Regional and Longitudinal Estimation of Product Lifespan Distribution

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Regional and Longitudinal Estimation of Product Lifespan Distribution: A Case Study for Automobiles and a Simplified Estimation Method Masahiro Oguchi*,† and Masaaki Fuse‡ †

Center for Material Cycles and Waste Management Research, National Institute for Environmental Studies, 16-2 Onogawa, Tsukuba, Ibaraki 305-8506, Japan ‡ Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, Japan S Supporting Information *

ABSTRACT: Product lifespan estimates are important information for understanding progress toward sustainable consumption and estimating the stocks and end-of-life flows of products. Publications reported actual lifespan of products; however, quantitative data are still limited for many countries and years. This study presents regional and longitudinal estimation of lifespan distribution of consumer durables, taking passenger cars as an example, and proposes a simplified method for estimating product lifespan distribution. We estimated lifespan distribution parameters for 17 countries based on the age profile of in-use cars. Sensitivity analysis demonstrated that the shape parameter of the lifespan distribution can be replaced by a constant value for all the countries and years. This enabled a simplified estimation that does not require detailed data on the age profile. Applying the simplified method, we estimated the trend in average lifespans of passenger cars from 2000 to 2009 for 20 countries. Average lifespan differed greatly between countries (9−23 years) and was increasing in many countries. This suggests consumer behavior differs greatly among countries and has changed over time, even in developed countries. The results suggest that inappropriate assumptions of average lifespan may cause significant inaccuracy in estimating the stocks and end-of-life flows of products.

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INTRODUCTION

Product lifespan also plays an important role by connecting material inflows, in-use stocks, and end-of-life flows in material flow analysis. Because direct observation of stocks and end-oflife flows of materials is time-consuming and expensive, material stocks and end-of-life flows are often estimated using the lifespan modeling approach.7 This approach estimates material stocks and end-of-life flows from the material inflows and product lifespan distribution, and has been applied in studies of various materials, including steel,8,9 aluminum,10,11 copper,12 PVC,13 and several other metal elements.14−16 Although many publications reported the actual lifespan distribution of durable goods,17 these distributions were only for a limited number of countries and goods. In addition, only a few studies discussed regional differences and temporal variation in average lifespans of some durable goods in several countries.1,18,19 Parameters of the product lifespan distribution were thus often assumed in material flow analysis based on past studies for limited numbers of countries and goods or were based on educated guesses. Average lifespan was often treated

Because the lifespan of a product determines the amount of material stocks and the end-of-life flows, extending the product lifespan could reduce waste generation and conserve natural resources.1,2 The potential contribution of this strategy has been discussed.3 An empirical analysis for automobiles in Japan demonstrated that extending the product lifespan decreased energy consumption and waste generation both directly, through in-use stocks, and indirectly, through automobile production activities.4 A study on household furniture and appliances in the U.K showed the substantial potential of extending their lifespan by reusing them, which reduces waste generation and virgin resource consumption.5 Extending the product lifespan may also contribute to reducing environmental impacts. An environmental benefit from increased product lifespan, however, depends on the impacts of use stage and technological progress such as improved energy and resource efficiency.6 Product lifespan is directly linked to these impacts; therefore, it is necessary to know the regional and longitudinal trends in product lifespan accurately in order to evaluate our progress toward sustainable consumption. © 2014 American Chemical Society

Received: July 5, 2013 Accepted: December 30, 2014 Published: December 30, 2014 1738

DOI: 10.1021/es505245q Environ. Sci. Technol. 2015, 49, 1738−1743

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Table 1. Maximum Likelihood Estimators of the Lifespan Distribution Parameters for Passenger Cars in 17 Countries at the End of 2008 country

average lifespan, yav (years)

shape parameter, b

coefficient of determination, R2

Australia Austria Brazil Canada Denmark Finland France Germany Ireland Italy Japan Netherlands South Korea Spain Switzerland United Kingdom United States

22.6 15.4 18.5 15.4 16.7 22.0 15.2 13.7 13.0 14.1 13.3 15.1 13.0 18.0 14.1 13.5 16.2

