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 Life time 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

8-C-iAPPENDIX 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 whic h the product is retired from service. Appliance magazine provides estimates of the low, high, an d 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 lite rature was uncertain, DOE developed a method using household survey data to estimate the distri bution of room air conditioner and clothes dryer lifetimes in the field.

8-C-1Table 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 2008 3
12.5 ASHRAE 2008 4

15 CEC 2005 5
12 European Rulemaking Draft Report 6 Average = 15; High = 20 NRDC 7
Other Sources Lifetime Source

9 Appliance Magazine, 1997 ENERGY STAR Savings Calculator a

18 EnerGuide 2005 Natural Resources Canada, 2008 8

15 NA New Mexico Market Assessment, Itron 2006 9

18 NA Nebraska Public Power District 10
12 See endnote NYSERDA SBC, 2002 11
9 NA RTF (Northwest), 2002 12
12.5 DOE TSD 1997 NCEP report, LBNL 2004 13

19 Aspen Memo, 2002 NYSERDA Deemed Savings Database: ENERGY STAR 14

13 (TTW) DOE TSD 2005 NYSERDA Deemed Savings Database: ENERGY STAR 13
Low = 8, High =16 NEMS Residential Demand Module, 2008 15

13 LBNL 2008 16 Average = 10–15, Low = 8–12, High = 14-18 LBNL 1994 17

10 Consortium for Energy Efficiency 18

10–12 American Council for an Energy Efficient Economy, 2007 19
NA means the data source is not stated in the reference.

a ENERGY STAR Savings Calculat or, Products, Room AC. Effici ent and conventional models.

8-C-2Table 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 2008 3
15 CEC 2005 5
18 CALMAC 2000 20
Other Sources Lifetime Source Average = 12; Low = 8;

High = 15 Appliance Magazine, 2006 BTS Core Databook, 2007 21

18 EnerGuide 2005 Natural Resources Canada, 2007 22

18 DOE Framework Document Itron, Report to CEC, 2007

18 NA CEC Consumer Ener gy Center website 18 See endnote CEC Flex Your Power website 14 NA Nebraska Public Power website

18 NA New Mexico Market Assessment, Itron 2006 8

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 resi dences. By combining the results of both surveys with the known history of appliance shipments (c ollected 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 aver age 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 distribut ion, 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/ >. 8-C-3that 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 for x > e and 

# e 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 tim e, 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 applia nce ages. For several appliances, including room air conditioners and clothes dryers, the surv ey 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.

8-C-4Table 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 1 8 20 22 24 26 28 30**Annual Retirement Rate**

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

8-C-5Figure 8-C.2.2 Clothes Dryers: Lifetime Function

8-C-6REFERENCES

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