8

- F

- i APPENDIX 8

- F. RESIDENTIAL BOILER LIFETIME DETERMINATI ON

TABLE OF CO NTENTS

8

- F.1 INTRODUCTION

................................ ................................ ................................ . 8

- F

- 1
8

- F.2 LIFETIME LITERATURE REVIEW

................................ ................................ ... 8

- F

- 1
8

- F.3 METHODOLOGY

................................ ................................ ................................ 8

- F

- 48

- F

- 1 APPENDIX 8

- F. RESIDENTIAL BOILER LIFETIME DETERMINATI ON

8

- F.1 INTRODUCTION

DOE define s lifetime as the age when a product is retired from service. DOE notes that a large percentage of boiler equipment now on the market were not available 10+ years ago and
therefore comprehensive lifetime data is not yet available . Also

, there is an ongoing evolution of the boiler component l ifetime of which has n o t been thoroughly assessed yet

. 1

DOE used national survey data, along with manufacturer shipment data, to calculate the
distribution of boiler lifetimes. DOE assumed that the lifetime of a boiler is the same at different efficiency levels. DOE assumed a median lifetime valu e of 22 years for both gas and oil

- fired
boilers based on an updated literature review from that which was performed in the analysis for the 2007 Final Rule Rulemaking. 2

8

- F.2 LIFETIME LITERATURE REVIEW

In order to capture lifetime variances due to new boiler technology, DOE performed a
lifetime literature review. Table 8

- F.2.1 presents a range of product lifetime s and sources found by DOE . The data show that DOE’s assumed lifetime for boilers fits within the bounds of the
current boiler lifetime estimates

.8

- F

- 2 Table 8

- F.2.1 Reside ntial Boilers: Product Lifetime Estimates and Sources
Typical Lifetime or Range (years) Source
Unspecified Boiler Fuel Type

10

- 20 Federal Trade Commission 3

10

- 15 PM Engineer (2012) ∞ 4

15 WAPTAC 5 , Creating Better Homes 6 , CIBSE ‡ ∞ 7

15

- 20 Dunlop (2003) ‡† 8

17 Keman, et al. 9

18

- 32 1998 Gas Research Institute a 10

20 1994 Gas Research Institute b 1

, PM Engineer (2002)
† 11

21 PM Engineer (2002) ‡ 11

25 CIBSE * 7

25

- 35 AHR The NEWS (1999) 12

29 PM Engineer (2002) *^ 11

30 Old House Web 13

30

- 50 Dunlop (2003) * 8

80 (coal to oil to gas) Dunlop (2003) * 8

20

- 30 EIA (2013)

Gas Boilers

10 CIBSE 7

Low = 13, Ave=17, High=22 1990 Gas Research Institute (GRI) study 14

15

- 20 4ecotips 15

18 Mid

- Atlantic Technical Reference Manual (2011) 16

Average = 20; Low = 17; High = 24 Appliance Magazine ( 2009 ) 17

20 PM Engineering(2001) † 18 , Mid

- Atlantic Technical Reference Manual (2011) 16

a GRI notes that the expected (based on historic expectations on traditional equipment) lifetime of boilers was 30

- 50 years however they believed (based on contemporary equipment as indicated by interview and focus g roup responses) boiler lifetime would be 20

- 40 years. Actual lifetime range is listed in table and is based on actual data

collected.

b Lifetime value represents weighted median age for servicing of a non

- condensing boiler primary heat exchanger.

The GRI s ample includes 84 units which had a mean service lifetime of 18.9 years, weighted mean of 18.9 years, and median of 20 years.8

- F

- 3 20

- 30 RAND Engineering ‡ 19

21 2007 National Association of Home Builders Study 20 , PM Engineering (2001) ‡ 18

