a vehicle's condition. By leveraging these technologies, the PRL model could be transformed from a static tool to a more responsive and adaptive framework capable of providing accurate, real-time insights into vehicle reliability.

In conclusion, the PRL model complements existing sustainability frameworks, such as the A-SAM, by providing accurate life cycle assessments at the individual vehicle level. Future research can extend the PRL model to perform broader life cycle analyses, integrating emerging technologies such as artificial intelligence and machine learning to refine predictions and incorporate dynamic variables. In particular, real-time monitoring of vehicle health through IoT technologies could provide continuous updates on a vehicle’s condition, while machine learning models could enhance the model’s capacity to process large datasets and integrate a broader range of variables. These advancements would allow the PRL model to offer more personalized and accurate predictions, further strengthening the transparency and sustainability of the Italian used car market. Furthermore, its alignment with circular economy principles establishes the model as a valuable tool for assessing resource efficiency and waste reduction strategies, with potential applications in other sectors that emphasise sustainable life cycle management.