APPENDIX 8-C. LIFETIME DISTRIBUTIONS 


TABLE OF CONTENTS
 

8-C.1

8-C.2

INTRODUCTION ................................................................................................. 8-C-1

8-C.1.1 Product Lifetime .................................................................................. 8-C-1

ESTIMATION OF SURVIVAL FUNCTION....................................................... 8-C-3

LIST OF TABLES 

Table 8-C.1.1 Room Air Conditioners: Product Lifetime Estimates and Sources ........... 8-C-2

Table 8-C.1.2 Clothes Dryers: Product Lifetime Estimates and Sources ......................... 8-C-3

Table 8-C.2.1 Lifetime Parameters................................................................................... 8-C-5

LIST OF FIGURES 

Figure 8-C.2.1 Room Air Conditioners: Lifetime Function............................................... 8-C-5

Figure 8-C.2.2 Clothes Dryers: Lifetime Function ............................................................ 8-C-6

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APPENDIX 8-C. LIFETIME DISTRIBUTIONS 

8-C.1 INTRODUCTION 

For each product class, DOE characterized the product lifetime using a Weibull 

probability distribution that ranged from the minimum to maximum lifetime estimates described 

in chapter 8, Life Cycle Cost and Payback Period Analyses. The Weibull distribution is 

recommended for application to lifetime data because it can be shaped to match low, average, 

and high values while still allowing some probability of exceeding the high value.1, 2 

8-C.1.1 Product Lifetime 

The product lifetime is the age at which the product is retired from service. Appliance 

magazine provides estimates of the low, high, and average years of an appliance’s lifetime. The 

estimates, which are based on first-owner use of the product, represent the expert judgment of 

Appliance staff based on input obtained from various sources. DOE also identified other sources 

that give lifetimes for room air conditioners and clothes dryers (see Tables 8.C.1.1 and 8.C.1.2). 

Because the basis for the estimates in the literature was uncertain, DOE developed a method 

using household survey data to estimate the distribution of room air conditioner and clothes dryer 

lifetimes in the field. 

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Table 8-C.1.1 Room Air Conditioners: Product Lifetime Estimates and Sources 


Typical Lifetime or Range (years) Source 

Original Sources 

Average = 9; Low = 7 Appliance Magazine, September 20083 

12.5 ASHRAE 20084 

15 CEC 20055 

12 European Rulemaking Draft Report6 

Average = 15; High = 20 NRDC7 

Other Sources 

Lifetime Source 

9 Appliance 

Magazine, 1997 ENERGY STAR Savings Calculatora 

18 EnerGuide 2005 Natural Resources Canada, 20088 

15 NA New Mexico Market Assessment, Itron 20069 

18 NA Nebraska Public Power District10 

12 See endnote NYSERDA SBC, 200211 

9 NA RTF (Northwest), 200212 

12.5 DOE TSD 1997 NCEP report, LBNL 200413 

19 Aspen Memo, 

2002 

NYSERDA Deemed Savings Database: ENERGY 

STAR14 

13 (TTW) DOE TSD 2005 NYSERDA Deemed Savings Database: ENERGY 

STAR13 

Low = 8, High =16 NEMS Residential Demand Module, 200815 

13 LBNL 200816 

Average = 10–15, 

Low = 8–12, High 

= 14-18 

LBNL 199417 

10 Consortium for Energy Efficiency18 

10–12 American Council for an Energy Efficient 

Economy, 200719 

NA means the data source is not stated in the reference. 

a

 ENERGY STAR Savings Calculator, Products, Room AC. Efficient and conventional models. 

