Product Life Trade-Offs: What If Products Fail Early? - Environmental

Article pubs.acs.org/est

Product Life Trade-Offs: What If Products Fail Early? Alexandra C. H. Skelton and Julian M. Allwood* Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom S Supporting Information *

ABSTRACT: Increasing product life allows the embodied emissions in products to be spread across a longer period but can mean that opportunities to improve use-phase efficiency are foregone. In this paper, a model that evaluates this trade-off is presented and used to estimate the optimal product life for a range of metal-intensive products. Two strategies that have potential to save emissions are explored: (1) adding extra embodied emissions to make products more sturdy, increasing product life, and (2) increasing frequency of use, causing early product failure to take advantage of improvements in use-phase efficiency. These strategies are evaluated for two specific case studies (long-life washing machines and more frequent use of vehicles through car clubs) and for a range of embodied and use-phase intensive products under different use-phase improvement rate assumptions. Particular emphasis is placed on the fact that products often fail neither at their design life nor at their optimal life. Policy recommendations are then made regarding the targeting of these strategies according to product characteristics and the timing of typical product failure relative to optimal product life. analysis for refrigerators, and Regnier et al.10 compare different methods for calculating the economically optimal replacement period for cars. In this paper, these two methods are combined. A simple irregular replacement model is used to calculate the optimal lifethat minimizes embodied and use-phase CO2 emissions associated with energy useof a selection of metal-intensive products. Rather than assuming that the characteristics of these products are predetermined (as is usually the case in the optimal life literature), two strategies are explored that alter the product use-phase and embodied emissions profiles. The two strategies are (1) adding extra embodied emissions to make products more sturdy, increasing product life; and (2) increasing frequency of use, causing early product failure to take advantage of improvements in use-phase efficiency. The viability of saving emissions through these strategies is then assessed, bearing in mind that products frequently fail neither at their design life (as envisaged when they are manufactured) nor at their optimal life (as calculated by optimal life models).

1. INTRODUCTION A quarter of global industrial carbon emissions are caused by the production of steel, of which a third currently serves as replacement demand.1 In the future, as per capita demand for steel saturates in developing countries (as it has in developed countries2), we expect this replacement demand share to rise, reaching 80% by 2050.1 If we could extend the life of metalintensive productscars, buildings, appliances, machinery, and equipmentwe would reduce the replacement demand for steel and also the emissions associated with producing it. However, the pursuit of such savings can cause greater emissions by reducing opportunities to exploit advances in use-phase efficiency. This results in a trade-off: longer life products allow upfront embodied emissions to be spread across a longer period, and shorter life products take advantage of improvements in usephase efficiency. The existing literature on the environmental consequences of product life choices tackles this trade-off using two broad methods. The first involves the comparison of cumulative emissions across discrete product choices. The intention of these papers is to identify whether a particular decision (e.g., buying a more durable product or extending product life through repair) is justified. Examples include a comparison of standard and extended-life products,3 a comparison of new and remanufactured products,4 a comparison of washing machines that are reused at different ages,5 and the identification of a “break even” point at which the environmental burden of a new product is less than that from the continued use of an incumbent product.6,7 The alternative method is to calculate optimal product life given a set of improvement assumptions. For example, Kim et al.8 calculate the product life that minimizes emissions of a range of pollutants for a midsized United States passenger car over the period 1985−2020. Kim et al.9 also present the equivalent © 2013 American Chemical Society

2. MATERIALS AND METHODS This section explains the methodology used. Section 2.1 sets out the definitions of product life. Section 2.2 presents the boundaries of the analysis and the input assumption. In Section 2.3, two models of optimal product life are presented, one of which is chosen for analysis. 2.1. Product Life Definitions. In this analysis, the actual life of a product is defined as the time until the product is discarded Received: Revised: Accepted: Published: 1719

August 21, 2012 December 20, 2012 December 26, 2012 January 23, 2013 dx.doi.org/10.1021/es3034022 | Environ. Sci. Technol. 2013, 47, 1719−1728

