8-F-i

APPENDIX 8-F. RESIDENTIAL BOILER LIFETIME DETERMINATION

TABLE OF CONTENTS

8-F.1 INTRODUCTION ................................................................................................. 8-F-1

8-F.2 LIFETIME LITERATURE REVIEW................................................................... 8-F-1

8-F.3 METHODOLOGY ................................................................................................ 8-F-4
8-F-1

APPENDIX 8-F. RESIDENTIAL BOILER LIFETIME DETERMINATION

8-F.1 INTRODUCTION

DOE defines 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 lifetime of which has not 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 value 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 lifetimes 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 Residential Boilers: Product Lifetime Estimates and Sources

Typical Lifetime or Range (years) Source

Unspecified Boiler Fuel Type

10-20 Federal Trade Commission3

10-15 PM Engineer (2012) ∞4

15 WAPTAC5

, Creating Better Homes6, CIBSE‡∞7

15-20 Dunlop (2003) ‡†8

17 Keman, et al.9

18-32 1998 Gas Research Institutea10

20 1994 Gas Research Instituteb1

, 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 Web13

30-50 Dunlop (2003)*

8

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

8

20-30 EIA (2013)

Gas Boilers

10 CIBSE7

Low = 13, Ave=17, High=22 1990 Gas Research Institute (GRI) study14

15-20 4ecotips15

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 group 

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 sample 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 

Study20, 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 2003

23, RAND Engineering19*, DCA (2011)24

Average = 25; Low = 20; High = 30c Residential Boilers Final Rule 20072

25.3 LBNL study(2011)25

29 PM Engineering(2001) *^18

30 Atlanta Gas Light Company26, RSMeans (2013)27

35 ASHRAE (2011) *

21

40 1994 Gas Research Institute∞d1

Oil Boilers

Low = 12, Ave=15, High=19 1990 Gas Research Institute (GRI) study14

20 Nelson and Small Energy Solutions∞28

22 DCA (2011)24

Average =25; Low = 20; High = 30e Residential Boilers Final Rule 20072

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 Study20

15 ASHRAE (2011)21

18 GDS Associates(2012) ∞30

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

25 CIBSE7

* 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 RECS31 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 second 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 known 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, provides 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 exponential 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 that 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 delay 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, 

which 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

P x

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 to 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 

2011. 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 appliance age.

DOE used appliance age data derived from RECS, AHS total installed stock data, and the 

historical boiler shipments to generate an estimate of the residential boiler survival function. For 

example, DOE summed the total shipments from 5 to 9 years prior 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 Boilers
8-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,

RECSi = the number of appliances reported by RECS in bin i,

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

Survi = 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), 

σi,RECS = the standard error (square root of the variance) of the RECS data point for 

bin i, and

σj,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 the 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. Adjustments 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 of 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 j AHS

j j

i i RECS

i i RECS Surv AHS Surv

2

,

2

2

,

2

σ σ
8-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 lifetime 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 surveys 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 are 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 sharp changes in consumer behavior or 

appliance survival immediately following the “delay” period.
8-F-8

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