>22 ASHRAE (2011) ‡ 21

Average = 23 Keman, et al. * 9

24

- 25 ASHRAE (2011) ‡ 21

24

- 30 American School & University ‡ 22

25 DOE 200 3 23 , RAND Engineering 19 *, DCA (2011) 24

Average = 25; Low = 20; High = 30 c Residential Boilers Final Rule 2007 2

25.3 LBNL study(2011) 25

29 PM Engineering(2001) *^ 18

30 Atlanta Gas Light Company 26 , RSMeans (2013) 27

35 ASHRAE (2011) * 21

40 1994 Gas Research Institute ∞ d 1

Oil Boilers

Low = 12, Ave=15, High=19 1990 Gas Research Institute (GRI) study 14

20 Nelso n and Small Energy Solutions ∞ 28

22 DCA (2011) 24

Average =25; Low = 20; High = 30 e Residential Boilers Final Rule 2007 2

30 DCA (2011) 24 , RSMeans (2013) 27

134 (coal to oil) AHR The NEWS (2005) 29

Electric Boilers

13 2007 National Association of Home Builders Study 20

15 ASHRAE (2011) 21

18 GDS Associates (2012) ∞ 30

20 GDS Associates (2012) 30 , DCA (2011) 24

25 CIBSE 7

* Cast iron † Copper tube
^ Stainless steel ‡ Steel

∞ Condensing

c Triangular distribution was used.

d Lifetime value represents median age for servicing of a condensing boilers primary heat exchanger. GRI notes that five units which had a mean service lifetime of 19.9 years, weighted mean of 36 years, and median of 20 years.

e Triangular distribution was used.8

- F

- 4 8

- F.3 METHODOLOGY

DOE’s lifetime methods are based on the "Using national survey data to estimate lifetimes of residential appliances" paper. 25

EIA’s RECS 31 surveys occupied primary housing units, noting the presence of a range of appliances and placing the age of each appliance into several

- year bins. The U.S. Census’s American Housing Survey (AHS) 32 surveys all housing, including vacant and s econd homes. Using the AHS data allowed DOE to adjust the RECS data to reflect some appliance use outside of primary residences. AHS also has a larger sample size, with correspondingly smaller sampling error. By combining these survey results with the know n history of appliance shipments (collected from manufacturer trade associations) DOE estimated the fraction of appliances of a given age still in operation. This survival function, which DOE assumed has the form of a cumulative Weibull distribution, provi des an estimate of the average and median appliance
lifetime.

The Weibull distribution is a probability distribution function commonly used to measure

failure rates. 33 Its form is similar to an exponentia l distribution, which would model a fixed failure rate, except that it allows for a failure rate that changes over time in a particular fashion.
The cumulative distribution takes the form:

for x > θ and P(x) = 1 for x ≤ θ

,

Where:

P(x) = probability tha t the appliance is still in use at age x ,

x = appliance age,

α = the scale parameter, which is the decay length in an exponential distribution, β = the shape parameter, which determines the way in which the failure rate changes in time, and
θ = the dela y parameter, which allows for a delay before any failures occur.

When β = 1, the failure rate is constant over time, and this distribution takes the form of a cumulative exponential distribution. For the case of appliances, β is commonly greater than 1,
wh ich results from a rising failure rate as the appliance ages. A plot of a Weibull distribution (DOE’s calculated boiler survival function) is shown as Figure 8

- F.3.1

. 

# e x



### x P β

α

θ 

    

−

−


### = ) (8

- F

- 5 Figure 8

- F.3.1 Lifetime Distribution for Residential Boilers

The RECS survey is DOE’s primary resource for boiler ages. For several appliances, including boilers , the survey asks respondents to place the appliance’s age into one of these bins:

• less than 2 years;

• 2 to 4 years;

• 5 to 9 years;

• 10 t o 19 years and

• more than 20 years.

The RECS survey has been conducted every 3 or 4 years for the last several decades. For this analysis, DOE used the surveys conducted in 1990, 1993, 1997, 2001, 2005 , and 2009 . The AHS survey is conducted every other year, and DOE used the surveys conducted from 1991 to
20 11 . DOE used the AHS count of housing units with boilers to scale the RECS data to better match the total installed stock. DOE used the surveys’ household

- level micro

- data to count households with shared or multiple boilers . Households that did not know the age of their appliances were allocated among the remaining age bins according to the distribution of respondents who did report their applianc e age.