Environmental Science & Technology

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Table 1. Data Boundariesa

a

This table outlines the boundaries of the product-specific input parameters to the model. OB = office block; WM = washing machine; C = car; P = plane. Only CO2 emissions that are associated with energy use are taken into account; other pollutants such as carbon monoxide (CO), nonmethane hydrocarbon (NMHC), and oxides of nitrogen (NOx) are excluded. Use-phase emissions that are not directly attributable to product choice have been excluded, e.g., trends towards washing at lower temperatures (facilitated by advances in detergents) and the decarbonization of the electricity grid, both of which reduce washing machine use-phase emissions without requiring product replacement, have been excluded. The data come from multiple sources, limiting cross-product comparisons, e.g., use-phase improvement rates are based on regulatory requirements (for car and office block), on expected penetration rates for the best available technology (for washing machine), and on expected technological improvements (for plane). Where necessary, units of energy have been converted to tCO2e using U.K. electricity grid emission factors. The limit to embodied emissions improvement was calculated using the theoretical emissions reduction potential for the principle materials that make up each product, taking into account changes in product weight for the car and plane. The limit to use-phase improvement was taken from Cullen et al. Further information on the assumptions made is provided in the Supporting Information.

Table 2. Product Specific Assumptions (2 sig. fig.)a E0 (tCO2e) office block washing machine car plane

360 0.27 2.9 52 000

u0 (tCO2e)

Elim (% initial)

16 0.14 1.8 100 000

68 75 79 100

ulim (% initial) 1 9 9 54

1 − α (% pa) 7.4 6.9 3.2 5.0

1 − β (% pa) 0.17 0.88 3.2 1.9

a

This table sets out the input assumptions to the model. As specified in Section 2.3.2, E0 = initial embodied emission; u0 = initial annual use-phase emission; Elim = embodied emissions limit; ulim = use-phase emissions limi; 1 − α = annual embodied emissions improvement towards limit; and 1 − β = annual use-phase improvement towards limit. An overview of the underlying assumptions is given in Table 1. Further information is provided in the Supporting Information.

or recycled. A product may go through multiple ownership cycles within its actual life, and actual life may extend beyond design/ service life (as envisaged when the product was made) because uncertain events do not occur (e.g., if a 50 year storm does not hit a building) or because consumers are willing to compromise

product quality to realize cost savings (e.g., second hand cars). Alternatively, a product’s actual life may fall short of its design/ service life because it is replaced prematurely. For example, according to Allwood et al.,11 products fail due to their physical performance (“degraded”), due to a decline in their performance 1720

dx.doi.org/10.1021/es3034022 | Environ. Sci. Technol. 2013, 47, 1719−1728


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relative to other alternatives (“inferior”), or due to individual and more systemic changes in preferences that alter the value placed on them by their users (“unsuitable” and “unwanted”). The term optimal product life is used to refer to the product life that minimizes total emissions (including embodied and use-phase emissions) attributed to a string of product replacements within a given time horizon. Only CO2 emissions associated with energy use are taken into account. 2.2. Boundaries and Input Assumptions. Table 1 outlines the boundaries of the product-specific input parameters to the model. Care has been taken to include only emissions that can be directly attributed to product choice. As the data come from multiple sources, it is not possible to draw a direct comparison across products. Nevertheless, the analysis is sufficiently realistic to provide a baseline from which the viability of different strategies can be assessed. A full dynamic LCA of the type conducted by Kim et al.,8 using consistent data sources, is recommended for more definitive estimates of optimal life. Table 2 gives the resultant product specific assumptions. 2.3. Model Outline and Choice. Two optimal product life models are outlined in this section. The first assumes regular replacement (Section 2.3.1); the second allows irregular replacement (Section 2.3.2). The models are compared in Section 2.3.3. 2.3.1. Regular Replacement Model. Equation 1 gives the emissions associated with replacing a product in year t, where E0 represents the embodied emissions in the product (denoted in upper case, as they apply to the entire product life), u0 represents the current annual use-phase emissions associated with the product (denoted in lower case, as they are incurred annually). α and β are the constant annual fractional changes in embodied and use-phase CO2 emissions associated with energy use (such that α = E(t + 1)/E(t), β = u(t + 1)/u(t), and (1 − α) and (1 − β) are the constant annual embodied and use-phase improvement rate, respectively).

