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Inferring First and Second Use Lifespan Indicators for Household Appliances from Peruvian Survey Data

This study utilizes an EM–Weibull mixture model applied to Peruvian National Household Survey data to estimate the first and second-use lifespans of 12 household appliance categories, revealing distinct ownership diffusion patterns and providing the first nationally representative assessment of appliance longevity and reuse in Peru from 2008 to 2024.

Original authors: Pedro Chumpitaz-Flores, Marco Gusukuma

Published 2026-07-24

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CC BY 4.0

Original authors: Pedro Chumpitaz-Flores, Marco Gusukuma

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world as a giant, bustling workshop where everything we own is made of tiny, valuable building blocks like metals, plastics, and rare minerals. When we throw things away, we usually send them to a landfill, which is like burying those precious blocks under a mountain of dirt forever. But scientists have a cooler idea called the "circular economy." Think of it as a giant recycling loop where old items don't die; they just get a second chance. Instead of digging new holes in the ground to find materials, we "urban mine" our trash, digging through our old gadgets to recover the gold, copper, and steel inside them. To make this work, we need to know how long things actually last. Do they break quickly? Do people keep them for decades? Or do they get passed down to a friend or stored in a closet for years? This is the tricky part: we often don't know exactly when an old toaster stops working or gets sold, because nobody writes down the date they throw it away.

This is where a team of researchers from Peru steps in with a clever detective story. They wanted to figure out the "lifespan" of household appliances—things like refrigerators, TVs, and washing machines—without ever seeing them get thrown out. They used a massive survey of Peruvian households that asked people, "When did you buy your newest appliance?" but didn't ask, "When will you throw it away?" Since they couldn't see the end of the story, they built a mathematical model, like a time-traveling crystal ball, to guess the hidden patterns. They used a special tool called an "EM–Weibull mixture model," which is essentially a way of sorting a mixed bag of ages into two invisible piles: the "First Use" pile (appliances still with their original owners) and the "Second Use" pile (appliances that have been resold, donated, or stored for a while).

The researchers analyzed data from 2008 to 2024 covering 12 different types of appliances. Their main finding suggests a clear split in how long things last. On average, the "First Use" phase lasts about 10.6 years, while the "Second Use" phase is much shorter, lasting only about 4.3 years. It's like a first owner treating a gadget like a cherished pet for over a decade, while a second owner might only keep it for a few years before it finally retires. The study also spotted three distinct "personality types" for these appliances. Some, like gas stoves and color TVs, are "Essential Goods" that almost every home has and keeps for a long time. Others, like DVD players and VHS recorders, are "Obsolescent Devices" that are disappearing fast as technology changes. Then there are the "Rapid Saturation" items that are everywhere but might be replaced sooner than we think.

Interestingly, the data suggests that during the pandemic years (around 2020–2021), more appliances seemed to jump into the "Second Use" category. The model estimates that the share of appliances in this second-hand phase jumped by about 20 percentage points, likely because people were holding onto things longer or passing them around more due to economic shifts, though the survey didn't ask exactly why. The study also found that for some items, like microwaves and sound systems, the time people keep them in their first home is slowly getting longer every year, adding about 4 extra years to their lifespan over the last decade. However, the authors are careful to say these are "model-based estimates," not direct measurements of every single appliance. Because the survey only asks about the newest item and not the history of old ones, the model has to make some educated guesses. Still, this approach gives us a vital map for understanding how to recover valuable materials from our old gadgets and plan for a future where we waste less and reuse more.

Technical Summary: Inferring First and Second Use Lifespan Indicators for Household Appliances from Peruvian Survey Data

Problem Statement
The transition toward a circular economy requires accurate estimates of household appliance (HA) lifespans to assess the potential for material recovery through "urban mining." However, a critical data gap exists: official household surveys, such as Peru's National Household Survey (ENAHO), typically record appliance ownership and acquisition years but lack direct data on disposal, resale, donation, or transfer dates. Consequently, traditional survival analysis methods (e.g., Kaplan–Meier estimators) cannot be directly applied because the "event times" (retirement or transfer) are unobserved. Furthermore, existing literature often conflates first-use and second-use phases, hindering the ability to distinguish between original ownership duration and the lifespan of appliances circulating in secondary markets.