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Table 8-C.1.2 Clothes Dryers: Product Lifetime Estimates and Sources
 

Typical Lifetime or Range (years) Source 

Original Sources 

Average = 12; Low = 8; High = 15 Appliance Magazine, September 20083 

15 CEC 20055 

18 CALMAC 200020 

Other Sources 

Lifetime Source 

Average = 

12; Low = 8; 

High = 15 

Appliance Magazine, 2006 BTS Core Databook, 200721 

18 EnerGuide 2005 Natural Resources Canada, 200722 

18 DOE Framework Document Itron, Report to CEC, 2007 

18 NA CEC Consumer Energy Center website 

18 See endnote CEC Flex Your Power website 

14 NA Nebraska Public Power website 

18 NA New Mexico Market Assessment, Itron 

20068 

12 Nexant, PECI Questar Gas, Utah, from Deemed Savings 

Database, 2006 

14 RTF (Northwest) CW/CD spreadsheet, 2008 

NA means the data source is not stated in the reference. 

8-C.2 ESTIMATION OF SURVIVAL FUNCTION. 

The Residential Energy Consumption Survey (RECS) records the presence of various 

appliances in each household, and places the age of each appliance into bins comprising several 

years. Data from the U.S. Census’s American Housing Survey (AHS),23 which surveys all 

housing including vacant and second homes, enabled DOE to adjust the RECS data to reflect the 

presence of appliances outside of primary residences. By combining the results of both surveys 

with the known history of appliance shipments (collected from Appliance magazine or directly 

from manufacturer trade associations), DOE estimated the percentage 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 average and a median appliance lifetime. 

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

rates.b Its form is similar to an exponential distribution, which models a fixed failure rate, except 

b

 For reference on the Weibull distribution, see sections 1.3.6.6.8 and 8.4.1.3 of the NIST/SEMATECH e-Handbook 

of Statistical Methods, <www.itl.nist.gov/div898/handbook/>. 

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that a Weibull distribution allows for a failure rate that changes over time in a particular fashion. 

The cumulative Weibull distribution takes the form: 

P(x) = − 

 

( x−θ

α 

 

J

β

e
 for x > e and


P(x) = 1 for x : e

 Where:
 

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

x = appliance age, 

a = scale parameter, which would be the decay length in an exponential 

distribution, 

f = shape parameter, which determines the way in which the failure rate 

changes through time, and 

e = delay parameter, which allows for a delay before any failures occur. 

 When f = 1, the failure rate is constant over time, giving the distribution the form of a 

cumulative exponential distribution. In the case of appliances, f commonly is greater than 1, 

reflecting an increasing failure rate as appliances age. 

RECS is DOE’s primary resource for appliance ages. For several appliances, including 

room air conditioners and clothes dryers, the survey asks respondents to identify the appliance’s 

age as: 

• less than 2 years old, 

• 2 to 4 years old, 

• 5 to 9 years old, 

• 10 to 19 years old, or 

• more than 20 years old. 


•
 

The RECS has been conducted every three or four years for the past several decades. For 

this analysis, DOE used the surveys conducted in 1990, 1993, 1997, 2001, and 2005. DOE used 

the AHS count of housing units that contain room air conditioners or clothes dryers to scale the 

RECS data to better match the total installed stock. Table 8.C.2.1 shows the lifetime parameters 

for room air conditioners and clothes dryers. 

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Table 8-C.2.1 Lifetime Parameters 


Product Class 

Calculated Values 

Weibull 

Parameters 

Minimum 

(years) 

Average 

(years) 

Maximum 

(years) 

Maximum 

percentile 

(%) 

Alpha 

(scale) 

Beta 

(shape) 

Room Air Conditioner 3 10.5 30 97 7.47 1.00 

Clothes Dryer 5 16.03 30 94 12.1 1.38 

0.0% 

2.0% 

4.0% 

6.0% 

8.0% 

10.0% 

12.0% 

14.0% 

0 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

Annual Retirement Rate 

Figure 8-C.2.1 Room Air Conditioners: Lifetime Function
 

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Figure 8-C.2.2 Clothes Dryers: Lifetime Function
 

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Programs Should Target Replacements to Maximize Energy Savings. 2002. 

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Equipment and Buildings: Additional Opportunities, July 2004, 2004. Lawerence 

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