Equation 4 can be solved numerically for optimal product life (T*). All that is needed to calculate the constant optimal replacement interval of a product over an infinite time horizon is the annual improvement rate in embodied and use-phase emissions (both assumed to be constant) and the current ratio of embodied to use-phase emissions. The emissions Z(tmax) associated with product ownership and use over a finite period, tmax, can then be found as N−1

Z(tmax ) =

i=0

where N is defined so that the replacement at NT* is the last replacement before the time horizon tmax and the first replacement after the time horizon is at (N + 1)T*. The last term of eq 5 apportions both embodied and use-phase emissions of the last product replacement in proportion to the fraction of its life that is used. 2.3.2. Irregular Replacement Model with Technical Limits. This model allows product life to vary over time. Here, both embodied and use-phase emissions improve toward limits (denoted Elim and ulim). α and β are defined as before but in this case describe improvement rates toward a limit. The embodied and use-phase emissions of a product made at time t are given by eq 6. E(t ) = E lim + α t (E0 − E lim) u(t ) = ulim + β t (u0 − ulim)

Z= (1)

∝

∑ E(t ) = E0 + αTE0 + α 2TE0 + ... t=0 ∝

t=0

+ ...

δZ δE = δti δt

1 − αT

⎡ δE t *i + 1 = t *i − ⎢ ⎢⎣ δt

(2)

Tu0

(8)

t *i

⎤ δu + u(t *i − 1) − u(t *i )⎥ / ⎥⎦ δt

t *i

(9)

The required derivatives of eqs 6 are (3)

δE = α t Ed ln α , where Ed = E0 − E lim δt δu = β t ud ln β , where ud = u0 − ulim δt

The optimal product life (T*) is found when the derivative of eq 3 with respect to T equals zero, so ⎛ E0 ⎞ αT *ln α 1 − β T * + Tβ T *ln β + =0 ⎜ ⎟ ⎝ u0 ⎠ (1 − αT *)2 (1 − β T *)2

t *i

δu δt t *i

Rearranging eq 8,

Tu0

1 − βT

+ u(t *i − 1) − u(t *i ) + (t *i + 1 − t *i )

= 0 for all t *i

Summing these two series gives the total emissions, Z, as +

(7)

At the optimal set of replacement times (t1*, t2*,...), it is a necessary (but not sufficient) condition that the derivative of Z with respect to each ti* in turn is zero, as expressed in eq 8.

E0

1 − βT

∑ [E(ti) + (ti+ 1 − ti)u(ti)] i=0

∑ u(t ) = Tu0 + TβT u0 + Tβ 2T u0

1−α

(6)

The cumulative emissions, Z, over an infinite time horizon for some specified set of replacement times ti are given by

Assuming that α,β < 1, the total embodied and use-phase emissions caused over an infinite time horizon by replacing a product every T years are

T

(5)

∞

u(t ) = β t u0

E0

tmax − NT * T*

* × (α NT *E0 + T *β NT u0)

E (t ) = α t E 0

Z=

∑ (α iT*E0 + T *β iT*u0) +

(4)

(10)