DOE used appliance age data derived from RECS , AHS total installed stock data, and the
histor ical boiler shipments to generate an estimate of the residential boiler survival function. For example, DOE summed the total shipments from 5 to 9 years pri or to the RECS survey, and compared this number with the number of units of those ages still in use, to calculate one approximation of the surviving appliance fraction within that age bin. The AHS total stock acts as an “all ages” bin. By combining the age bins from five RECS surveys and nine AHS surveys Residential Boilers8

- F

- 6 with shipments data, DOE had enough data to build a fit to a Weibull distribution and find the parameters ( α , β

, θ ) that best approximate the surviving units, using a least

- squares method.
Because the first two (youngest) RECS bin data tend to have a large scatter relative to the shipments in those years, DOE combined the RECS and shipments data in the first two bins. Generally, appliances do not tend to fail in large numbers during this period, so combining bins does not appreciably lower the accuracy of the shape of the distribution. DOE weighted each bin’s contribution to the sum of squares by the inverse of the variance in the survey results, which controls for the changes in sample size between RECS bins , between RECS and AHS, and within each survey over time. 33 RECS and AHS have complicated error models; DOE used only the error due to finite sample size to determine the variance used to weight each data point’s contribution. The error due to sampling is less than 1% for AHS survey data and is typically
about 5% for RECS age bins. The equation for the sum of squares DOE minimized is therefore:

Where:

i = the identifier for a bin from a single RECS, j = the identifier for a single AHS survey,
RECS i = the number of appliances reported by RECS in bin i

, AHS j = the number of appliances reported by AHS in survey year j

, Surv i = the number of surviving appliances in bin i predicted by the Weibull distribution applied to the number of appliances shipped (a function of α , β , and θ ),

σ

i,RECS = the standard error ( square root of the variance) of the RECS data point for
bin i, and

σ

j,AHS = the standard error (square root of the variance) of the AHS data point for

year j.

DOE adjusted the RECS and AHS survey data in several ways to place it on an even footing with th e historical shipment data. In particular, DOE adjusted for the fact that the RECS survey is scaled to July of its reference year, the AHS survey is conducted in the middle portion of the year, and shipment data is provided for each calendar year. Adjustme nts included:

• DOE modeled the additional retirement of older appliances and their replacement by new ones that took place in the latter half of the survey year (after a given respondent had been surveyed), using the survival function. This had the effect o f moving households from the older RECS age bins to the youngest age bin.

• For appliances installed directly in new construction, such as boilers , DOE added units to the youngest RECS age bin and to the AHS total stock to represent half of the new construction for the final year of the survey, which were known to have installed the appliance type in question, using data from the U.S. Census for new construction starts. 

## ( ) 

# ( ) ∑ ∑ − + −

j AHS j j j

i RECS i i i 

### Surv AHS Surv RECS

2

, 2

2

, 2



### σ σ8

- F

- 7 

### Assumptions

DOE’s lifetime

- calculation technique depends on several assumptions:

• Appliance lifetime can be modeled by a survival function. In particular, a Weibull distribution is an appropriate survival function.

• The appliance survival function does not change over time.

• The survival function is independent of other household factors (such as household size, region, etc.) as well as product class (within boilers ).

• The age bin for the appliance as reported by the RECS respondent is correct.

• The historical shipment data is correct.

• The Weibull delay parameter, θ , is limited to between 1 and 5 years.

Three of these assumptions are of particular importance. The first is the assumption that a Weibull distribution is the correct distribution to use for appliance retirement rates. This
distribution is the standard distribution for use in life time analysis, but it is not guaranteed to reflect actual consumer behavior. The second assumption is that consumer behavior and mechanical appliance lifetime have not changed over time. This assumption required DOE to
treat all data from different RECS su rveys on an equal footing. Using only recent surveys (to potentially better reflect recent consumer behavior and appliance lifetime) would result in attempted least

- squares fits using a small number of data points, leading to large statistical uncertainty.

DOE limited the delay parameter to between 1 and 5 years to reflect the range of common appliance warranties. A delay of less than 1 year would imply that some appliances fail or are replaced within their initial year of use, a period during which they ar e commonly covered by parts and labor warranties. A delay of greater than 5 years implies that no appliances are replaced for some length of time after the end of the longest standard warranty. Fits with θ > 5 also commonly show nonsensical behavior with s harp changes in consumer behavior or appliance survival immediately following the “delay” period.8

- F

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