3.0 4.2 2.8 4.4 3.5 2.9 4.2 3.1 4.0 4.0 3.4 3.7 2.7 4.7 3.4 3.9 2.8

0.80 0.98 0.98 0.77 0.90 0.99 0.99 0.89 0.95 0.99 0.95 0.99 0.96 0.92 0.98 0.96 0.92

the survival rate distribution of passenger cars follows the Weibull distribution function and estimated its parameters by means of maximum likelihood method on the assumption that the errors follow the normal distribution. The survival rate function is expressed by using the Weibull distribution function as follows:

as a constant in time-series estimations, even though this parameter can vary among countries and years. The accuracy of the product lifespan distribution is important, however, because it affects the estimated material stocks and flows, and their implications. More precise data on product lifespan distribution for different countries and years are therefore needed based on actual regional differences and temporal variation in the product lifespan distribution. The reason for the lack of data could be that obtaining the primary data used for estimating product lifespan distribution is time-consuming, expensive, and sometimes quite difficult. According to a review by Oguchi et al., product lifespan distribution has most often been estimated based on the age profile of in-use products or discarded products.20 To obtain such detailed data, however, it is necessary to conduct extensive surveys for consumers or collected end-of-life products or to obtain complete data sets from registration systems such as those for automobiles. These approaches are time-consuming and expensive, and this is an important obstacle that prevents the collection of information on the actual lifespan distribution of products. A simplified estimation method would therefore allow more information to be gathered on the actual lifespan distribution of products in various countries and years. The aims of the present study were to estimate the product lifespan distribution in various countries and years, using passenger cars as an example, so as to provide evidence for regional and longitudinal trends, and to propose a simplified method for estimating the product lifespan distribution by conducting a sensitivity analysis of the effects of the distribution’s shape parameter.

R(y) = exp[− {y /yav }b × {Γ(1 + 1/b)}b]

(1)

where y is vehicle age, yav is the average lifespan, b is the shape parameter, and Γ is the gamma function. The Weibull distribution is widely used in reliability analysis to model the failure rate of technical objects.22 It has also been demonstrated that the Weibull distribution function provides a good approximation of the actual lifespan distribution of automobiles and other consumer durable goods.1,4,21 A Japanese study reported the likelihood ratio tests supported the hypothesis that vehicle lifespans in Japan follow the generalized gamma distribution.23 Similar statistical tests, however, did not reject the hypothesis that vehicle lifespan follow the Weibull distribution for several countries (see Supporting Information, SI). The Weibull distribution function also showed a good approximation for the target countries of this study compared with the generalized gamma distribution function, and the differences in the estimated average lifespan were not significant for understanding the regional and longitudinal trends (see SI). In addition, the Weibull distribution function has only two parameters, and this is of large advantage for enabling the simplified estimation. On the basis of these circumstances, we chose the Weibull distribution function for the estimation in this study. The information for the primary data used for this study are described in the SI. As the number of in-use cars used in this study excludes cars in dead storage, the estimated lifespan in this study is defined as the “domestic service lifespan,” which represents the length of time from the sale of a car to its end-ofuse with the final owner in each country.20 The number of new car sales, St‑i, represents the number of cars that were sold during the year t-i, whereas the number of in-use cars, Nt(i), represents the number of in-use cars at the end of the year t. In addition, Nt(i)/St‑i is a discrete value, while eq 1 is a continuous function. This should be considered in the

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MATERIALS AND METHODS We estimated the lifespan distribution of passenger cars for several countries based on the age profile of in-use cars. To do so, we used a procedure that has been used in past studies of the lifespan distribution of consumer durables.1,21 In this procedure, we calculated the survival rate of passenger cars with vehicle age i (years) at the end of the year t by dividing the number of in-use cars with age i at the end of the year t, Nt(i), by the number of new car sales in the corresponding sales year (t − i), St‑i. We then assumed that 1739