Substituting these derivatives into eq 8, 1721



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Figure 1. Impact of replacement assumptions on use-phase emissions. This figure is used to compare the performance of the regular replacement model (outlined in Section 2.3.1) and the irregular replacement model (outlined in Section 2.3.2). The figure shows that under the irregular replacement model (shown on the right) the use-phase emissions benefits of replacement (shown in red) always exceed the embodied emissions incurred (shown in blue), and the improvements in use-phase emissions are better exploited (use-phase emissions foregone, shown in green, are relatively small). The regular replacement model (shown on the left) under performs relative to the irregular replacement model, as over time the embodied emissions incurred for replacement exceed the use-phase emissions saved through replacement, and improvements in use-phase emissions remain under-exploited relative to the irregular replacement model. Together these findings show that the irregular replacement model is preferable to the regular replacement model in identifying the series of product lives that minimize CO2 emissions associated with energy use over the time horizon.

outweighs the embodied emissions cost. This is not the case in the regular replacement model, where the constant product life assumption eventually forces replacements that result in a net increase in total emissions. As a result, the irregular replacement model is used in the ensuing analysis.

t *i + 1 = t *i − [α t *iEd ln α + ud(β t *i−1 − β t *i )]/β t *i ud ln β ⎛α⎞ 1 − β t *i−1 −t *i , = t *i − k ⎜ ⎟ + ln β ⎝β⎠ E ln α with k = d ud ln β t *i

3. RESULTS In this section, the irregular replacement model outlined in Section 2.3.2 is used to estimate the optimal life of a range of metal-intensive products (Section 3.1). The case for adding extra embodied emissions in order to extend the life of products (Section 3.2) and the case for increasing frequency of use causing earlier product failure to take advantage of improvements in usephase emissions (Section 3.3) are then explored. 3.1. Optimal Product Life of a Range of Metal-Intensive Products. The opposing forces of use-phase and embodied emissions allow an optimal product life to be defined. When product life is relatively short, there are large gains to be had from spreading embodied emissions over a longer period. As product life increases, the use-phase efficiency of the product compared to the latest product available on the market diminishes. Eventually, the use-phase gains from replacement outweigh the benefits of spreading embodied emissions, and product replacement rather than product life extension saves emissions. The model outlined in Section 2.3.2 can be used to evaluate this trade-off and calculate the product life that minimizes emissions for specific products. In the first column of Table 3, this “optimal” product life is reported for a range of metal-intensive goods. The second column gives estimates of typical product replacement. Where possible these estimates of “actual” life are based on consumer behavior (as recorded in scrappage data25 or estimated by industry26) or otherwise estimated from stock models27 or design lives.19,28 Table 3 shows that the office block and the washing machine typically fail prematurely, before their

(11)

The second replacement period can be calculated for any given first replacement period using eq 11. This method can then be used iteratively (the second replacement period defining the third, etc.) to find all replacement periods over a given time horizon (tmax). The total emissions over tmax are N−1 ⎡t −t ⎤ N ⎥ Z = [ ∑ [E(ti) + (ti + 1 − ti)u(ti)]]⎢ max t − t ⎣ N + 1 N⎦ i=0

× [E(tN ) + (tN + 1 − tN )u(tN )]

(12)

where the timing of product replacements are denoted ti and where t0= 0, tN is the last replacement within the time horizon and tN + 1 is the first replacement after the time horizon. The optimal first replacement period that minimizes total emissions can be found numerically using eqs 11 and 12. For the purpose of this analysis, a time horizon of 500 years is used. Although this may seem excessive for relatively short-lived products (such as planes and washing machines), it is necessary in order to allow meaningful results to be obtained for long-lived products such as buildings. 2.3.3. Model Choice. Figure 1 demonstrates the different emissions impacts of the two models. Figure 1 shows that the irregular replacement model (outlined in Section 2.3.2) is preferable to the regular replacement model (outlined in Section 2.3.1), as in the irregular replacement model, replacement only occurs where the use-phase emissions benefit 1722



