**Oguchi M.**

National Institute for Environmental Studies, Tsukuba, Japan

**Keywords:** actual product lifetime; estimation methodology; definition; durable goods; import of secondhand products.

**Abstract:** This paper introduces the methodologies for estimating actual product lifetime distribution. On the basis of a literature review, it was found that there are three common approaches for estimating actual product lifetime distribution in literature. Theoretically any of the three approaches can be selected for estimation as far as representative primary data is available, but unless accurate data are available the estimated average lifetime can vary. In addition, various different definitions of ‘lifetime’ can be defined and the lifetime definitions are determined by estimation approaches and primary data used for the estimation. The paper also introduces a simplified estimation method which does not require detailed information of product-age profile and enables estimation from the total number of in- use products that is easier to investigate.

## Introduction

Product lifetime is important information for understanding progress toward sustainable consumption and estimating the stocks and end-of-life flows of products. A certain amount of actual lifetime data is available in literature; however, it varies in the definition and the employed estimation methods. This paper discusses the characteristics of methodologies for estimating actual product lifetime distribution on the basis of literature review. The paper also introduces a more simplified method for easier estimation of actual product lifetime distribution.

## Common approaches for estimating actual product lifetime distribution

Actual lifetime differs among individual products (i.e. owners); therefore, lifetime of a particular product-type is expressed as a distribution. Three common approaches for estimating actual product lifetime distribution were found in literature (Table1, Oguchi et al., 2010).

These approaches estimate product lifetime distribution based on the past sales and the number of in-use products or discarded products with their product-age profile. The large differences among the approaches are the required information and the directly estimated distribution. The approach (1) estimates the discard rate distribution which directly represents lifetime distribution. The other two approaches estimate the survival rate distribution or the failure rate distribution. But theoretically they can be converted to the discard rate distribution.

The approaches (1) and (2) are often used for automobiles and consumer durable goods. The approach (3) is often used for buildings because it needs no sales data which is usually hard to obtain for buildings.

Any of these three approaches can be selected for the estimation as long as good primary data (i.e. complete dataset) is available such as the case of passenger cars. In the case of electrical and electronic equipment, however, there were a few years difference in the estimated average lifetime between approaches. These differences can be attributed to biases of sample surveys, because technically similar results can be obtained approaches if accurate data is available as confirmed from the case of passenger cars. We must be cautious about the representativeness of primary data when the estimation is based on a sample survey.

## Various ‘lifetime’ definitions

Various different definitions of ‘lifetime’ can be defined according to the starting and ending points for the periods (Figure 1, Murakami et al., 2010). Some of the lifetime definitions are completely different from others, so we must distinguish these definitions clearly to avoid misunderstanding and misuse of reported or estimated actual lifetime data. Four major definitions were found in the literature; ‘total lifetime,’ ‘domestic service lifetime,’ ‘possession span,’ and ‘duration of use.’ The former two basically denotes how long a product stays in society, and the latter two denotes how long a single owner possesses or uses a product. The most common definition in the literature was ‘domestic service lifetime’ and another common one was ‘duration of use.’

The ‘lifetime’ definition is determined by the estimation approach and/or primary data used for the estimation. For example, if the lifetime distribution is estimated by using the approach (1) based on the investigation of the number and age-profile of collected end-of-life products at recycling facilities, the estimated lifetime should be ‘total lifetime.’ If the estimation is done by using the approach (2) based on a questionnaire survey to consumers asking how long they use their old products, the estimated lifetime should be ‘duration of use,’ or ‘possession span.’

## A simplified method for estimating actual product lifetime

The method and a case of passenger cars To apply the approaches introduced above, it is necessary to conduct some extensive surveys to obtain detailed information on the age profile of in-use products or discarded products. Because this is time-consuming and cost- intensive, this should be one big obstacle that prevents the collection of actual product lifetime data. Regionally- and temporally-static product lifetime is often assumed in material flow analysis and lifecycle assessment based on the results from limited studies or educated guesses. Inappropriate assumption, however, may cause a large inaccuracy in the results; therefore, more precise data on regional differences and temporal variations in the actual product lifetime needs to be estimated.

In this context, the author and a colleague proposed a more simplified method for estimating product lifetime in different countries and years which does not require detailed information of product-age profile (Oguchi and Fuse, 2015). With this method, product lifetime distribution is estimated on the basis of mass- balance of products. Assuming that the survival rate distribution of products follows any statistical distribution function such as the Weibull distribution function, the survival rate distribution can be determined so that the total number of in-use products calculated from past sales and the survival rate distribution consists with the observed number. Thus, average lifetime can be estimated only from the past sales and the total number of in-use products, which is easier to investigate.

To apply this simplified method, unknown parameter should be only one, i.e. practically parameters other than ‘average lifetime’ must be given. The author and a colleague examined the possibility of applying a constant value to the distribution parameter by using passenger cars as an example. It was assumed that the lifetime distribution follows the Weibull distribution function with two parameters: average and shape parameter. Then the applicability of a constant value to the shape parameter was examined.

Distribution shape slightly changed according to the value of the shape parameter, but it appeared that the sensitivity is not so high. Thus, average lifetime was estimated by assuming shape parameter to be a constant value 3.5, which is the average value of 18 countries. As a result, the estimated average lifetime with the constant shape parameter was almost the same as the original estimates for each country. Reasonably good approximation results were obtained suggesting that the shape parameter can be replaced by a constant for various countries in the case of passenger cars.