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Table 2. Temporal Variation in the Lifespan Distribution Parameters for Passenger Cars in Four Countries for Which Data Were Available average lifespan, yav (years) 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 a

shape parameter, b

Germany

United Kingdom

Japana

United States

Germany

United Kingdom

Japana

United States

na 13.4 13.5 13.6 13.6 13.7 13.9 14.1 13.5 13.7 13.3 na

na 13.9 13.8 13.7 13.7 13.6 13.7 13.6 13.6 13.5 na na

na 10.6 10.8 11.0 11.1 11.4 11.6 11.7 11.9 12.0 12.2 12.3

15.0 15.0 15.0 na na na na 15.9 na 16.2 na na

na 3.6 3.6 3.5 3.3 3.2 3.0 2.9 3.2 3.1 2.8 na

na 4.1 4.0 4.0 4.1 4.2 4.2 4.1 4.1 3.9 na na

na 3.7 3.6 3.6 3.5 3.5 3.4 3.4 3.3 3.2 3.3 3.3

3.5 3.3 3.2 na na na na 2.7 na 2.8 na na

Estimated values for a subset of cars with engines of less than or equal to 660 cm3, at the end of each fiscal year.

estimation process. In this study, we assumed that St‑i represents sales that occurred in the middle of the sales year (at the end of June of each year), i.e., y = i + 0.5 years. From some data sources, only the aggregated number of inuse cars was available for older cars (e.g., cars older than 14 years old). In such cases, we obtained results that were consistent with the statistical data for in-use cars by estimating the parameters under a constraint in which the calculated aggregated number of in-use cars for “older” cars (cars older than a years old) were consistent with the statistical data. That is, the following equation was satisfied: Nt =

∑ {St− i × R t(i + 0.5)} i>a

passenger cars (yav) differed greatly among the 17 countries (Table 1). The estimated average lifespan was the shortest in Ireland and South Korea (both 13.0 years) and the longest in Australia (22.6 years). Germany, the U.K., and Japan showed relatively short average lifespans (13.7, 13.5, and 13.3 years, respectively), whereas Finland and Brazil showed relatively long average lifespans (22.0 and 18.5 years, respectively). The shape parameter also differed among the countries, with a range from 2.7 to 4.7. We also estimated the lifespan distribution parameters for multiple years based on data from Germany, the U.K., Japan, and the United States, for which we obtained the number of inuse cars for each age in multiple years (Table 2). Note that the parameters for Japan were estimated for a subset of passenger cars with engines of over 660 cm3 because of statistical data availability, and thus are different from the values in Table 1. From 1999 to 2010, the average lifespan of passenger cars remained nearly stable in Germany and the U.K., but increased in Japan and the United States. The values of the shape parameter were almost stable in the U.K.; however, they changed from year to year in the other three countries. Sensitivity Analysis for the Shape Parameter. If either of the lifespan distribution parameters can be regarded as a constant value for all, regardless of the country or year, then eq 1 will be a function of only one parameter. It would then be possible to estimate the lifespan distribution based on only the number of sales and the total number of in-use products to satisfy the mass balance between sales and total in-use numbers.20 That is, no information on the number of in-use cars as a function of vehicle age would be needed for the estimation. We conducted a sensitivity analysis of the shape parameter and confirmed the sensitivity of the approximated lifespan distribution to changes in the value of the shape parameter was low (see the SI). Even though the estimated shape parameter values were different among the countries (Table 1), the analysis suggests that we can treat this parameter as if it were a constant for all countries. On this basis, we estimated the average lifespan and shape parameter for the 17 countries simultaneously by means of maximum likelihood method. The resulting shape parameter was 3.6, and Figure 1 compares the average lifespan estimated using a fixed value of the shape parameter (3.6) with the original estimates shown in Table 1.

(2)

The estimation was conducted for 17 countries: Australia, Austria, Brazil, Canada, Denmark, Finland, France, Germany, Ireland, Italy, Japan, The Netherlands, South Korea, Spain, Switzerland, the U.K., and the United States. These countries were selected because the primary data were considered reliable (which we determined by checking the consistency between data sources), and the number of imported secondhand cars24 was negligible compared with new car sales. The second reason is important because imported secondhand cars are not included in the number of new car sales, but are included in the number of in-use cars as long as they have been properly registered. If the number of imported secondhand cars is not negligible, then it is necessary to adjust the number of sales to include the imported secondhand cars, taking into account their age profile to calculate the survival rate properly. Thus, such countries were excluded from our estimates. However, the same method can be applied for estimating lifespan distribution in such countries if the number of imported secondhand cars can be included in the number of car sales, St‑i, with consideration of their age profile. Estimation for such cases is a future challenge for more comprehensive analysis.