Methodology
To address data scarcity, the authors propose a latent-component modeling approach using an Expectation–Maximization (EM) algorithm applied to a two-component Weibull mixture model.

Data Source: The study utilizes ENAHO data from 2008 to 2024, covering over 530,000 household interviews. The analysis focuses on 12 appliance categories mapped to United Nations University (UNU) waste classification keys.
Operational Constraint: The model operates under a "data scarcity" condition where the only longitudinal signal is the current age of the newest unit owned by a household ( $t_h = \text{SurveyYear} - \text{AcquisitionYear}$ ). No direct observation of end-of-life or secondary transactions exists.
Model Structure: The observed age distribution is decomposed into two unobserved (latent) components:
1. First-use component: Time from acquisition to first divestment.
2. Second-use component: Time from transfer (resale, donation, storage) to final retirement.
Statistical Framework:
- The probability density function is modeled as a mixture: $L_h = \sum_{j=1}^{2} \theta_j f_j(t_h | \lambda_j, \rho_j)$ , where $\theta_1 = 1-\pi$ and $\theta_2 = \pi$ (the population share assigned to second use).
- Each component $j$ follows a Weibull distribution with scale $\lambda_j$ and shape $\rho_j$ .
- A weighted EM algorithm maximizes the log-likelihood using survey weights ( $w_h$ ). The E-step estimates the probability of an observation belonging to a specific component, and the M-step updates the parameters ( $\pi, \lambda_j, \rho_j$ ).
- To ensure robustness against local maxima, the authors employ a multi-start strategy combining random initialization and a deterministic grid search.
Metrics: Upon convergence, the model estimates the mean first-use lifespan ( $\mu_1$ ), mean second-use lifespan ( $\mu_2$ ), and the estimated share of appliances in the second-use phase ( $\hat{\pi}$ ).

Key Results
The study provides the first nationally representative, model-based assessment of HA longevity and reuse patterns in Peru.

Ownership Diffusion Patterns: Three distinct patterns emerged:
1. Rapid Saturation: Gas stoves and Color TVs reached >70% ownership by 2016 and stabilized.
2. Obsolescence: Legacy media devices (VHS, DVD players) showed declining ownership, with VHS dropping from >20% to near zero.
3. Stable Ownership: Items like blenders, irons, and radios fluctuate around 55–60% ownership.
Lifespan Indicators:
- First vs. Second Use: The model-based mean first-use lifespan ( $\mu_1 \approx 10.6$ years) is approximately 2.5 times longer than the mean second-use lifespan ( $\mu_2 \approx 4.3$ years).
- Correlations: Appliances with increasing penetration (e.g., PCs, Color TVs) show positive correlations between market penetration and in-use age. Conversely, obsolescent or low-cost items (e.g., irons, radios, DVD players) exhibit strong negative correlations, suggesting shorter retention times or faster replacement cycles.
- Temporal Trends: Most appliances show a gradual lengthening of first-use durations since 2008. Notably, the estimated share of appliances assigned to the second-use component ( $\hat{\pi}$ ) increased significantly during the COVID-19 period (a ~20 percentage point median increase), stabilizing roughly 22 percentage points above the 2019 baseline by 2024, particularly for kitchen appliances and small electrics.
Category Specifics: By 2024, over 60% of the observed stock for gas stoves, blenders, irons, and Color TVs was assigned to the second-use component, whereas radios remained largely unchanged.

Significance and Claims
The paper claims to provide a preliminary but necessary stage for estimating the potential of household appliances as a source of valuable materials (urban mining) in Peru. Its primary contribution is methodological: demonstrating how mixture models can infer latent lifespan dynamics (first vs. second use) from limited survey data that lacks explicit disposal or transfer records.

The authors emphasize that their estimates are model-based indicators derived under specific latent-use assumptions, not direct measurements of individual appliance retirement events. The study underscores that understanding the divergence between first-use and second-use durations is critical for circular economy planning. Specifically, longer first-use durations influence the timing of end-of-use flows, while the dynamics of the second-use phase are vital for planning reuse channels, particularly for devices subject to rapid obsolescence. The findings offer policy-relevant insights for managing e-waste streams and recovering secondary raw materials in a data-constrained environment.

Technical Summary: Inferring First and Second Use Lifespan Indicators for Household Appliances from Peruvian Survey Data

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