Taking passenger cars as an example, the proposed method was applied for estimating the longitudinal trend in the average lifetime from 2000 to 2010 in 20 countries. Figure 2 shows the results. The estimated lifetime is defined as ‘domestic service lifetime.’

The estimated average lifetime differed greatly among the countries from 9 years to 23 years. The average lifetime had been almost stable in Austria, Belgium, Brazil, Germany, Ireland, Italy, Spain, Sweden, and the UK. In other countries, the average lifetime had been increasing. Especially large increases (2–5 years) was seen in Australia, Finland, Switzerland, South Korea, and the United States. These results suggest that consumer behaviour on using and discarding passenger cars differed among countries and changed over the years even in developed countries.

The introduced simplified method can be used for estimating actual product lifetime in various countries and years more easily. Based on the results, we can understand the differences in actual product lifetime between countries and its change along years.

### Applicability to other product types

It is also useful if the proposed method can be applied to other product-types such as electrical and electronic equipment 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 lifetime to the value of the shape parameter is low as noted previously, the method may be applied for other types of products when the values of the shape parameter are not significantly different.

The possible applicability can be discussed based on two Japanese studies. Oguchi et al. (2006) estimated parameters of the actual lifetime distribution (average ‘domestic service lifetime’ and shape parameter) of various types of electrical and electronic equipment in 2003. The estimation was done by using the estimation approach (2) based on a questionnaire survey to 9000 households and 5000 enterprises on the number and the product age of in-use products. According to the results, the estimated shape parameters differed from 1.7 to 3.3 for 22 product-types. However, the similar values were obtained for the average lifetime when the shape parameter was replaced by a constant value within the range of 1.7–3.3. In addition, Tasaki et al. (2001) demonstrated that the shape parameter can be replaced by a constant value over time by using the data for seven common home appliances. These results suggest that it would be possible to apply the proposed simplified method to various types of electrical and electronic equipment in one country.

There is no sufficient data of actual lifetime distribution of those product-types for verifying the applicability of the simplified method to electrical and electronic equipment in various countries. The application of the proposed method would be further extended by obtaining empirical data on lifetime distribution for other countries and emerging technologies as well.

### A future challenge: estimation taking into account imported second-hand products

High incidence of imported second-hand products may be likely in developing countries. The proposed simplified method can be applied to such countries; however, the number of imported second-hand products needs to be taken into account with consideration of their age profile. Imported second-hand products are not included in sales data but are included in the number of in-use products. Unless the number of sales is adjusted to include the imported second-hand products, average lifetime will be overestimated because the number of sales is undercounted. This is quite challenging because obtaining quantitative data for the age-profile of imported second-hand

products is quite hard. A possible solution is to assume the age-profile of imported second- hand products as a certain distribution function and include the imported second-hand products into the number of sales by taking into account the age-profile. If the applicability of this approach is verified, the method can contribute to assessing how the product lifetime is extended by international reuse.

## Conclusions

This paper discussed the methodologies for estimating actual product lifetime distribution. There are three common approaches used for estimating actual product lifetime distribution in literature. Theoretically any of the three methods can be selected when representative primary data is available, but unless accurate data is available the estimated average lifetime can vary. In addition, various different definitions of ‘lifetime’ can be defined. As the lifetime definitions are determined by estimation approaches and primary data used for the estimation, an appropriate methodology needs to be selected according to the purpose of utilizing the estimated lifetime data. A simplified estimation method was also introduced by taking passenger cars as an example. The method would contribute to obtaining more data in various countries and years. The applicability of the proposed simplified method to other products was also discussed for the case of Japan; however, future research is needed on other countries’ cases.

## Acknowledgments

The content of this paper is based on the results of collaborative works with Shinsuke Murakami, Tomohiro Tasaki, Ichiro Daigo, Seiji Hashimoto, and Masaaki Fuse. The work is supported by research grants from Ministry of the Environment, Japan (K2031, 3K143010) and JSPS KAKENHI grant (22710156).

## References

Murakami, S., Oguchi, M., Tasaki, T., Daigo, I., Hashimoto, S. (2010) Lifespan of commodities, Part. I: The creation of a database and its review. Journal of Industrial Ecology, 14 (4), 598–612.

Oguchi, M., Kameya, T., Tasaki, T., Tamai, N., Tanikawa, N. (2006) Estimation of lifetime distributions and waste numbers of 23 types of electrical and electronic equipment. Journal of the Japan Society of Waste Management Experts, 17, 50–60 (in Japanese with English abstract, figures, and tables).

Oguchi, M. & Fuse, M. (2015) Regional and longitudinal estimation of product lifespan distribution: A case study for automobiles and a simplified estimation method. Environmental Science and Technology, 49, 1738–1743.

Oguchi, M., Murakami, S., Tasaki, T., Daigo, I., Hashimoto, S. (2010) Lifespan of commodities, Part. ΙΙ: Methodologies for estimating lifespan distribution of commodities. Journal of Industrial Ecology, 14 (4), 613–626.

Tasaki,T., Oguchi, M., Kameya, T., Urano, K. (2001) A prediction method for the number of waste durable goods. Journal of the Japan Society of Waste Management Experts, 12, 49–58 (in Japanese with English abstract, figures, and tables).