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RESULTS AND DISCUSSION Lifespan Distribution of Passenger Cars in Different Countries. Table 1 shows the estimated lifespan distribution parameters for the 17 countries at the end of 2008. The coefficient of determination was high for all countries, and the survival rate of the passenger cars was approximated well using the Weibull distribution function. The average lifespan of the 1740

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could be assumed to be a constant among years also in countries other than Japan. A Simplified Method for Estimating the Lifespan Distribution. Our results demonstrated that the shape parameter of the lifespan distribution can be assumed to be the same fixed value for different countries and years. This finding enables us to estimate the average lifespan of passenger cars without detailed data on the number of in-use cars for each vehicle age. By assuming the shape parameter to be a constant value, eq 1 has only one unknown parameter: the average lifespan, yav. Because the calculated total number of in-use products by eq 3 should be equal to that from the statistical data, the lifespan distribution can be estimated by determining the value of yav, which makes the calculated total number of inuse products, Nt equal to the statistical data.

Figure 1. Relationship between the average lifespan of passenger cars estimated with a fixed shape parameter (b = 3.6) and the original values estimated with the actual shape parameter for each country. Data is for the end of 2008.

Nt =

∑ {St− i × R t(i + 0.5)} i

(3)

This method was used in some past studies to estimate the number of discarded items of electrical and electronic equipment.26−28 The method can also be utilized as a simplified method to estimate the lifespan distribution because it determines the number of discarded products and their average lifespan simultaneously. By using a constant value of 3.6 for the shape parameter, we estimated the average lifespan of passenger cars at each yearend so that the total number of in-use products calculated by eq 3 is equal to the statistical data. Figure 3 shows the results for the 17 countries in our study, as well as for three other countries: Belgium, Portugal, and Sweden, for which the accurate statistical data of total number of in-use cars were available. The difference between the average lifespan estimated using the simplified estimation method and the values in Tables 1

The difference between the estimated average lifespan with the fixed shape parameter (3.6) and the original estimation was less than or equal to 0.6 years (5% of the originally estimated values) for all of the countries. This suggests that the shape parameter of the lifespan distribution of passenger cars can be regarded as a constant value in estimating the lifespan distribution, regardless of the country, when errors of up to several percent can be accepted in the estimated average lifespan. In addition, assuming the constant shape parameter does not greatly affect the estimated in-use stock and end-of-life generation (see the SI). The shape parameter can be regarded as a constant value of 3.6 for all countries from the perspective of stock and end-of-life generation estimation. A Japanese study showed that the shape parameter of the distribution can be assumed to be a constant among the years in Japan by analyzing the lifespan distribution of automobiles (passenger cars and freight vehicles) and common home appliances.25 It has not been, however, investigated for other countries. We therefore performed a similar estimation using the fixed shape parameter (3.6) for multiple years using the data for Germany, the U.K., Japan, and the United States (Figure 2). The difference between the average lifespan estimated using the fixed shape parameter and the original estimation in Table 2 was 0.5 years or less in most cases, and the value did not differ greatly in any year. The results of the present study newly demonstrated that the shape parameter

Figure 2. Average lifespan of passenger cars estimated with a fixed shape parameter (b = 3.6). The original estimates (data points) are the values shown in Table 2. The results of Japan are for passenger cars, excluding cars with engines of less than or equal to 660 cm3.

Figure 3. Average lifespan of passenger cars at each year end in different countries estimated using the simplified estimation method based on a constant shape parameter. In the legend, countries are listed in the order of the estimated values for the year 2009. 1741

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Figure 4. Difference in stock and end-of-life estimates for the year 2008 between static and country-specific average lifespans, showing the ratio of estimated number of in-use cars (A) and end-of-life cars (B) in each country using average lifespan from the other 19 countries as substitutes to that using a country-specific average lifespan. The bars show the minimum and maximum values.