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Table 3. Actual and Optimal Product Lifea

than its typical life (60 years) would run that office block for just over four years. Figure 3 explores the sensitivity of optimal product life to different input assumptions and shows that the use-phase assumptions (both improvement rate and limit) have a larger bearing on optimal product life that the embodied emissions assumptions. Figure 3 also corroborates Kim et al.’s8 statement that “optimal lifetimes tend to be longer as the ratio of fixed to marginal environmental burden becomes greater”. The sensitivity analysis in Table 3 confirms that optimal product life is most sensitive to use-phase improvement assumptions and to the initial ratio of use-phase to embodied emissions. Two case studies are presented in the next sections: an extended-life washing machine to explore the justification of increasing embodied emissions to enhance durability (Section 3.2) and a car club to explore the case for increasing frequency-ofuse to cause early product failure and exploit improvements in use-phase emissions (Section 3.3). In light of the sensitivity analysis, to generalize these findings, in each section the analysis is conducted for the case study product and for two products that represent the extremes of the E0/u0 continuum (an office block and a plane) under different use-phase improvement assumptions. 3.2. Justification of Durable Products with Higher Embodied Emissions. More durable and more adaptable products often require additional material to make them more sturdy, less susceptible to wear, and more likely to meet the changing needs of users. Such additional material increases embodied emissions. Figure 4 illustrates this point using the example of standard and extended-life washing machines. Timing replacement to minimize emissions (T0* = 21 years for the standard machine, and T1* = 22 years for the extendedlife machine) would result in marginally higher emissions from the extended-life machine compared to the standard machine. The same is true if each machine were to last for its design life (T0d = 12 years and T1d = 31 years). However, Hopwood16 estimates that the average life expectancy of a washing machine in the United Kingdom is 5.5 years. If attributes of the long-life machine ease the causes of premature failurebecause the machine is more costly to purchase and so more care is taken to maintain it, because its aesthetics do not degrade as much, or because more durable parts require less maintenance emissions can be saved by choosing the long-life option: an extended-life machine that is used for at least 13 years (T1min in Figure 4) saves emissions relative to a standard machine that is used for 5.5 years. Notably, this is 3 years longer than the 10 year guarantee offered with the extended-life machine. Returning to the failure modes presented by Allwood et al.,11 the above analysis means that adding embodied emissions to products to enhance durability can only be justified if there is a high degree of confidence that the product will not fail because it is “inferior”, “unsuitable”, or “unwanted” prior to this minimum increase in product life. The point is explored more generally in Figures 5 and 6 in which the minimum increase in product life required to justify a 10% increase in embodied emissions and the resultant maximum potential emissions savings are reported for the washing machine and for the two products that represent the extremes of the E0/u0 continuum under different use-phase scenarios. The following conclusions can be drawn from Figures 5 and 6:

sensitivity analysis (−10%) base case assumptions

office block washing machine car plane

E0/u0

Elim

ulim

α

β

optimal life

actual life

135 21

60 6

135 19

135 20

135 21

135 21

23 7

10 12

14 25

10 10

10 11

10 10

10 12

6 5

optimal life

a

Using this table, the optimal product life that minimises CO2 emissions associated with energy use (calculated using the model set out in Section 2.3.2 under the product specific assumptions set out in Table2) can be compared to the actual life of four metal-intensive products. All estimates are shown to the nearest year. The second part of the table (labled “Sensitivity analysis” to the right) presents the results of a sensitivity analysis in which each input parameter was reduced individually in turn by 10%. The sensitivity analysis shows that optimal life is most sensitive to the use-phase improvement rate and to the original ratio of embodied to product specific use emissions.

optimal lives are reached, whereas the car and plane tend to outlive their optimal lives. Figure 2 shows how the timing of first replacement effects total emissions over the time horizon. From Figure 2, it is clear that

Figure 2. Emissions near optimal product life. This figure shows the effect of the timing of first replacement on total emissions over the time horizon for a range of metal-intensive products. For each product, the optimal product life and emissions at optimal product life, calculated using the irregular replacement model outlined in Section 2.3.2, have been set equal to one to create an index. As a result, the curves show changes in emissions over the time horizon (shown on the y-axis and calculated according to eq 12) when the timing of first replacement (product life, shown on the x-axis) deviates from the optimal. The product specific assumptions are outlined in Table 1. The curves in this figure are not smooth. This is particularly evident for the office block but is true for all the curves. As explained in Section SI.7 of the Supporting Information, the local maxima are caused by the limited time horizon; the constrained life of the last replacement is not long enough for the full use-phase effect of the timing of the last replacement to be realized. In order to remove this distortive effect, these curves have been smoothed in the remainder of the analysis.

across all the products the burden of early replacement is at least as great as that of delayed replacement. Although the emissions savings from moving to optimal life are proportionately small, the absolute savings are sizable. For example, the emissions savings from using an office block for its optimal life (135 years) rather

• Built-in-redundancy can only be justified if products typically fail significantly below their optimal life (at least 1723



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Figure 3. Optimal life: Sensitivity to input assumptions. This figure shows the sensitivity of the optimal first replacement period (optimal life, shown on the y-axis) to different input assumptions. Namely, to the ratio of initial embodied to initial annual use-phase emissions (x-axis) to different assumptions regarding the improvement in embodied and use-phase emissions (shown in red and pink) and to different assumptions regarding the limit to embodied and use-phase improvements (shown in dark and light blue). The following assumptions have been made for each scenario: base case assumptions (α = β = 99.5%, ulim/u0 = Elim/E0 = 70%); strong use-phase improvement (same as base case assumptions apart from β = 97%); strong embodied improvement (same as base case assumptions apart from α = 97%); low use-phase improvement limit (same as base case assumptions apart from ulim/u0 = 30%); low embodied improvement limit (same as base case assumptions apart from Elim/E0 = 30%). The graph has been generated by calculating optimal product life under each set of assumptions for the full E0/u0 continuum, using the irregular replacement model outlined in Section 2.3.2.

Figure 4. Comparison of emissions from standard and long-life washing machines. This figure compares the total emissions over the time horizon for a standard washing machine (as specified in Table 1) and an extended-life washing machine supplied by ISE (as specified in Section SI.8 of the Supporting Information) calculated according to eq 12. The extended-life machine has 22% higher embodied emissions than the standard machine, increasing the design life from 12 to 31 years. For each machine, optimal product life, which minimize emissions, is shown in green. Total emissions over the time horizon (y-axis) are expressed as an index, which has been set equal to one at the emissions at optimal product life for the standard machine. As a result, the graph shows changes in cumulative emissions relative to this optimum for different assumed product lives of the two machines.

• The time required to justify built-in-redundancy is lower and the potential to save emissions is greater when there is a strong improvement in use-phase emissions and the product typically fails before its optimal life. However, this situation is unlikely as a strong improvement in use-phase emissions shortens optimal life.

one-third to two-thirds below optimal life across the scenarios explored here). With reference to Table 3, this means that built-in-redundancy should be considered for the office block and the washing machine, but not for the car and the plane. • The potential for emissions savings through built-inredundancy is greater for embodied emissions intensive products (such as the office block) than for use-phase emissions intensive products (such as the plane).

3.3. Justification of More Frequent Use of Products. There are many productsfor example, cars, washing machines, and batteriesfor which design life is defined as a level of service output. Using these products more frequently causes them to fail 1724



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Figure 5. Minimum increase in product life required to save emissions through 10% built-in-redundancy under different use-phase improvement scenarios. This figure is used to explore the case for building in redundancy to improve product durability over a range of products that span the E0/u0 continuum (ranging from the embodied emissions intensive office block on the left to the use-phase intensive plane on the right, and including the case study productthe washing machineto represent the center of the continuum) and over a range of use-phase improvement scenarios. The high and low use-phase improvement scenarios are characterized as follows: low use-phase improvement, β = 99.99%; high use-phase improvement, β = 95%. Product specific improvement rates and initial use-phase and embodied emissions are outlined in Table 1. To allow comparison across products, the embodied and use-phase improvement limits have been standardized to the average across products. The plots have been constructed by calculating the emissions profiles of two products (a standard product, as defined in Table 1, and one with 10% extra embodied emissions) using the irregular replacement model outlined in Section 2.3.2. The minimum increase in product life required to save emissions is then calculated using the method used to identify T1min in Figure 4. This analysis is conducted for a range of actual product lives. The equivalent plot for the car is provided in Section SI.10 of the Supporting Information.