and 2 was 0.5 years or less in most cases. The average lifespan of passenger cars can be practically estimated using the proposed simplified estimation method, with an acceptable error. The longitudinal trend for the estimated average lifespan of passenger cars was almost stable in Austria, Belgium, Brazil, Germany, Ireland, Italy, Spain, the U.K., and Sweden during the study period. The average lifespan increased over time in the other countries. There were especially large increases (by 2 to 5 years) from 2000 to 2009 in Australia, Finland, Switzerland, South Korea, and the United States. These results suggest that consumer behavior related to using and discarding passenger cars differed among the countries we studied, even in developed countries, and that the lifespan has increased in many countries. The regional and longitudinal trends in product lifespan should affect the levels of material inputs and waste generation related to automobiles in each country. A quantitative analysis of these effects is needed in future research. Our results also showed that the average lifespan of products can differ greatly among countries and years, which indicates that inappropriate assumptions may lead to significant inaccuracy in material flow analysis. Figure 4 shows an example of the inaccuracy in the stock and end-of-life generation estimation caused by assuming regionally static average lifespans. We estimated the number of in-use and end-of-life cars for each country by using the average lifespans for the other 19 countries as substitutes. Equations for the estimation are shown in the SI. The figure compared the results with the estimates using the country-specific average lifespan. Assuming regionally static average lifespan caused an inaccuracy of up to 100% compared to the estimates using the country-specific average lifespan. Assuming temporally static average lifespan also causes a large difference in the estimation results as shown in SI. These sensitivity analyses indicate that if the average lifespan must be assumed, then the assumed values should be carefully selected and the impacts of the uncertainty of the assumptions on the estimation should be evaluated. In addition, product lifespan obviously affects the environmental impact at use stage, eventually affecting the results of life cycle assessment (LCA) for the product life cycle. The

proposed simplified method will contribute to more precise material stocks and flows estimation and LCA within each country by providing more quantitative data on actual product lifespans for different countries and years. Because we included Brazil in our study, it is also possible to assume the shape parameter to be a constant for developing countries. Countries with large amount of imported secondhand passenger cars, however, were excluded from the target of this study. High incidence of imported secondhand passenger cars is most likely in developing countries. The proposed method can be applied to such countries; however, the number of imported secondhand cars needs to be included in the car sales data with consideration of their age profile. Without this, the average lifespan will be overestimated because the number of car sales is undercounted. Because obtaining the quantitative data for the age-profile of imported secondhand automobiles is quite hard, a possible way is to assume the age-profile of automobiles as a certain distribution function. If its applicability is verified in future research, then the proposed simplified estimation method can be used for assessing how the product lifespan is extended by international reuse of secondhand products. Total lifespan in the extended geographic boundary, which includes both exporting and importing countries of secondhand products can be estimated using aggregated data of in-use products and sales in the exporting and the importing countries. Comparing the domestic lifespan of each country and the total lifespan of the extended geographic boundary, we can assess the extended product lifespan by international reuse, which is useful for evaluating the effect of international reuse of secondhand products on global waste products generation and the life cycle environmental impacts. It is also very useful if the proposed method can be applied to other durable goods, including home appliances, electronic products, and buildings, because detailed information on the number of in-use products for each product age is usually not easily available. Since the sensitivity of the estimated average lifespan to the value of the shape parameter is low as shown previously, the method can be applied for other types of products when the values of the shape parameter are not significantly different. A past study in Japan demonstrated that the shape parameter can be regarded as a constant for more 1742

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Environmental Science & Technology than 20 types of electrical and electronic equipment,29 indicating that it is likely that the method can be applied for other product types. The application of the proposed method would be further extended by obtaining empirical data on lifespan distribution for other countries as well as emerging technologies.

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ASSOCIATED CONTENT

* Supporting Information S

Comparison of the distribution parameters estimated by using the Weibull and generalized gamma distribution functions, information for the data used in the study, sensitivity analysis for the shape parameter, analysis of the inaccuracy in stock and end-of-life estimates caused by assuming static average lifespans. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +81-29-850-2784; fax: +81-29-850-2091; e-mail: oguchi. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Aiko Oba and Nick Coyle of R. L. Polk Japan for helpful information on the statistical data and the results. This work was supported by a JSPS KAKENHI grant (22710156). We thank two anonymous reviewers for their valuable comments.

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REFERENCES

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