Figure 6. Maximum emissions savings through 10% built-in-redundancy under different use-phase improvement scenarios. This figure shows the maximum potential emissions savings that could be achieved for the three products and three use-phase scenarios set out in Figure 5. As before, the low use-phase improvement scenario assumes β = 99.99%, the high use-phase improvement scenario assumes β = 95%, and the assumed product specific improvement rates and initial use-phase and embodied emissions are outlined in Table 1. In this figure, the maximum emissions saving that could be achieved are calculated by comparing the emissions at any given actual life of the standard product to emissions at the optimal life of a product that has 10% extra embodied emissions. These maximum potential savings are therefore calculated under the assumption that the product with 10% built-inredundancy is used for its optimal life. In each case, actual product life is expressed as an index that has been set equal to one for optimal product life of the standard product (calculated using the irregular replacement model outlined in Section 2.3.2), and the maximum potential savings are expressed as an index that is set equal to one at the emissions (calculated using eq 12) associated with using the standard product for the given actual life.

earlier. If there is no improvement in the emissions intensity with which these products are made and used, logically there will be no emissions savings per unit service output through more frequent use. However, if improvements in use-phase emissions

and embodied emissions are expected, the same logic used in the previous section can be applied to estimate emissions savings that result from more frequent use. The example of a car-sharing scheme is taken to illustrate this point. 1725



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Figure 7. Comparison of emissions from privately owned and car-sharing scheme vehicles. This figure compares the total emissions over the time horizon for a privately owned vehicle and a vehicle in a car-sharing scheme. Total emissions have been calculated according to eq 12. The underlying assumptions are reported in Section SI.9 of the Supporting Information. For each vehicle, optimal product life, which minimize emissions, is shown in green. Total emissions over the time horizon (y-axis) are expressed as an index, which has been set equal to one at the emissions at optimal product life for the privately owned vehicle. As a result, the graph shows changes in cumulative emissions relative to this optimum for different assumed product lives of the two vehicles. The higher frequency of use of vehicles within the sharing scheme increases annual use-phase emissions. Although this initially causes an upward shift in the emissions profile for any given vehicle life, once adjusted for the number of people using the vehicle, the emissions associated with one individual’s travel (shown in Figure 7) are significantly lower.

Figure 8. Emissions savings from tripling frequency of use under different use-phase improvement scenarios. This figure is used to explore the case for increasing frequency of use over a range of products that span the E0/u0 continuum (ranging from the embodied emissions intensive office block on the left to the use-phase intensive plane on the right, and including the case study productthe carto represent the center of the continuum) and over a range of use-phase improvement scenarios. The high and low use-phase improvement scenarios are characterized as follows: low use-phase improvement, β = 99.99%; high use-phase improvement, β = 95%. Product specific improvement rates and initial use-phase and embodied emissions are outlined in Table 1. To allow comparison across products, the embodied and use-phase improvement limits have been standardized to the average across products. In each case, actual product life is expressed as an index that has been set equal to one for optimal product life of the standard product (calculated using the irregular replacement model outlined in Section 2.3.2). Similarly emissions savings are expressed as an index that is set equal to one at the emissions (calculated using eq 12) associated with using the standard product for the given actual life.

vehicle that is driven for half the average noncommuting mileage is compared to a car that is included in a car-sharing scheme in which members on average drive this same distance. According to Figure 7, emissions can be saved across the board regardless of the relative position of actual and optimal life. If the vehicles are assumed to fail at their design life (the point at which they reach 150,000 km32.4 years for the privately owned

In a car-sharing scheme, members pay a subscription fee, giving them the right to book a car from the pool of vehicles owned by the scheme. Such schemes are typically not financially viable for commuters but can offer substantial financial savings to occasional users for whom the overheads of private car ownership (e.g., the purchase price of a vehicle, insurance, road tax, etc.) appear high. As such, in Figure 7, a privately owned 1726



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occasionally used car and 2.16 years for the car club car) emissions are reduced by approximately 60% in the car-sharing scheme. In Figure 8, the case for increasing frequency of use is explored more generally for three products that span the E0/u0 continuum and three use-phase emission improvement assumptions. The following conclusions can be drawn from Figure 8: • There is potential to save emissions through increasing frequency of use of products with limited service output regardless of the relative magnitude of initial use-phase and embodied emissions and regardless of the timing of typical product replacement relative to optimal product life. • The magnitude of emissions savings is highly sensitive to the use-phase improvement rate. Increasing this rate from 0.1% to 5% pa increases the potential savings from 5% to over 50% of initial emissions. As such, opportunities to increase frequency of use should be sought especially for products that exhibit strong use-phase improvements.

shortening product life, and better exploiting use-phase improvements. This results in emissions savings regardless of when the product fails. The greatest savings occur when strong improvements in use-phase efficiency are expected. Of the products considered here, this strategy is recommended for the plane (e.g., through improved logistics), the car (e.g., through car clubs), and the washing machine (e.g., through communal washing machines in blocks of flats). The model used is highly stylized: (1) maintenance and repair are not taken into account; (2) performance of the product is assumed not to deteriorate; (3) no emissions credits are assigned according to end-of-life routes; and, (4) both embodied and usephase emissions are assumed to improve at a constant rate over time. The allocation of use-phase emissions to products is particularly cumbersome for the building for which analysis at a component or subassembly level is likely to be more appropriate. The building is also a poor example for the argument regarding frequency-of-use, as buildings do not have a fixed level of service output. It was nevertheless useful to include the building in the analysis as an example of an embodied emissions intensive product.

4. DISCUSSION In this paper, a simple model of time-varying optimal product life has been presented and used to assess the viability of different product life strategies under the assumption that products do not always fail when they are expected to. The following policy relevant conclusions can be drawn from the analysis: • A common concern is that replacing products later causes higher emissions because use-phase emissions savings are foregone. This paper has shown that the emissions cost of premature product replacement is at least as great as that of delayed replacement even for products for which a strong use-phase improvement is expected (e.g., cars). • Optimal product life is particularly sensitive to assumptions regarding improvements in use-phase emissions; a higher use-phase improvement rate results in a shorter optimal product life. As a result, stronger use-phase emissions standards will reduce the emissions burden of products that are replaced early because they become “inferior”, “unsuitable”, or “unwanted”. • Policies should be aimed at fully exploiting standard products before built-in-redundancy is considered, ensuring that a standard washing machine is used for its design life, e.g., through incentives for better maintenance and replaceable aesthetic components (draws/doors), has a greater potential to save emissions than the promotion of longer life, higher embodied emission machines. • Built-in-redundancy is only justifiable when products fail significantly below their optimal product life and results in the greatest proportionate emissions savings in embodied emissions intensive products that exhibit strong use-phase improvements. Of the products considered in this paper, built-in-redundancy should only be considered for the washing machine and the building, not for the plane and the car. • A high confidence that significant increases in product life can be achieved is required in order to exploit emissions savings through built-in-redundancy. Long-life, higher embodied emission products should only be targeted at users that are likely to use them for longer than average (these users may be self-selecting if the long-life option is more expensive). • When a product has a defined level of service output, emissions can be saved by increasing frequency of use,

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ASSOCIATED CONTENT

S Supporting Information *

Details of the assumptions made about the four case study products examined in the results section. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +44 (0)1223 338181; e-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Both authors are supported by a Leadership Fellowship from the U.K. Engineering and Physical Sciences Research Council (EPSRC), Reference EP/G007217/1.

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REFERENCES

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Product Life Trade-Offs: What If Products Fail Early? - Environmental

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